Assessing Highway Tolling and Pricing Options and Impacts: Volume 2: Travel Demand Forecasting Tools (2012)

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24 All features discussed in the this chapter are short-term improvements in the sense that either they have been already successfully incorporated in some applied models or can be incorporated without principal difficulties that would require a substantial research effort. All the model features discussed are available within either the 4-step or ABM framework, although the 4-step structure requires a significant simplifi- cation of some of the recommended features. The classification scheme adopted is essentially a systematic reflection of the State of the Practice in the modeling of road pricing projects, rather than an accounting of all the possibilities offered by the most advanced modeling practices. More fundamental long-term improvements that would represent the state of the art in the modeling of road pricing are discussed in Chapter 5 that follows. 4.1 Classification of Model Features Required for Pricing Studies 4.1.1 Model Features for Different Pricing Projects Based on the accumulated modeling experience with various pricing projects described in Chapter 2, as well as taking into account the possible data collection techniques described in Chapter 3, the required model features that stem from the planning needs associated with different project types are classified. These same model features will also be arrayed by their correspondence to the four main stages of the pricing project decision-making process defined in Volume 1. As shown in Table 5, some model features are absolutely essential from the very beginning of any pricing study, while other more advanced desirable features may be reserved for subsequent stages of project development (detailed feasibility and investment grade studies). The more advanced features, however, may become extremely relevant even early on, if a corresponding pricing strategy is included in the range of options of the particular study, and a robust analysis is required, consistent with other more easily modeled alter- natives. Both essential and advanced modeling features still belong to the category of short-term improvements and are not explicitly distinguish between 4-step and ABM frameworks classification. The following features are essential for practically all pricing studies, and their inclusion in the modeling system to be used for a pricing study should be assessed at the outset. • Toll facilities must be properly coded in the highway net- work with appropriate toll value equivalents (e.g., minutes, based on VOT) incorporated in volume-delay functions. The subsequent refinement of this component for more advanced stages should include a detailed coding of toll plazas and access ramps in order to realistically represent delays associated with these facilities. In over-congested areas, where toll facilities and their access point are asso- ciated with queuing, the most promising tool to realistically portray the traffic conditions is DTA and microsimulation (discussed in Section 5.3). • The demand model should be segmented by at least 4-5 travel purposes and 3-4 income groups with VOT specific for each combined segment. An additional step is to apply differential travel time coefficients by segments and con- sequently VOT estimates by congestion levels that would represent a simple proxy for highway reliability (discussed in Section 5.2). • The traffic assignment should incorporate and distinguish relevant vehicle classes (auto, commercial vehicles, trucks, taxis, etc.) with the average VOT per class. The technique of multi-class assignment is supported in all major trans- portation software packages (TransCAD, EMME, and Cube) and can be further applied to differentiate between VOT groups within the same vehicle class. • It is highly recommended (although not an absolute require- ment in the early stages of pricing studies) to incorporate a C h a p t e r 4 Critical Issues and Directions for Short-Term Improvements

25 binary route type choice model (toll versus non-toll facility), either as a lower-level sub-nest in mode choice, or as a pre- assignment procedure. This sub-model allows for captur- ing a toll bias associated with the perception of the generally improved reliability and safety of the toll facility, as well as provides for better (non-linear) specifications of the trade- offs between travel time savings and extra costs. • It is essential to equilibrate the demand model (at least mode choice and pre-route choice) and the highway assignment to ensure that the results correspond to (or at least approx- imate) a stable equilibrium solution. It is more difficult to include the trip distribution (and other sub-models like time-of-day choice and/or trip generation) in the global equilibrium, which might require multiple iterations and special averaging algorithms. However, it is essential to eventually ensure a reasonable level of convergence of the entire model system. Recent experiences with the New York activity-based model has shown that effective strategies of equilibration based on a parallel averaging of trip tables and LOS skims can achieve a reasonable level of conver- gence in 3–4 global iterations, even in one of the largest and most congested regional networks (Vovsha et al. 2008). Other important model features are associated with par- ticular pricing projects and forms: • If the pricing forms to be studied include vehicle eligibil- ity and/or toll differentiation by car occupancy, the cor- responding sub-choice (SOV, HOV2, HOV3, HOV4+) should be included in the auto sub-nest of mode choice model. So far in practice, an HOV4+ lane has been the maximum considered (HOT lane Atlanta Study in Vol- ume 1). Further on in the modeling, the same car occu- pancy categories should be separated in the assignment procedure. • If area pricing or other large-scale pricing schemes are considered, it is reasonable to expect a global effect on trip generation rates (activity patterns), in addition to mode, route, time-of-day, and destination shifts. This requires a flexible trip generation (activity pattern) model that is appropriately sensitive to accessibility measures. A specific but important issue that can be addressed with ABMs is the possible shift in usual work schedules, in particular, to a greater prevalence of compressed work weeks and tele- commuting. In most cases, this type of response can only Pricing Study Model Features Essential Advanced All types of pricing Toll facilities coded in the highway network with toll incorporated in the volume-delay functions Toll plazas and access ramps coded with realistic delay functions Segmented VOT by travel purpose and income group in demand model Perceived highway time by congestion levels / reliability Segmented VOT by vehicle class in traffic assignment Additional vehicle class stratification by VOT Pre-route (toll vs. non toll) sub-choice Mode choice and assignment equilibration Inclusion of trip distribution in equilibration through mode choice logsum HOV/HOT lanes Car occupancy (SOV, HOV2, HOV3+) sub-choice in mode choice Additional vehicle class stratification by occupancy in assignment Area and other large-scale pricing schemes Trip generation sensitive to accessibility/generalized cost Accounting for trends in flexible / compressed work schedules and telecommuting Highway pricing in parallel with transit improvements Mode choice with developed transit nest Bus speeds linked to highway congestion Congestion pricing Peak spreading model Time-of-day choice model Accounting for trends in flexible / compressed work schedules and telecommuting Dynamic (real-time) pricing Special network / toll equilibration procedure Highway pricing in parallel with parking policies Parking cost inclusion in mode choice Parking choice model for auto and drive-to-transit trips with parking constraints Equity analysis Model segmentation and reporting of user benefits (time savings and extra cost) by 3-4 income groups Table 5. Model features for different pricing studies.

26 be estimated with models based on SP surveys (discussed in Chapter 3). • Highway pricing decisions may be considered in tandem with transit improvements. These include direct transit integration in the highway pricing project: bus rapid tran- sit (BRT) on the HOV/HOT lane, or indirectly through improvements of bus speeds in mixed traffic on congested links, and augmented transit services funded by the road pricing actions and aimed at providing improved transit choices for drivers who could change mode. In order to model these types of effects, the model choice should include a transit nest that adequately portrays the transit options competing with highway options (toll and non-toll). On the network side, bus speed functions should be integrated with highway speed (volume-delay) functions to properly describe the mixed traffic conditions. • Congestion pricing (i.e., toll differentiation by time-of- day periods and hours) specifically targets departure time of trips. In addition to route and mode shifts, congestion pricing results in departure time shifts within the peak periods (from the peak hour to so-called “shoulders”), as well as between periods (for example, from the AM peak to midday off-peak period). The corresponding choice model components, referred to as “peak spreading” and “time of day choice” should be added to the model system. So far, inclusion of these sub-models in the standard travel demand model system has been problematic, revealing one of the 4-step model’s weakest aspects. The ABM framework offers significant advantages in this respect, allowing for the estimation of the impact of time of day charging on all travel over the course of the full day (discussed in Section 5.2.6). • Real-time dynamic pricing, widely recognized as one of the most advanced and promising pricing forms, represents a special challenge to modeling because it requires a special toll equilibration procedure (discussed later in this chapter). • Highway pricing (especially area/cordon pricing forms) can be effectively combined with parking pricing and supply policies. If parking is included in the study, the travel model (specifically mode choice) should include parking cost in the auto utility functions. If parking policies become a major policy focus of the study, it is suggested that a more advanced model component be included—an explicit choice of parking location (that can be different from the zone of the person trip destination). This component can be effectively and consistently incorporated in the activity- based model framework only. • One of the important aspects of any pricing study is equity analysis across income groups and geographic areas. From this perspective, it is essential to segment all sub-models by income groups and ensure that summaries of travel time savings and extra costs that constitute User Benefits could be produced and reported by income group. 4.1.2 Model Features for Different Stages of Decision Making The model improvement process and desired features can be arrayed in parallel with the basic generalized stages of pricing studies. A framework of gradual corresponding improvements is outlined in Figure 5. Four major stages of the project development (described in Volume 1, Chapter 4) and four broad stages of improvement of the forecasting tools were examined. This is an approximate framework, since many details are dependent on the specifics of pricing study scope and the alternatives that need to be compared. In general, having an advanced model from the very early stage will only be an advantage; however, this is certainly not always necessary. A pricing study could begin with a simplified model while the data and modeling tools are improved in the process, sub- ject to the specific pricing alternatives identified at the earlier stages for further analysis. The timeline of the pricing study and the implementation of the model improvements to sup- port it should be established in a realistic way. In particular, it should be understood that the final stage of Investment Grade study will require at least a year to implement and as much as $1,000,000 or more, of which a large share of the costs will be for model improvements. Consequently, it is recommended to advance, rather than delay, the model improvement steps vis-à-vis the project development stages whenever possible. In a majority of cases where decision making about highway pricing was done in a systematic way, supported by forecasting tools, the existing regional model (typically that of the MPO) was employed in some manner. The development of a new regional model from scratch is a time consuming and costly effort. Also, the timing of a major model improvement effort, driven by periodic data availability, might not coincide well with the road pricing study. Consequently, in many cases the best available model, along with some short-term improve- ments, is typically applied. There is, however, a growing rec- ognition of the importance of travel model improvements in view of the scrutiny by rating agencies and private investors of T&R forecasts, and many agencies have made substantial efforts to improve their models for pricing studies. In many cases, the RFP issued by the interested agency for a T&R study explicitly included a model improvement task. An additional benefit of this effort, as perceived by MPOs, is this study would contribute to the general improvement of the regional model as well and can spur additional useful data collection, model validation, and testing. There were very different cases observed with respect to the level of model sophistication versus the decision-making stage. In some cases, the agencies advanced their pricing projects to the last stage (and effectively started implementation) with no substantial improvement of the forecasting tools. Despite fulfilling the understandable intention to speed up

27 the decision-making process, a more detailed analysis of the existing long-term concessions and associated financial terms has indicated that these may not be examples of unqualified success, especially where the absence of a solid and defendable forecast may have resulted in financial conditions that were highly favorable for the private concessionaire, but leave ques- tions open from the public perspective. There is also a clear note of warning from the numerous pub- lications of the leading rating agencies that they will increas- ingly consider the quality of the T&R study as one of the major risk factors that can significantly reduce a project’s rating (especially for start-up projects). In some other cases, where agencies had already developed an advanced model, it was employed from the initial stage of the decision making, even though the level of detail provided by the model was prob- ably excessive for this early stage of the preliminary project development. Notwithstanding possible deviations based on different project development frameworks and varying states of existing regional modeling capabilities, there are several clear patterns that can be generalized and used to characterize both prevail- ing and best practice. In general, the following correspondence between the stage of decision making and appropriate model- ing tools can be recommended. Stage 1: Exploratory General strategic go/no-go decisions about highway pricing possibilities are made in this stage. The existing regional model should be applied with at least a minimal set of short-term improvements that would normally include the following common steps, corresponding to the list of general model features essential for all pricing studies identified in the pre- vious sub-section: Ge nera l im p roveme nt of re gion al mo de l Sp ec ifi c im pr ov e m e n ts fo r pr ic in g st ud y by d e c i s i o n -m a k i n g s t a g e Ex pl orat ory / De ci ding to st ud y Pr el im in ar y / In it ia l Fe as ibilit y EI S, T& R Fe as ibilit y St ud y In ve st m ent Gr ad e St ud y w/ ri sk an al ys is Ex is ti ng mode l Im p roved se g men ta ti on & pa ra me te rs Imp roved st ru ct ur e & es ti ma ti on Ad va nc ed mo de l — Ne tw or k co ding of pr ic in g — To ll in co rp or at io n in mo de ch oi ce & ot he r mo de ls — Eq u ili br iu m / f eed ba ck — Ca li br at io n to ma tc h tr af fi c co un ts & ti me s — Mu lt i- cl as s a ssi gnme nt an d VO T es ti ma te s — Mo de ch oi ce an d ot he r mode l se gm en ta ti on by pu rp os e / in co me — Bi na ry pr e- rout e ch oi ce mo de l as pa rt of mode ch oi ce — Ti me -o f- da y ch oi ce (p ea k sp re ad ing) mode l — Mo de ch oi ce lo g- su m in de st in at io n ch oi ce (t ri p di st ri bu ti on ) — Tr an si t in co rp or at io n — Es ti ma ti on by av ai la bl e so ur ce s — De ma nd mi cr os im ul at io n (a ct iv it y- ba se d to ur - ba se d st ru ct ur e) — Tr af fi c mi cr os imul at io n / DT A — VO T di st ri bu ti on — In co rp or at io n of re li ab ili ty me as ur es — Ri sk an al ys is — Ne w su rv ey s Figure 5. Forecasting tools by stage of project development.

28 • Coding of highway facilities with the corresponding pric- ing forms (flat, fixed variation by time-of-day, variable real-time, etc.), converted into travel time equivalents for highway assignments and skimming. • Incorporation of tolls in the current demand models, specifically mode choice and trip distribution models. • Proper implementation of network equilibrium and asso- ciated feedbacks, at least between the assignment and mode choice models, with a subsequent consideration of the trip distribution model as well. • Calibration effort (through proper adjustment of model coefficients, mode specific constants, and/or distributional K-factors) in order to reasonably match traffic counts in the base year, and observed aggregate district-level OD flows if available, as well as approximate travel times and speeds, in the relevant corridor/sub-area. Stage 2: Preliminary Feasibility Study Further improvements are recommended depending on the pricing project nature. These improvements mostly include better model segmentation (poor segmentation that is too crude for analysis of willingness-to-pay is one of the common drawbacks of many conventional models), as well as a dif- ferentiation of the model coefficients related to VOT. At least two additional improvements are generally needed: • Mode choice (and trip distribution if technically possible) segmentation by travel purpose and income group (that have a strong impact on the VOT). • Multi-class assignment procedure distinguishing traffic by vehicle types (auto, commercial vehicle, heavy truck, taxi, etc) and auto occupancy (SOV, HOV2, HOV3+, etc.) directly related to the pricing differentiation and eligibility. Stage 3: Environment Impact Statement (EIS) This stage is associated with full T&R studies, when the model structure should be improved in order to incorporate additional important sub-models. The following improve- ments are generally warranted at this stage: • Introduction of a binary pre-route (toll versus non-toll) choice model as part of the mode choice model (at the lower level of mode hierarchy). In cases such as for intercity highways, with high percentages of trucks (where mode choice is not playing a significant role), the binary choice model essentially represents a user decision-making mech- anism and the perception of tolls. This is essential in order to incorporate a sensitivity of demand, beyond travel time savings, to the additional travel quality and reliability typi- cally associated with toll roads. • Introduction of a time-of-day choice and/or an incremental peak-spreading model that is essential for urban toll roads and congestion pricing variable pricing analysis. • Constructing a proper linkage between mode choice and destination choice (trip distribution) models through the log-sum accessibility measure, essential to ensure logical sensitivities of the model when multiple pricing alternatives are compared. • The implementation of this linkage may also require model (re)estimation efforts based on the existing household travel survey and other available sources, or the collection of new survey data in the corridor, typically OD, and possibly with a SP component. Stage 4: Investment Grade Study In the course of the pricing study’s progress, the model improvement process can finally lead to a complete or gradual transition toward an advanced model structure that would fully support specific requirements of the Investment Grade Study, including comprehensive risk analysis across different relevant factors. The following features of advanced model are especially relevant for highway pricing projects at this stage: • Individual (household/person) microsimulation of the travel demand choices in an Activity-Based Tour-Based structure. • Individual (vehicle) microsimulation of traffic using DTA technique. • Detailed analysis of travel markets and associated proba- bilistic VOT distributions, essential for capturing such important factors as situational variation in VOT. • Explicit incorporation of travel time reliability measures and willingness to pay for reliability improvements, along with average travel time savings. • Integration of the T&R forecasting and financial risk analy- sis through a set of well designed sensitivity tests, and an analytical representation of risk factors with multivariate simulations. • Implementation of multiple model runs with different toll values for the purpose of toll optimization, imple- mented with respect to the revenue, network conditions (measured by minimal speed, maximum V/C ratio, or maxi- mum throughput), or by social welfare (utility) function. • Implementation of new RP household travel surveys, with supplementary SP components, designed to be applied in the estimation of advanced models. The improvements to the regional model made from stage to stage can be accumulated, and, if the model improvement process is well-coordinated and well-thought out from the beginning, it can result in an advance state-of-the-practice model suitable for robust pricing analysis. The timing and

29 requirements for project development and the model improve- ment process, however, might not be well correlated in some situations. In these situations, simpler model versions may need to be employed initially and over the course of the decision- making process, with an acknowledgement of the consequence that additional risk will be assigned to the project due to the reliance on simplified T&R forecasting methods and data. While the development of an advanced activity-based model with all these features in place might be the best long-term goal and most desirable for Investment Grade analysis, these do not need to be brought altogether and implemented in the initial development of modeling approach for pricing, but can be staged over time. It will also be shown how some particular improvements (for example, incorporation of reli- ability measures or preparing data for risk analysis) could be done within the structure of more conventional and commonly used 4-step models. 4.1.3 Specific Requirements for Forecasting Tools for Investment Grade Studies Rules of Financial World Rating agencies put travel forecasting procedures under a high level of scrutiny that is generally different from the model evaluation/validation criteria applied in the public sector. This section discusses: risk analysis, risk mitigation methods (including more extensive data collection and model calibra- tion, revised population and jobs forecasts), toll rate optimiza- tion, and sensitivity tests with different toll scenarios. Investment Grade studies are characterized by more strin- gent requirements on traffic and revenue forecasts, added levels of scrutiny on the model structure and calibration, and a number of additional post-modeling steps compared to the preliminary Financial Feasibility studies. The quality of the forecast may directly affect the project bond rating (i.e., the possibility to obtain the necessary loans and the interest rate associated with them). The three major rating agencies (i.e., Fitch Ratings, Moody’s, and Standard & Poor’s) conduct various tests on T&R forecasts (especially those pro- duced by public agencies), and examine variations in many of the input parameters, as well as the model structure itself [(Standard and Poor’s 2002–2005, Fitch Ratings 2003-2005)]. For these reasons, Investment Grade studies require an advanced and well calibrated travel model integrated with network simulation. It is not uncommon for an investment grade forecast to take approximately one year or longer and upwards of $1 million to complete. While a general principle that “a good model for an Investment Grade study should first be a good behavioral model in a common sense” holds true, it is only a starting point. There are several important technical specifics of an Investment Grade study compared to a T&R forecast produced for Feasibility studies that should be addressed and are not necessarily included even in advanced activity-based models. They relate to the model structure and calibration, model application, and a number of post-modeling steps that convert the model outputs into the inputs needed for a Financial Plan. The following aspects relate to the model structure and calibration: • Presence of all three major relevant choice dimensions— route, mode, and time-of-day choice—that represent first- order responses of the travelers as described in Chapter 1. • More elaborate time-of-day choice or peak-spreading model distinguishing between the peak hour and “shoulders” within each broad period. • Flexible trip generation model sensitive to accessibility improvements. • Flexible trip distribution model fundamentally linked to the mode choice model by mode-choice inclusive values (Logsums) as impedance measures. • User segmentation by VOT across travel purposes, income groups, times of day, vehicle type and occupancy, as described earlier in Chapter 1 and will be elaborated further in Sec- tions 4.3 and 4.4. Special attention should be paid to VOT segmentation by occupancy, since most models in practice assume that VOT is simply proportional to travel party size (as discussed in Chapter 1). In more advanced ABMs, VOT can be specified in a probabilistic way (to account for situational variation), and can include Value of Reliability (VOR) as well (as discussed in Chapter 5). • Extensive newly collected data and more rigorous model calibration is normally assumed. It should be understood that even a well-calibrated regional model might have certain discrepancies compared to traffic counts and/or speed surveys in a particular corridor or facility. It is essen- tial to recalibrate the model based on the most recently collected data, including traffic counts, special surveys (e.g., users of a particular toll facility), and speed mea- surements in the relevant corridor. With these data, the calibration targets for a particular pricing study can be set in a more rigorous way. For example, while a range of ±15% from average (daily) traffic counts is considered an acceptable range for a general purpose regional model, a range of ±5% can be set for each time-of-day period for the relevant priced corridor. Additionally, a historical set of traffic counts for validation of the growth tendencies is highly recommended. The following aspects relate to the model application: • Toll rate optimization and multiple sensitivity tests with different toll and toll escalation scenarios.

30 • Risk analysis and risk mitigation measures. This includes identification and quantification of risk factors. A good overview of the common “suspects” in travel forecasting is provided in the periodical publications of the rating agencies (Standard and Poor’s 2002–2005; Fitch Ratings 2003–2005) as well as in (Washington State’s tolling study CSI 2006). Contrary to the conventional travel forecasting culture that has been based on a deterministic interpretation of the model outcome, the culture of the investment world is based on a probabilistic view of the model outcome. A theoretically consistent inclusion of the probabilistic risk analysis in traffic and revenue forecasting procedures is an important avenue for bringing these two worlds together and is an essential theme of the current synthesis. The following general risk factors are under scrutiny by rating agencies: • Start-up toll facilities are considered the most risky and are put under a stress test, especially if the forecast was implemented by a public agency. • Accurate traffic and revenue forecasting in dense urban areas will always lie at the opposite end of a reliability spectrum from a river crossing with a clear competitive advantage over limited alternatives. • Traffic patterns associated with well-defined, strong radial corridors appear to be more reliable. • Forecasts prepared by project sponsors and bidders (interested parties) are generally higher than prepared by investors/bankers; this optimism bias is estimated at 20% or more. More aggressive forecasts can be accepted for PPP that do not need rating. • VOT miscalculation and improper aggregation across different income groups/travel markets (that’s why a proper model segmentation is essential). • Recession/economic downturn (GDP growth is correlated with traffic growth with some lags). • Slower future-year land-use development along the corridor. Reconsideration of population, employment, and income growth forecasts prepared by the MPO or DOT for the region/corridor is one of the frequent requests. • Lower time savings than the modeled ones. • Improvements considered to competing free roads. • Potential for lower usage of toll roads and managed lanes by trucks than modeled. • Lower possible off-peak/weekend traffic (40–50% of week- day) than is normally assumed (70–75% of weekday). • Specific risk factors for trucking market are essential if trucks constitute a significant share in the traffic. In particular, less reliability should be placed on forecast if the trucking market is composed of a large number of small, owner-driver general haulers. Additionally, markets consisting of several, very large haulage companies transporting high-value or time-sensitive commodities are likely to be less volatile. The following aspects normally relate to the post-modeling steps, though any of them might be considered for direct modeling as well: • Annualization of revenues including assumptions on weekend and holiday revenues, seasonality, within-week variability, etc. TTA of TxDOT developed a five-factor qualitative indexing scheme for Equivalent Revenue Days per year (TTA Toll Feasibility Analysis Process 2005). The factors may vary from corridor to corridor and the best way for established facilities is to develop individual factors based on the observed patterns. It is also important to consider that a weekend’s VOTs are generally lower due to a mix of purposes and schedule flexibility. Whereas weekend and holiday traffic on a non-toll facility is generally around 70–75% of weekday traffic in urban areas, the portion of traffic using toll roads during weekends tends to be less. • The yearly T&R stream needed for the Financial Plan is calculated by interpolating between horizon model fore- casts and extrapolating beyond modeled years for long periods (40–50 years and longer). Capacity constraints (and adverse effects of congestion when traffic volume approaches capacity) should be taken into account for deep forecasts if they are not directly simulated in the model. • Detailed consideration of a ramp-up period. If it is not modeled as a dynamic behavioral response in the model (which is unfortunately the case with even the most advance AB models), certain assumptions are made based on the past experience with similar projects. Specific ramp-up con- siderations are associated with ETC if no cash payment option is provided. In this case, the ramp-up period is almost none for routine users and commuters, but might be significant for occasional users and visitors. The following initial ramp-up period assumptions for start-up projects (as revenue-stressed test) are recommended by Standard & Poor’s (2004) (Table 6). • Detailed consideration of bulk discounts, person/vehicle type discounts, toll evasion (if any), and other revenue loss factors, such as accidents/incidents, extreme weather, or special events, among others. • Consideration of toll rates escalation (CPI, GDP, floor, ceiling) versus population income (and VOT) growth over a long period of time. • The model output needs to be processed in a form that is suitable for subsequent analysis. It is important to ensure transparency of the results and identify key areas (OD pairs, core travel markets) for which the calculations can be demonstrated for practitioners (open the “black box”). The following three output formats are very useful for the

31 subsequent Financial Plan: (1) toll revenues by year (most probable with 80% and 95% confidence intervals forming optimistic and pessimistic curves); (2) toll revenue distribu- tion for some representative years (density and cumulative); and (3) possible distribution of revenue available for Debt and Equity (most probable, lowest reasonable, highest rea- sonable) and such parameters as likely debt-to-equity ratio and associated debt service residual revenues available for equity participants. Several preliminary steps are suggested before completion of a T&R forecast and Financial Plan. Rating agencies can be asked to provide a preliminary opinion and advice on how to strengthen the creditability of the forecast. A discussion can be initiated with the TIFIA Credit Program to ascertain the type of assistance that could be reasonably expected. Investment Grade studies are often completed in parallel with environmental assessments. Information on preliminary capital and annual Operating & Maintenance (O&M) cost from these studies is frequently used in order to obtain a pre- liminary indication on the financial feasibility. Refined cost estimates are used for the final Financial Plan. Preparation of T&R for Financial Plan The Financial Plan is based on a computerized cash flow model that allows the testing of different financial structures and assumptions (Tillman, et al. 2006). Discounted cash flow analysis should demonstrate that the project-specific cash flow payout schedule can be met. It is essential to analyze Financial Plans in detail if there are several competing proposals for the same project. A reasonable criticism of some “fast” practices with accepting private-sector financial proposals, with insuf- ficient detailed scrutiny, can be found in Dornan (2006) and Enright (2006). Toll-based financial models should be comprehensive and should address different relevant funding sources (govern- ment grants, impact fees, and credit enhancements), as well as generated bonding capacity (take advantage of tax-exempt municipal bond market). Tolls can generally supplement the funding, but cannot replace it completely for many expensive projects. General use of the toll revenue includes paying for toll system operation and maintenance, funding (in whole or in part) construction and maintenance (including capital rehabilitation), and funding related parts of the transportation system (potentially, including transit). The Financial Plan must be based on the detailed estimates of construction and O&M cost for each major segment includ- ing all components. The Association for the Advancement of Cost Engineering (AACE) publishes risk factors for cost estimates that can be used in the Risk Analysis. In general, the Financial Plan should be based on conservative assumptions regarding the cost of financing, interest rates, coverage ratios, and reserve accounts. The specific metrics and limitations of the Financial Plan include: • Credit quality (equity contributions and guarantees), • Statutory limitations for the agency to issue investment quality debt and for the state to support the financing, • Debt service repayment, • Debt service reserve accounts funded by the bond issue (usually 125% of the average annual debt service), • Debt service coverage ratio, • Capitalized Interest During Construction, • Cost of finance (bonds), • Cost escalation over years, • Period of finance and interest rates, including stress tests, and • Project equity and secondary sources of funds (subordinate debt, TIFIA loans, or direct contributions). The Financial Plan must be reviewed carefully by poten- tial lenders, as well as any public agencies that may be pro- viding financial support to the project (FHWA, TIFIA Credit program). As a rule, each pricing project must be analyzed as a stand-alone, single asset facility, and then, several selected projects can be analyzed under an integrated system approach to gauge levels of feasibility. Several strategies can be applied depending on the project pool formulation and the adopted regional pricing concept: • Full funding of construction cost through tolls, • Leveraging up several projects in a “Regional System” (cross-subsidy), and • Supporting projects with some federal/state monies. If the project is to be rated by one of the major rating agencies (i.e., Standard & Poor’s, Fitch, or Moody’s), the following important aspects should be taken into account. Year 1st 2nd 3rd Low-risk% 80 90 100 4th 5th 6th Projects Average-risk% 65 75 80 85 88 90 7th 8th 9th and later High-risk% 45 53 60 65 70 73 76 78 80 Table 6. Recommended ramp-up assumptions for T&R of start-up projects.

32 Documents required by rating agencies include: • T&R forecast with risk analysis, • Financial plan, • Contractual documents for the construction and operation of the project (including all environmental and construc- tion permits needed), • Financing documents (trust indenture, bond insurance, or letters of credit), • Regional and local economic trends and other input data (population growth, employment growth, income levels, traffic counts, etc.), • Independent T&R forecasts (if available) and engineer’s feasibility report. General rules and requirements include: • Stand-alone basis for assessment, • Reliable and conservative T&R forecasts, • BBB rating (minimum needed for issuing bonds) for start- up roads requires net revenue at least 1.7 greater than senior lien debt payments, and • Government subsidy/credit guarantees are required for non-toll part of funding. A preliminary rating is often requested to assist a project sponsor in identifying further steps that must be taken to secure an investment-grade ranking BBB or higher. It is likely that most start-up toll roads will require some form of credit assistance and/or guarantees to gain this rating. Rating analysts evaluate and the most important risk factors: • Reasonability of T&R forecast assumptions, • External political and economic factors, • Existing or planned competition for the roadway, • Regional economic conditions, • The break-even point for servicing debt. Specific Requirements for Forecasting Tools Modeling tools to support highway pricing decisions need to comply with the specific requirements associated with rev- enue forecasting in the context of project ratings for private financing. The analysis of the existing models done to date, as well as the tracking history of model applications and associ- ated (well-published) criticism from the rating agencies, have clearly shown that some principal improvements in modeling tools are needed to ensure the credibility of T&R forecasts, as well as to better integrate the transportation modeling cul- ture with the culture of the investment analysis community. As a result, the following important model features could productively be improved: • Rating agencies and private investors consider stand- alone start-up projects as the most risky, uncertain, and subject to over-optimistic modeling assumptions. It must be recognized that static validation of a transportation model for the base year does not at all guarantee that the model will properly respond to changing travel conditions, including those associated with a new toll road or pricing action. • Revenue forecasts have to be presented in a probabilistic form (not just a single series of forecast numbers) suitable for subsequent investment risk analysis and rating. The current practice is characterized by a sequential imple- mentation of T&R forecast followed by independent/ simplified risk analysis. The latter is frequently based on an arbitrary scaling of the revenue and assigning of risk probabilities based on the record history of toll road forecasts. The following are the most important factors that should be included in the risk analysis, and the technical methods for their assessment are recommended in Section 4.4.4: • Model inputs on the demand generation side, such as land- use and socio-economic growth assumptions, overall regional economic trade and political environment, and the cost of fuel (including taxes). • Model inputs on the network supply side including the improvement of competing roads and transit modes in the corridor, possible delays in the deployment of comple- mentary projects and improvements. • Travel model structure and parameters including structural assumptions on VOT (savings) by user segments, assump- tions regarding traffic that are not directly modeled, such as off-peak, weekend, holiday, seasonal, extreme-weather traffic, etc. • Non-travel traffic components (modeled by ancillary mod- els) including heavy trucks, light trucks, and commercial vehicles. • Post-model assumptions that include ramp-up period, toll evasion, bulk discounts, traffic incidents, and their management. An important improvement in current best practice could be an integration of the revenue forecasting and risk analysis through a two-stage procedure: 1. Set of designed sensitivity tests (scenarios) applied with the full model, and

33 2. Post-processing of the results through aggregate regression analyses and simulations that will allow for assessment of the “confidence bands” around the forecasts that would be used in the subsequent financial analysis. This technique will ensure that traffic and revenue fore- casts are analyzed and prepared in formats acceptable and trusted by the financial community. At the same time, it should be understood that the uncertainty associated with T&R forecasts is only one of the risk factors for the road pric- ing projects. There are many other factors associated with these projects, including of course cost estimates, for which a separate risk analysis should be implemented (and the cor- responding accuracy ranges are well established). At the final stage when the financial plan is formed, both sides of the risk equation, revenue and cost, are taken into account, as well as the distributions of such important measures as the likely equity-to-debt ratio, debt service, and residual revenues over years which are produced in a probabilistic fashion. It is believed that improvements of the analytical procedures on the T&R side will be especially helpful for obtaining better rating and acceptance of start-up projects that are subject to very rigorous “stress” tests by rating agencies. 4.2 Prototype Structure of Travel Model for Pricing Studies 4.2.1 Main Travel Dimensions Affected by Pricing A travel model can be constructed to include a wide range of possible responses to congestion and pricing, in the approxi- mate hierarchical order, from the short-term to long-term, as shown in Table 7. Most of the existing models applied for pricing (both in research and practice) have been largely focused on the sub- set of trip-level short-term responses, including route choice, pre-route choice, car occupancy choice, mode choice, and time-of-day (or trip departure time) choice (Brownstone, et al. 2003; Brownstone and Small 2005; Lam and Small 2001; Mahmassani, et al. 2005; Mastako 2003; Verhoef and Small 2004). These choice dimensions are generally recognized as the most important for pricing, and are classified as first- order responses. Within this limited framework, there have been only few examples of a full integration across all these choices—in the existing ABMs developed for Columbus, OH (MORPC 2005] and Montreal, QC (Travel Demand Model Development for Traffic and Revenue Studies in the Montreal Choice Dimension Time Scale for Modeling Expected Impact Network route choice Short-term – trip episode Stratified response by user group Pre-route choice (toll vs. non-toll) Short-term – trip episode Stratified response by user group Car occupancy Short-term – tour/trip episode Planned and casual carpool Mode choice Short-term – tour/trip episode Shift to transit, especially to rail and for low/medium income groups Time-of-day / schedule Short-term – tour/trip episode Peak spreading Destination / stop location Short-term – tour/trip episode Improved accessibility effect combined with negative pricing effect on trip distribution for non-work trips. Joint travel arrangements Short-term – within day Planned carpool / escorting Tour frequency, sequence, and formation of trip chains Short-term – within day Lower tour frequency and higher chaining propensity Daily pattern type Short-term – weekly (day to day) More compressed workdays and work from home Usual locations and schedule for non-mandatory activities Medium term – 1 month Compressed / chain patterns; weekly planned shopping in major outlets Household / person mobility attributes (transponder, transit path, parking arrangements at work) Medium term – 1-6 months Higher percentage of transponder users and parking arrangements for high incomes, higher percentage of transit path holders for low incomes Household car ownership choice Long term – 1 year Stratified response by income group (higher car ownership for high incomes, lower car ownership for low incomes) School / university location and schedule Long term – 1-5 years Choice by transit accessibility; flexible schedules Job /usual workplace location and schedule Long term – 1-5 years Local jobs for low incomes; compressed / flexible schedules Residential location Long term – 5 years + Income stratification (high income suburbs around toll roads, low income clusters around transit ) Land-use development Long term – 5 years + Urban sprawl if no transit; otherwise shift to transit Table 7. Possible traveler responses to congestion and pricing.

34 Region, 2003). There are, however, many other important travel dimensions that have been less explored in either prac- tice or research. These include long-term impacts of con- gestion and pricing such as fundamental changes in travel behavior patterns that cannot be captured and understood at the single trip level. For example, in over-congested urban areas (e.g., New York, Chicago, and San Francisco), many employers offer workers compressed work schedule oppor- tunities (e.g., 4 days, 10 hours per day). This new choice dimension can have a very significant impact on the amount of travel produced and its temporal distribution. This choice, however, is clearly not a trip-level decision comparable to choice between Managed and Free Lanes (or between toll and non-toll road) for a particular trip. Choices such as this should be modeled within a proper behavioral framework that includes an extended time scale, with a robust set of explanatory variables, and linkages to the other short-term and long-term choices (Pendyala 2005, Spear 2005). Depend- ing on the project scale and time horizon, these second-order responses might become as significant as the first-order ones. Important behavioral responses that are generally beyond traditional trip-level modeling choices can be grouped into the following broad classes: • Trip/tour destination choice that is equally important for both AB and 4-step models; it is normally assumed that impacts of congestion and pricing should be captured through the generalized cost or mode choice Logsum (Erhardt, et al. 2003, Dehghani and Olsen 1999); however, there can be more direct and specific impacts that are worth exploring. • Short-term choices that relate to daily activity-travel patterns that cannot be fully captured at the elemental trip level. They include explicit joint travel arrangements (Vovsha, et al. 2003, Vovsha and Petersen 2005), tour formation [(NYMTC 2004)], and daily pattern type (MORPC 2005) (for example, decision to stay at home on a given day). These choices can be effectively applied only in an ABM framework. There might be an additional (though very limited) use of this for 4-step models in order to investigate congestion and pricing impacts on trip generation through accessibil- ity measures. It is important to address these dimensions alongside conventional trip dimensions, since many new pricing forms are not trip-based (for example, daily area pricing schemes applied in London (Litman 2005) and cur- rently envisioned/modeled in New York, San Francisco, and Los Angeles). • Medium-term choices relating to usual location and schedule for non-mandatory activities (like shopping or entertainment). A deeper understanding and ability to forecast such choices may be beneficial in order to put certain choices into a medium-term framework in order to explore the impacts of congestion and pricing beyond the short-term single-trip consideration. These choice dimensions can be incorporated into an advanced AB model only. • Medium- and long-term choices that relate to person and household mobility attributes (e.g., car ownership, tran- sponder acquisition, transit path, parking arrangements, etc.). There is a growing recognition of the importance of these choices in understanding and modeling impacts of congestion and pricing. There have been some initial attempts to formulate and estimate choice models related to the acquisition of transponders simultaneously with pre-route, departure time, and/or car occupancy choices, although the estimation was implemented at the single- trip level (Yan, et al. 2002, Yan and Small 2002). • Long-term location choices of residential place, work- place, and school as well as land-use development impacts. A special methodology for analysis of congestion and pric- ing impacts on these choices has not yet been developed. The existing long-term models of this type operate with standard trip-level measures of accessibility (Vovsha et al. 2005); thus, the effect of different and extended time scales is lost. There are plans, however, to explore data sets that include information on long-term choices (along with trip records) to ascertain the differential impacts of congestion and pricing over various time scales. Several of these choice dimensions represent relatively new choice models that have not yet been widely accepted or even explored (only first attempts to formulate and estimate these models have been made and reported). These relate to the integration of the binary pre-route choice (toll versus non- toll) in the mode choice nesting structure, payment type, and associated vehicle equipment (cash, E-Z pass, transponder), as well as models of carpooling mechanisms (explicit model- ing of joint travel). 4.2.2 Observed Impacts of Pricing on Different Travel Choices (PSRC Experiment) The Traffic Choices Study was a unique behavioral experi- ment carried out by Puget Sound Regional Council (PSRC) for the FHWA Value Pricing Pilot Program. A sample of selected Seattle region households reacted to variations in toll levels by road type and time of day over an 18 month period, with in-vehicle GPS units used to record behavior as accurately as possible and to keep track of toll fees charged to respondents. The information in this section is based primarily on two PSRC documents: Traffic Choices Study: Summary Report, from April 2008, and Appendix 19 to that report Traffic Choices Study: Toll Impact Models.

35 Description of the Experiment The Traffic Choices Study combines some of the best fea- tures of RP and SP data collection for support of the analysis of travel behavior and the improvement of demand models. Similar to SP, the experiment was able to obtain behavioral responses to a policy that has not yet been implemented— namely ubiquitous, mileage-based congestion pricing on all freeways and main arterials in the Seattle region. In this case, the study was able to overcome the hypothetical nature of SP methods by applying the pricing during real trips that the respondents made over an extended period of time and charging those respondents real money for using specific roads at specific times of day and week. This was done using an innovative approach of providing respondents with a fixed sum of money in an account at the beginning of the experiment. Respondents were also provided a toll map and schedule to inform them of toll levels as they varied across roads and time periods, and in-vehicle GPS determined the level of per-mile toll applied at any instant and that informa- tion was relayed to the driver. At the end of the experimental period, respondents were allowed to keep whatever funds remained in their account. This system mimicked as closely as possible the way that funds would be charged against user credit cards for an actual electronic tolling system. The main differences compared to an actual congestion pricing system were that (a) only a small subpopulation of all drivers on the roads were faced with the experimental pricing, so there was no noticeable effect of pricing on overall traffic levels or congestion, and (b) respondents spent money given to them as part of the experiment, which, for some, could evoke the sense that the money is not really their own. The implications that these differences may have for behavioral modeling are discussed later on in this section. For the study, GPS units were installed in all household vehicles in 275 randomly recruited households in the region, providing a sample of more than 400 instrumented vehicles. Before tolling was “turned on,” respondents drove with the GPS units in their vehicles for a period of three months (see timeline in Figure 6). This initial non-priced period served a few different purposes: (a) to make sure that the GPS units were working and transmitting data properly to the central facility, (b) to collect baseline behavioral data against which data from the tolled situation could be compared in analysis, and (c) to get an idea of how many miles each house- hold regularly drove on the tolled links, so that the initial funding level of the user account could be set. The objective was to set the budget high enough so that users would not fully deplete the account and have to leave the pricing experi- ment early, while at the same time not setting it so high that some households would still receive a significant reward at the end, even if they did not adjust their trips to avoid paying the tolls. Figure 7 shows the Toll Roads Map that was provided to respondents. The map shows two types of roads that were priced: the main freeways shown in green, and other main arterials shown in white. The toll rates per mile for freeways were set twice as high as for the other arterials, ranging from 10 cents to 50 cents per mile on weekdays and 10 cents to 20 cents per mile on weekends, varying by time of day. On weekdays, the highest priced period was the PM peak from 4 pm to 7 pm, followed by the AM peak from 6 am to 9 am. Prices were lower midday (9 am to 4 pm) and in the evening (7 to 10 pm). On weekends, the high toll period was 10 am to 7 pm. No tolls were charged between 10 pm and 6 am on any day. All respondents received the same toll schedule for the entire experiment—no variation was used across the sample or across seasons/months. The pricing was operational beginning on July 1, 2005, and continued through February 2006, a period of eight months. During that time, respondents could obtain information in their vehicle indicating the amount being charged at any moment and also in total for that trip or that day. Respon- dents could also go online to the project website and find the amount of money remaining in their account as well as a historical overview of the toll roads they had used, when they were used, and what tolls had been charged. During the total project period, across the sample, the GPS units logged over 750,000 individual trips, including over 100,000 toll transac- tions. The central system also sent out over 4,000 customer billing invoices, mimicking the type of monthly invoice that would be sent in an actual system. After the tolling period ended, additional control data was collected for roughly one month. Behavioral Analysis of Traveler Responses to Pricing Some behavior analysis has already been performed by PSRC and EcoNorthwest and reported in the study report. Figure 6. Traffic choices project timeline.

36 Figure 7. Traffic choices study: toll roads map.

37 This section provides a brief summary of the findings. The majority of the analyses has been done at a fairly aggregate level where the unit of analysis is not a particular trip or route, but the average travel per week during the tolling period versus during the control period. One reason for a more aggregate level of analysis at this stage, is a data issue particular to GPS data, which any analysis of the data must deal with. This issue is that all the data is passive and vehicle-based. As a result, for any particular trip, the basic GPS data is missing three items of information that are often used in analysis of household travel survey data: (1) the person in the household driving the vehicle, (2) the number of occupants in the vehicle, and (3) the type/purpose of activities completed at each stop loca- tion. The initial analyses have partially addressed this issue by identifying the location of regularly visited workplaces. With this information, all tours (or partial tours) could be catego- rized into four types: home-to-work, work-to-home, home- to-home (non-work tours), and work-to-work (work-based sub-tours). Also, analyses were performed at three levels of aggregation: each household, each vehicle, and each workplace. Overall, compared to the control period, the introduction of the tolls was found to produce the following impacts on travel patterns across all participating households: • 7% reduction in all vehicle tours (tours per week) • 6% reduction in tour segments (segments of tours per week) • 8% reduction in tour drive time (minutes of driving per week) • 12% reduction in vehicle miles traveled (miles per week) • 13% reduction in miles driven on tolled roads (tolled miles per week) From these numbers, we can infer a number of behavioral findings: • In the big picture, the tolling had a large enough effect on various dimensions of behavior that the data should be suitable for further analysis on the effects of pricing and congestion. • Since tour segments (trips) were reduced slightly less than the number of tours, a slight increase in trip chaining was experienced—i.e., the number of trips per tour increased by about 1%. • Because vehicle miles traveled decreased by 12% while the number of tours decreased by only 7%, the average tour distance was reduced by about 5%. This could be because longer distance tours were most likely to be suppressed, but it could also be due to travelers’ switching to closer destinations. A comparison of tour distance distributions with and without tolling would provide further insight. • The fact that vehicle miles traveled on toll roads decreased slightly more than vehicle miles travelled overall implies at least a small amount of shifting from tolled routes to non-tolled routes and/or to the non-tolled night period (although this comparison does not identify route shifting to routes and/or times of day that are still tolled but at a lower toll level). • Since total travel distance decreased by 12%, but the total drive time decreased by only 8%, overall average driving speed was reduced by about 4%. This likely results from less travel on the tolled freeways, which have the highest speeds. An additional analysis was carried out to look at departure time shifts for home-to-work journeys. From the travel pat- terns in the control period data, it was possible to determine the usual departure time from home to work for the majority of regular commuters. Then, an analysis was performed to relate the percentage of those commuters who shifted to a lower toll period as a function of the number of minutes the departure time had to be shifted away from the usual time. The reported results are shown in Figure 8 from the PSRC report, with a clear relationship showing over 30% of com- muters shifting time when the required shift was 30 minutes or less, down to less than 10% shifting when the required shift was more than two hours. Although it is difficult to interpret these results without knowing more detail about the analysis, some implications of these findings in the context of further research that could be supported with these data are: • There appears to be enough systematic departure time shifting in the data to support disaggregate departure time modeling, at least for home-to-work journeys. It is likely that work-to-home journeys could be analyzed in a similar way, preferably in a joint context with the home-to-work journey. • The data could be analyzed to find other regular non-work journeys that particular households make during both the control and tolling periods. Home-to-school/university tours and tours to escort children to school seem likely candidates, and school locations would be fairly easy to pinpoint in the data by matching to a GIS parcel database. School start and end times are typically fixed and home- to-school distances are typically short and thus not a good candidate for departure time shifting to avoid tolls. Perhaps there are other types of regular journeys, although infer- ring the destination purpose of the journeys would require GIS analysis. • A multivariate analysis approach would provide more use- ful behavioral models, including the amount of time shift necessary, but also the direction of shift, the difference in toll levels and travel times between the periods, and other characteristics of the household: the driver (if known), the destination, and the tour.

38 • People may shift their route of travel instead of (or in addition to) their departure time. An advantage of GPS data over typical household survey data is that the exact route of travel can be identified. With the data available, it seems that a joint route-departure time choice model would be a more complete and valid way of identifying the simultaneous effects of pricing, travel time, and congestion. Route choices for home to work journeys were also analyzed by the PSRC project team. Identified in the data was the per- centage of times that each commuter chose to use an alternative lower toll or non-tolled route, which was analyzed with respect to the toll difference and travel time difference between the routes, in order to infer VOT for each commuter. The results were then interpreted as a function of household income, with the resulting VOT function shown below in Figure 9 from the PSRC report. Except for the very low income households, the imputed VOT appears to be 70% to 80% of the wage rate across the full range of incomes. These are somewhat higher than VOT typically estimated from SP data on route choice under pricing, although in line with typical VOT from RP data. It is difficult at this stage to provide an interpretation or critique of these results without knowing more detail about the analysis method. Some key points to be considered in the context of further analysis of the data set are: • Shifting route is only one possible way that travelers can reduce or avoid paying tolls. Shifting departure time is the Figure 8. Home-to-work tour probability of moving to lower toll. Figure 9. Observed home-to-work VOT (as function of route choice).

39 other most likely way, but other possibilities include shift- ing mode to transit or non-motorized (this would only be seen in the GPS data as a reduction of commute frequency), increasing car occupancy (this would not be seen in the GPS data at all), shifting destination (very unlikely for work tours, at least in the short term), and canceling commute trips, e.g. by telecommuting (in the GPS data, this would be indistinguishable from switching mode). Since these other shifts would most likely be made by people with the low- est VOT (highest marginal disutility of toll and/or lowest marginal disutility of travel time) and those cases are not in the route choice data, this may lead to a higher imputed VOT than is typically the case. However, if route choice is truly the “lowest level” choice in the decision hierarchy, then the high VOT may be suitable for the particular con- text of route choice. • In the context of departure time choice, the best way to sort out these issues is with a joint model that includes the three main identifiable dimensions of commuting behavior in the data set—route choice, departure time choice, and frequency of commuting by car—and analyzes them in an integrated manner, including as many household, person, land use, and contextual variables as possible. 4.2.3 Prototype Structure of Demand Model—4-Step Approach Taking into account the accumulated experience in appli- cation of 4-step models for pricing studies described in Chapter 2, necessary short-term improvements, and the most important travelers’ responses to pricing mentioned in the current section above, we can outline a prototype struc- ture for a 4-step model that includes all features essential for pricing studies; see Figure 10. The main sub-models have to be segmented by 4–5 trip purposes (for example, home-based-work, home-based- university, home-based-school, home-based other, and non-home-based), 3–4 household income groups (for exam- ple, 0–$50K, $50–$100K, $100K+), and 3–4 household car- sufficiency groups (for example, zero cars, cars fewer than drivers, cars equal to or greater than drivers) since these categories are characterized by very different VOTs and willingness to use toll roads, as described in Section 4.3. In general, it is not necessary to preserve a full Cartesian combi- nation of trip purposes and income groups; however, a strati- fication of home-based-work trips by income group is highly recommended. Figure 10. Prototype 4-step model for highway pricing studies. Tr ip ge ne ra ti on Tr ip di st ri bu ti on Tr ip mode , o ccu pa nc y, an d rout e ty pe ch oi ce Tr ip ti me of da y Mu lt i- cl a ss a ssi gnme nt (r ou te ch oi ce ) 1 s t o r d e r im pa ct s o f p r ic in g 2 n d o r d e r im pa ct s o f p r ic in g Se gm en te d by 4- 5 tr ip pu rp os es , 3- 4 in co me ca te go ri es , 3- 4 ca r su ffi ci en cy ca te go ri es , ur ba n de ns it y Se gm en te d by 4- 5 tr ip pu rp os es , 3- 4 in co me ca te go ri es , 3- 4 ca r su ffi ci en cy ca te go ri es ; us es mode ch oi ce Lo gs um Se gm en te d by 4- 5 tr ip pu rp os es , 3- 4 in co me ca te go ri es ; us es mode ch oi ce Lo gs um Se gm en te d by 4- 5 tr ip pu rp os es , 3- 4 in co me ca te go ri es , 3- 4 ca r su ffi ci en cy ca te go ri es ; in co rp or at es ca r o ccu pa nc y an d rout e- ty pe ch oi ce Im pl em en te d by 3- 5 TO D pe ri od s; 6- 8 ve hi cl e cl a sse s by oc cu pa nc y, ve hi cl e ty pe , an d w illi ngne ss to pa y

40 It is highly recommended to include vehicle occupancy choice (SOV, HOV2, HOV3+) and route type-choice (toll versus free) as lower-level sub-choices in the mode choice structure as explained in Section 2.2. This is especially impor- tant for HOV/HOT lane studies. Concurrently, the traffic assignment should be implemented in a multi-class fashion with vehicle classes distinguished by occupancy (SOV, HOV2, HOV3+) and vehicle type (auto, light truck, heavy truck). Auto classes can be additionally segregated by willingness to pay or income as suggested in Section 4.3.2. It is important to include a time-of-day choice model sen- sitive to congestion and pricing since it would be unrealistic to assume fixed time-of-day and peak-hour factors if such policies as congestion or dynamic pricing are to be applied. In accordance with the time-of-day choice model, the traf- fic assignment should be implemented for 3–5 time-of-day periods (AM peak, PM peak, off-peak that can be further subdivided into Midday, Night, and Early morning) that are characterized by different levels of congestion and may also be differentiated by toll rates. It is essential to integrate all demand sub-models and assign- ment procedures in an equilibrium framework of the model system. The LOS skims (travel times and cost including tolls) should be fed back to mode and time-of-day choice models to ensure the 1st-order impacts of pricing. Mode choice Log- sums (incorporating LOS variables) are then used as imped- ance measures in trip distribution and time-of-day choice to ensure the second order impacts of pricing. It has been shown that, if trip tables and LOS skims are properly averaged, a good level of convergence can be achieved after 3–4 global iterations (more detailed discussion of equilibration strate- gies is provided in Sections 6.1 and 6.2) 4.2.4 Prototype Structure of Demand Model—Activity-Based Approach Taking into account the accumulated experience in appli- cation of ABMs for pricing studies, necessary short-term improvements, as well as referring to some advanced model features, an outline for a prototype structure for an ABM that includes all features essential for pricing studies is shown in Figure 11. All general principles and short-term enhancements discussed in the previous sub-section with respect to 4-step models are basically valid for ABMs. However, a more advanced and flexible ABM structure offers multiple additional advan- Mu lt i- cl as s a ssi gnme nt (r ou te ch oi ce ) Da ily ac ti vi ty pa tt er n (g en er at io n of in di vi du al an d jo in t to ur s) To ur pr im ar y de st in at io n To ur ti me of da y ch oi ce To ur mo de ch oi ce St op fr eq ue nc y St op lo ca ti on Tr ip mo de , o ccu pa nc y, an d rout e ty pe ch oi ce 1 s t o r d e r im pa ct s o f p r ic in g 2 n d o r d e r im pa ct s o f p r ic in g Ge ne ra te to ur s by 8- 9 tr ip pu rp os es , 3- 4 in co me ca te gori es , 3- 4 ca r su ffi ci en cy ca te gori es , ur ba n de ns it y; a ddre sse s in di vi du al an d jo in t tr av el ex plic it ly Se gm en te d by 8- 9 tr ip pu rp os es , 3- 4 in co me ca te go ri es , 3-4 ca r su ffi ci en cy ca te gori es ; us es mo de ch oi ce Lo gs um Se gm en te d by 8- 9 tr ip pu rp os es , 3- 4 in co me ca te go ri es ; us es mo de ch oi ce Lo gs um ; ad dre sse s de pa rt ur e fr om hom e, ar ri va l ba ck ho me , an d du ra ti on Co nd it io na l up on th e to ur mo de , TO D, st op fr eq ue nc y, an d st op lo ca ti on ; se gm en te d by 8-9 tr ip pu rpos es , 3- 4 in co me ca te go ri es ; in co rp or at es ca r o ccu pa nc y an d rout e- ty pe ch oi ce Im pl em en te d by 3- 5 TO D pe ri od s; 6- 8 ve hi cl e cl a sse s by o ccu pa nc y, ve hi cl e ty pe , an d willin gn es s to pa y Se gm en te d by 8- 9 tr ip pu rp os es , 3- 4 in co me ca te go ri es , 3-4 ca r su ffi ci en cy ca te gori es ; in co rp or at es ca r o ccu pa nc y Se gm en te d by 8- 9 tr ip pu rp os es , 3- 4 in co me ca te go ri es , tr av el pa rt y si ze Co nd it io na l up on th e to ur de st in at io n, mo de , an d TO D; se gm en te d by 8- 9 tr ip pu rp os es , 3- 4 in co me ca te go ri es Figure 11. Prototype ABM for highway pricing studies.

41 tages for pricing studies. First of all, ABMs are inherently richer in terms of travel segmentation. For example, they normally incorporate 8–9 travel purposes (work, university, school, escorting, shopping, other maintenance, eating out, visiting relatives and friends, other discretionary). ABMs treat non-home-based trips as parts of the tours, thus there is no need to consider these trips as a separate purpose. The ABM framework ensures a more consistent approach to time-of-day choice modeling with an enhanced level of temporal resolution (1 hour or even 30 min). The time-of-day choice models applied in advanced ABMs treat departure time from home (in outbound half-tour direction), arrival back home (in inbound half-tour direction), and tour/activity duration in a coherent way (see Section 5.2.6 for a discussion on time-of-day choice models). This is one of the most clear and essential advantages of ABMs for congestion pricing studies. It has been generally recognized that a tour-based structure provides a more realistic response to congestion and dynamic pricing where a shift of trip departure times is expected or explicitly targeted by the policy. The ABM framework allows for a better modeling of car occupancy through an explicit treatment of joint travel as a special travel segment (see Section 5.2.7 for a discussion on modeling carpools). This is another significant advantage over 4-step models that is particularly beneficial for HOV/HOT lane studies. The ABM framework is based on individual microsimula tion that opens the way to account for situational variation in VOT for each travel segment. This principal model enhancement is discussed in detail in Section 6.1. In terms of integration of the demand model with network simulation, however, the current generation of ABMs still relies on conventional static assignments (improved by accounting for multiple vehicle classes). From this point of view, the equilibration principles described for 4-step models in the previous sub- section are applicable for ABMs. ABMs offer an innovative strategic direction, however, for an integration with advanced network simulation tools, based on the fact that their micro- simulation platform can provide a disaggregate input to a microsimulation process of DTA. This aspect is discussed in Section 5.4. 4.2.5 Prototype Structure of Network Assignments Regional travel models developed and applied so far (including both ABMs and 4-step models) have been inte- grated with conventional aggregate static equilibrium assign- ments. Evaluation of pricing (notably managed lanes) in congested areas is closely focused on understanding the effects of congestion, queuing, facility access/spacing, and other operational characteristics. Such aspects are not considered in a static assignment model. Consequently, there is a need for some guidance on how to incorporate a project’s unique operational characteristics/limitations into the travel demand forecasts and subsequent use for pricing analysis. An important issue that is difficult to fully resolve in practice relates to the need for a consistency between the segmentation applied in traffic assignment (vehicle and occupancy classes) and segmentation applied in the mode choice model (modes, travel purposes, and other segments). While it is compara- tively straightforward to use the same auto modes (occupancy classes) in both procedures, the additional segmentation by travel purpose, income group, and other possible dimensions pertinent to mode choice is difficult to preserve in the assign- ment procedure since it would result in an infeasibly large number of vehicle classes. Table 8 illustrates an ideal segmen- tation structure maintaining consistency across the mode choice and assignment model components, and including approximate VOT estimates for each segment. This structure is typically simplified in practice due to assignment/skimming run time constraints. The demand modeling part may also assume additional segmentation by various non-mandatory purposes, such as shopping, eating out, or other discretionary activities, while the network simulation part rarely includes more than three or four vehicle classes. The scaling parameters to account for vehicle occupancy O2 and O3 should be statistically estimated as part of mode choice model estimation, or by means of a special SP survey. In some model systems, these parameters are not actually estimated, but set equal to the actual occupancy. This means that the carpool willingness to pay is assumed equal to the total willingness to pay of all members of the travel party. More recent statistical evidence suggests that VOT is not directly proportional to the vehicle occupancy, and the actual coefficient values stand lower than 2 and 3. The logic behind this segmentation structure is to treat VOT consistently across all choices, while avoiding an exces- sive proliferation of travel segments and vehicle classes. Addi- tional segmentation of the behavioral choice models in the ABM framework is less onerous than in 4-step models, but issues associated with the multiplication of vehicle classes in the assignment procedure are shared by both ABMs and 4-step models. The choice of the number of vehicle occupancy catego- ries in the assignment procedure should be based on the expected nature of HOV and pricing policies. If significant projects with specific HOV3+ lanes or pricing policies are expected, explicit segmentation of trip tables by SOV, HOV2, and HOV3+ classes may be required. Otherwise, all HOV categories can be collapsed. However, even in the absence of specific traffic restrictions or pricing policies, a better segmentation by vehicle occupancy can be beneficial in capturing differential VOT.

42 In order to reduce the impact on assignment runtimes of the proliferation of segments, it may be possible to combine those segments or trip tables with similar VOT for assign- ment. This aggregation should also consider additional vehicle classes associated with non-passenger travel, such as heavy and light commercial trucks. A final decision about the aggregation of demand (trip tables) can only be made after statistical estimation of all VOT and occupancy-related coefficients. Table 9 illustrates a possible aggregation of vehicle classes based on the assumed values of time shown in Table 8 and scaling coefficients equal to occupancy. For simplicity, a value of 3.0 for occupancy of the HOV3+ cat- egory is used, while in reality it is likely closer to 3.2 or 3.3. In the assignment and skimming procedures, each vehicle class table is assigned based on the weighted average VOT across all components. It is possible to make this weighting specific to each assignment time-of-day period to ensure a better reflection on the differential mix of purposes across time-of-day periods. In addition to the fundamental issue of highway user segmentation by VOT, another important technical issue has manifested itself in almost all practical model applica- tions. This issue relates to how t demand models and net- work assignments are applied with respect to conditions of equilibrium, assuming multiple iterations between them. The problem manifests itself equally with sophisticated choice models (including many levels of hierarchy) or with simple binary pre-route choice models (most frequently applied in practice and sometimes taking the form of a toll-diversion model). The essence of the problem is that the trip table of toll users generated by the choice model (based on the travel time savings and toll skims from the previous iterations) cannot be fully assigned on toll paths in the next iteration. The associated leakage of toll users can be significant (frequently 15–20% or even more with sparse trip tables). It hampers the equilibrium process, as well as makes the results difficult to understand and interpret. There are several objective TOD/Mode choice segments Assignment vehicle classes Purpose Occupancy Occupancy Approximate VOT Commuting – low-income workers SOV SOV $10 HOV2 HOV2 $10× 2O HOV3+ HOV3+ $10× 3O Commuting – medium-income workers SOV SOV $15 HOV2 HOV2 $15× 2O HOV3+ HOV3+ $15× 3O Commuting – high-income workers SOV SOV $20 HOV2 HOV2 $20× 2O HOV3+ HOV3+ $20× 3O Work-based sub-tours SOV SOV $30 HOV2 HOV2 $30× 2O HOV3+ HOV3+ $30× 3O University / school tours SOV SOV $6 HOV2 HOV2 $6× 2O HOV3+ HOV3+ $6× 3O Non-mandatory tours – low income SOV SOV $8 HOV2 HOV2 $8× 2O HOV3+ HOV3+ $8× 3O Non-mandatory tours – medium income SOV SOV $10 HOV2 HOV2 $10× 2O HOV3+ HOV3+ $10× 3O Non-mandatory tours – high income SOV SOV $12 HOV2 HOV2 $12× 2O HOV3+ HOV3+ $12× 3O Table 8. Coordinated segmentation of mode choice and assignment.

43 reasons for this discrepancy that should be understood before any solution is considered: • Non-toll users are assigned onto the highway network with the tolled facilities blocked-out, guaranteeing choice of non-toll routes only. Toll users from the choice models, on the other hand, are assigned onto the highway network with both tolled and non-tolled facilities available to them. For these toll user flow, a full guarantee of choosing toll routes only can only be achieved by restrictive assignment techniques that are too complicated, unrealistically time- consuming, and not supported in any of the available software packages. • The time and toll skims used in the choice model to generate trip tables of toll and non-toll users at the previous iteration can never be fully identical to the travel times, tolls, and generalized cost produced in the subsequent equilibrium assignment procedure. Full convergence exists only in the- ory. In practice, with any reasonable number of iterations, there are always going to be certain discrepancies. • While the equilibrium assignment algorithm essentially pro- duces multi-path assignment results (at each assignment iteration), a single shortest path is found and loaded for each OD pair. This means that for some OD pairs where toll and non-toll routes are comparable in terms of generalized cost, there can be a split between toll and non-toll users in the toll user assignment. Several (empirical) procedures in applied models have attempted to overcome or at least mitigate the leakage of toll users in assignment: • Toll route promotion. In this method, tolls are either reduced or fully eliminated in the toll user assignment procedure, since the users have already made a decision to use the toll facility and “paid the toll in the choice model.” While this can mechanically reduce the leakage, it is only applicable for single-facility projects (such as a single toll bridge in the area) where essentially a single toll route is feasible. In cases where several toll facilities are involved (either on compet- ing or complementary basis), this technique can produce significant route distortions (biases toward higher tolls). • Disabling equilibrium time fluctuations. In some practi- cal applications, modelers decided to disable equilibrium time fluctuations after a certain number of iterations (where link travel times area already close to the equi- librium travel times). It means that the final assignment of toll users is implemented with the travel times frozen Purpose Occupancy Approximate VOT Trip tables by occupancy and VOT SOV $6-12 SOV $15-30 HOV2 $12-24 HOV2 $30-60 HOV3+ $18-36 HOV3+ $45-90 Commuting – low income workers SOV $10 X HOV2 $10×2=$20 X HOV3+ $10×3=$30 X Commuting – medium income workers SOV $15 X HOV2 $15×2=$30 X HOV3+ $15×3=$45 X Commuting – high income workers SOV $20 X HOV2 $20×2=$40 X HOV3+ $20×3=$60 X Work-based sub-tours SOV $30 X HOV2 $30×2=$60 X HOV3+ $30×3=$90 X University / school tours SOV $6 X HOV2 $6×2=$12 X HOV3+ $6×3=$18 X Non-mandatory tours – low income SOV $8 X HOV2 $8×2=$16 X HOV3+ $8×3=$24 X Non-mandatory tours – medium income SOV $10 X HOV2 $10×2=$20 X HOV3+ $10×3=$30 X Non-mandatory tours – high income SOV $12 X HOV2 $12×2=$24 X HOV3+ $12×3=$36 X Table 9. Example of vehicle class aggregation.

44 from the previous iteration (rather than in an equilibrium fashion). While this technique is helpful to assign almost all toll users onto toll path, it is dangerous in that the final assignment essentially corresponds to an all-or-nothing shortest path choice (despite having used equilibrium travel times) and can produce unrealistic link volumes through- out the network. It is clearly inappropriate for congested metropolitan networks with multiple toll facilities. • Explicit modeling of toll route components and non-toll access sub-routes. This might be considered as the most theoretically consistent approach that draws upon the applied techniques for combined multimodal transit trips. It is, however, quite complicated and requires additional network coding, and is applicable only for highway networks with a small number of toll facilities. With this approach, each point of entry to and exit from the toll facility is coded as a traffic zone. Then each toll user path is convoluted (using OD matrix manipulations) of the free access sub- route, toll sub-route (from the entry to exit), and free aggress sub-route. This technique becomes especially problematic in the presence of multiple toll facilities that might be intertwined with free facilities on the same route. • Using more elaborate skims to identify toll users. Most of the applied models are based on a simplified method of identification of toll users by a presence of a non-zero toll in the skim. The toll skim that is used for identification of toll users can be further elaborated by the addition of the facility index and toll route proportion (that is a fractional number between 0 and 1, rather than just a binary indicator). These “flags” in the OD skims can be used to prepare more effective promotion strategies, as well as to create more (facility-specific) trip tables for multi-class assignment. It is generally recognized that a combination of elaborate skimming and promotion would probably be the best general strategy, while the disabling of equilibrium and the explicit modeling of toll route components could be methods used for specific subset of projects only. An additional complexity is associated with modeling real- time variable tolls. In this case, several intermediate iterations of toll calculations have to be implemented between the assignment procedure and choice model. Modeling variable tolls depends on the adopted form of toll calculation. This technique has been currently tried in only a few applications and is still evolving. Several basic operational approaches have already been identified as possible methods for further evaluation: • Predetermined toll scales as function of LOS on the toll facility/lanes. In this case tolls are specified in advance as a function of V/C or speed, and depend solely on the traffic conditions on the toll facility/lanes. The application of tolls does not guarantee that the traffic conditions will meet the requirement. Model testing with different tolls is required. • Predetermined toll scales as function of LOS on the managed toll lanes compared to free general-purpose lanes. In this case tolls are specified in advance as a function of speed differences and are intended to maintain a better LOS on toll lanes. The application of tolls does not guarantee that the traffic conditions will meet the requirement, however, and model testing with different tolls is required. • Variable tolls as function of LOS on the toll facility/lanes. In this case tolls are incrementally adjusted as a function of the achieved V/C or speed and depend solely on the traffic conditions on the toll facility/lanes. It can be thought of as a shadow pricing technique, reflecting the scarcity of road capacity. The application of tolls guarantees that the traffic conditions will meet the requirement, assuming there are alternative free routes/general purpose lanes. • Variable tolls as function of LOS on the managed toll lanes compared to free general-purpose lanes. In this case tolls are incrementally adjusted as a function of the achieved speed differences between the toll and free lanes. The application of tolls guarantees that the traffic conditions will meet the requirement. 4.3 Summary of Key Model Parameters 4.3.1 VOT Values in Applied Models Tables 10–12 summarize VOT, the key model parameter that has been adopted in different applied models for selected pricing studies. This summary is intended to serve as a useful set of reference points for modelers who may need to borrow these coefficients for local pricing studies. Table 10 contains a summary of VOT estimates for travel demand models, Table 11 summarizes VOTs used for trucks and commercial vehicles, and Table 12 summarizes VOTs used in network assignment procedures. There is a great deal of variation in estimated and applied VOT across different studies, and it is difficult to find a clear common denominator. Part of the problem is due to the dif- ferent choice contexts and segmentation rules adopted in the different studies and models. Another important source of variation relates to the data used and method of estimation. It is well known that RP and SP data tend to have built-in dif- ferences, while calibration based on the aggregate data yields only very crude proxies for individual VOTs. Additionally, there may be objective regional differences in transportation conditions, including the level of congestion, prevailing high- way facility types, impacts of climate/weather, as well as the population mix by income and occupation that manifests itself in travel behavior (at least for passenger travel). Finally,

45 Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment VOT, $/hour San Francisco County Transportation Authority (SFCTA), Regional Pricing Model 9-County San Francisco Region, CA Yes RP/SP Mode & occupancy, route type (toll vs. non-toll) 2000 (RP) 2007 (SP) Work tours, low household income ($0- $30K) 3.6 Work tours, medium household income ($30- $60K) 10.9 Work tours, high household income ($60K+) 17.9 Other tours, low income 2.4 Other tours, medium income 7.2 Other tours, high income 12.0 New York Metropolitan Transportation Council (NYMTC), Applied Travel Demand Model 28-County New York Region, NY Yes RP Mode & occupancy 1997 Work tours 15.8 School tours 6,5 University tours 11.7 Maintenance tours 12.4 Discretionary tours 10.7 At-work sub-tours 40.0 Ministry of Transportation of Quebec (MTQ), Travel Demand Model for T&R Studies Montreal Region, QC No RP/SP Mode, occupancy, route type (toll vs. non-toll) 2000 (RP) 2003 (SP) Work tours, low income (0-$40K), peak 10.2 (CAD) Work tours, low income, off-peak 7.3 (CAD) Work tours, male, high income ($40K+) 10.2 (CAD) Work tours, female, high income 10.6 (CAD) Maintenance tours, male 4.0 (CAD) Maintenance tours, female, low income 6.4 (CAD) Maintenance tours, female, high income 7.3 (CAD) Discretionary tours, male 3.0 (CAD) Discretionary tours, female, low income 6.0 (CAD) Discretionary tours, female, high income 7.6 (CAD) Orange County Transportation Authority (OCTA), Applied Travel Demand Model Orange County, CA Yes Synthetic calibration Mode 1989 Home-based-work trips, low income 3.1 Home-based-work trips, medium income 8.4 Home-based-work trips, high income 19.4 Home-based-other trips, low income 1.5 Home-based-other trips, medium income 4.1 Home-based-other trips, high income 9.7 Non-home-based trips 6.7 Table 10. Summary of VOT estimates for passenger travel demand. (continued on next page)

46 Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment VOT, $/hour Travel Demand Model Home-based-work trips, high income 11.5 Home-based-school trips, low income 2.2 Home-based-school trips, high income 4.2 Home-based-other trips, low income 0.8 Home-based-other trips, high income 5.6 Non-home-based trips, low income 2.8 Non-home-based trips, high income 5.7 North-Central Texas Council of Governments (NCTCOG), Travel Demand Model Applied for T&R Studies Dallas-Fort Worth, TX Yes RP Mode 1999 Home-based-work trips 5.9 Home-based-other trips 4.1 Non-home-based trips 3.3 San Diego Association of Governments (SANDAG), Applied Travel Demand Model San Diego, CA No Synthetic calibration Mode 1995 Home-based-work trips, low income 1.8 Home-based-work trips, medium income 5.5 Home-based-work trips, high income 11.2 Home-based-other trips, low income 0.9 Home-based-other trips, medium income 2.7 Home-based-other trips, high income 5.6 Non-home-based trips 2.7 Applied Mode Choice model for Twin Cities Minneapolis –St. Paul, MN No RP Mode 2000 Home-based-work trips 12.2 Non-home-based-work trips 3.7 Home-based-other trips 1.9 Non-home-based-other trips 2.0 Denver Regional Council of Governments (DRCOG), Applied Travel Demand Model Denver, CO Yes Synthetic calibration Mode 1996 Home-based-work trips, low income 4.0 Home-based-work trips, medium income 8.0 Home-based-work trips, high income 16.0 Home-based-other trips 8.8 Non-home-based trips 8.4 Atlanta Regional Commission (ARC), Travel Demand Model Applied for Mobility 2030 Study Atlanta, GA Yes RP Mode 2000 Home-based-work trips 14.9 Home-based-other trips 13.5 Non-home-based trips 3.4 Mountain View Corridor, Applied Salt Lake, UT No RP Mode 1992 Home-based-work trips, low income 1.3 Table 10. (Continued).

47 Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment VOT, $/hour Orlando, FL Home-based-work trips, high income, peak 9.5 Home-based-work trips, low income, off-peak 4.0 Home-based-work trips, high income, off-peak 13.5 Home-based-other trips, low income, peak 4.0 Home-based-other trips, high income, peak 7.5 Home-based-other trips, low income, off-peak 3.0 Home-based-other trips, high income, off-peak 8.0 Puget Sound Regional Council (PSRC), VOT for Travel Forecasting and Benefits Analysis Seattle, WA No RP, Traffic Choices Study Mode 2000 (RP) 2006 (Traffic Choices) Home-based-work trips, low income 6.0 Home-based-work trips, medium-low income 10.9 Home-based-work trips, medium-high income 16.4 Home-based-work trips, high income 20.9 Home-based-other trips 9.7 Non-home-based trips 15.6 Validation of the Pennsylvania Statewide Travel Model (2007), TRB CD (paper 07-2401) Different locations in PA No Synthetic calibration Route & Mode 2002 Auto trips 18.5 The VOT: Estimates of the Hourly VOT for Vehicles in Oregon (2006), Oregon DOT Policy & Economic Analysis Unit Different locations in OR No Synthetic calibration Route & Mode 2005 Auto trips 16.3 Zmud, J, Bradley M, Douma F, Simek C. (2007) Panel Survey Evaluation of Attitudes and Willingness to Pay for Toll Facilities I-394/I-35W corridor, MN Yes SP Route & Mode 2005-2006 (3 waives) Baseline VOT for which different additions are applied: 9.6 Household income $100K-$125K +2.1 Household income $125K+ +6.2 Age under 35 +2.4 Age 35-45 +1.4 Age 65+ -2.9 AM commute trips +3.5 PM commute trips +0.9 Other PM trips -2.1 Work-related trips +3.8 Shopping, personal business trips +1.5 Trip length under 10 miles -1.9 Trip length over 20 miles +2.3 Dehghani et al, 2003 Florida Turnpike, Yes RP/SP Mode 2000 Home-based-work trips, low income, peak 4.5 Table 10. (Continued). (continued on next page)

48 Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment VOT, $/hour (2001) The Value of Time and Reliability: Measurement from a Value Pricing Experiment Orange County, CA Route & TOD 4.7 Route & Mode 24.5 Route & transponder 18.4 Route mode & transponder 22.9 Liu, H, and W. Recker (2006) Estimation of the Time-Dependency of VOT and its Reliability from Loop Detector Data SR-91, Orange County, CA Yes RP Route 2001 Auto trips, departure time 5-6 am 19.5 Auto trips, departure time 6-7 am 24.4 Auto trips, departure time 7-8 am 28.5 Auto trips, departure time 8-9 am 28.7 Auto trips, departure time 9-9:30 am 22.1 Brownstone et al. (2003) The San Diego I-15 Congestion Pricing Project I-15, San Diego, CA Yes RP Route 1998 Auto trips 30.0 Sullivan, E. (2000) Continuation Study to Evaluate the Impacts of the SR- 91 Value-Priced Express Lanes SR-91, Orange County, CA Yes RP/SP Route 1999 Auto trips 16.3 Light, T. (2007) A Time-Use Approach for Estimating Commuter’s VOT, American Time Use Survey No RP Mode 2003 Full-time urban worker 5.4 Urban Transportation Economics, Second Edition, (2003) Chapters 2 & 3 Different metropolitan areas No RP, synthetic Destination 2003 Auto trips 9.1 Bertini, R. (2006) You are the Traffic Jam: An Examination of Congestion Measures Different metropolitan areas Yes Synthetic Route & mode 2002 Auto trips 13.5 Kriger, D. (2007) The Cost of Urban Congestion in Canada: A Model- Based Approach Vancouver Edmonton Calgary Winnipeg Hamilton Toronto Ottawa- Gatineau Montreal Quebec City No Synthetic Mode & route 1992-2003 Work trips by auto 24.7- 31.4 (CAD) Non-work trips by auto 7.6-9.7 CAD Ozbay, K. (2006) Theoretical Derivation of VOT and Demand Elasticity: Evidence from NJ Turnpike Toll Road NJ Turnpike, NJ Yes RP Route, Mode, TOD, Destination, & Frequency 2000 Auto trips 15.0- 20.0 Lam, T, & K. Small SR-91, Yes RP/SP Route 1998 All SR-91 users (auto) 19.2 Table 10. (Continued).

49 Table 11. Summary of VOT estimates for trucks and commercial vehicles. (continued on next page) Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment VOT, $/hour San Francisco County Transportation Authority (SFCTA), Regional Pricing Model San Francisco, CA Yes RP/SP, synthetic calibration Route type (toll vs. non- toll) 2008 All trucks 30.0 New York Metropolitan Transportation Council (NYMTC), Applied Travel Demand Model 28-County New York Region, NY Yes RP, synthetic calibration Route type (toll vs. non- toll) 1997 Commercial vehicles 60.0 Trucks 120.0 Ministry of Transportation of Quebec (MTQ), Travel Demand Model for T&R Studies Montreal Region, QC No SP, synthetic calibration Route type (toll vs. non- toll) 2000-2003 Commercial vehicle 12.0 (CAD) Light truck 24.0 (CAD) Heavy truck 36.0 (CAD) Puget Sound Regional Council (PSRC), VOT for Travel Forecasting and Benefits Analysis Seattle, WA No Synthetic Route type (toll vs. non- toll) 2000, 2006 Light trucks 40.0 Medium trucks 45.0 Heavy trucks 50.0 The VOT: Estimates of the Hourly VOT for Vehicles in Oregon (2006), Oregon DOT Policy & Economic Analysis Unit Different locations in OR No Synthetic Route type (toll vs. non- toll) 2005 Light trucks 20.4 Heavy trucks 29.5 Meyer, M. and L. Saben (2006) Feasibility of a Truck-Only-Toll (TOT) Lane Network in Atlanta, GA Atlanta, GA No Synthetic Route type (toll vs. non- toll) 2000 Light trucks Heavy trucks 18.0 35.0 North-Central Texas Council of Governments (NCTCOG), Travel Demand Model Applied for T&R Studies Dallas-Fort Worth, TX Yes Network calibration, synthetic Route type (toll vs. non- toll) 1999 All trucks 12.0 Atlanta Regional Commission (ARC), Travel Demand Model Applied for Mobility 2030 Study Atlanta, GA Yes Synthetic calibration Route type (toll vs. non- toll) 2000 All trucks 25.0 Kawamura, K. (2000) Perceived VOT for Truck Operators Different locations in CA Yes SP Route type (toll vs. non- toll) 1998-1999 All trucks 23.4 Private business 17.6 For hire business 28.0 Truck load business 25.0 Less than truck load business 22.6 Hourly pay group 25.4 Other pay scale 15.1

50 Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment VOT, $/hour Kawamura, K (2007) Evaluation of the Application of Delivery Consolidation in the U.S. Urban Area Using Logistics Cost Analysis Different cities No Synthetic Route type (toll vs. non- toll) 2002 All trucks 28.1 Wilbur Smith Associates (2003) The National I-10 Freight Corridor Study I-10 Corridor No RP, synthetic Route type (toll vs. non- toll) 2003 All trucks 25.0 An Economic Analysis of Segregating Cars and Trucks, (2007) TRB CD (Paper 07- 1331) Different locations No Synthetic Route type (toll vs. non- toll) 2007 Light trucks 12.0 Heavy trucks 50.0 Survey of Motor Carrier Opinions on Potential Optional Truck Only Toll (TOT) Lanes on Atlanta Interstate Highways. (2007) TRB CD (Paper 07- 1664) Atlanta, GA Yes SP Route type (toll vs. non- toll) 2005 40% with low willingness to pay for TOT (5 cents per mile) 3.0 24% with medium willingness to pay for TOT (10 cent per mile) 6.0 7% with high willingness to pay for TOT (30 cents per mile) 18.0 Bertini, R (2006) You are the Traffic Jam: An Examination of Congestion Measures Different metropolitan areas Yes Synthetic Route type (toll vs. non- toll) 2002 All trucks 71.0 Table 11. (Continued). Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment (vehicle class) VOT, $/hour San Francisco County Transportation Authority (SFCTA), Regional Pricing Model San Francisco, CA Yes Synthetic calibration Route 2008 SOV, external traffic 15.0 HOV2 30.0 HOV3+ 45.0 Trucks 30.0 New York Metropolitan Transportation Council (NYMTC), Applied Travel Demand Model 28-County New York Region, NY Yes RP, synthetic calibration Route 1997 SOV, external traffic 15.0 HOV2 30.0 HOV3+ 45.0 Taxis 30.0 Commercial vehicles 60.0 Trucks 120.0 Ministry of Transportation of Quebec (MTQ), Travel Demand Model for T&R Studies Montreal Region, QC No RP/SP, synthetic calibration Mode & occupancy 2000, 2003 (SP) Auto 8.0 (CAD) Commercial vehicle 12.0 (CAD) Light truck 24.0 (CAD) Heavy truck 36.0 (CAD) Table 12. Summary of VOT estimates applied in network assignments.

51 Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment (vehicle class) VOT, $/hour Denver Regional Council of Governments (DRCOG), Applied Travel Demand Model Denver, CO Yes Synthetic calibration Route 1996 All vehicles, peak 8.0 All vehicles, off-peak 6.0 Atlanta Regional Commission (ARC), Travel Demand Model Applied for Mobility 2030 Study Atlanta, GA Yes Synthetic calibration Route 2000 SOV 15.0 HOV 20.0 Trucks 25.0 Puget Sound Regional Council (PSRC), VOT for Travel Forecasting and Benefits Analysis Seattle, WA No RP, Traffic Choices Study Route 2000 (RP), 2006 (Traffic Choices) SOV, home-based work trips, low income 9.6 SOV, home-based work trips, medium-low income 17.6 SOV, home-based work trips, medium-high income 25.7 SOV, home-based work trips, high income 33.3 SOV, non-home-based Work trips 10.0 HOV2, AM peak 27.9 HOV3+, AM peak 35.8 Vanpool, AM peak 99.4 HOV2, Midday 14.5 HOV3+, Midday 16.4 Vanpool, Midday 32.4 HOV2, PM peak 18.9 HOV3+, PM peak 22.9 Vanpool, PM peak 54.7 HOV2, evening 16.0 HOV3+, evening 16.4 Vanpool, evening 32.4 HOV2, night 23.4 HOV3+, night 31.5 Vanpool, night 84.5 Light trucks 40.0 Medium trucks 45.0 Heavy trucks 50.0 Mountain View Corridor, Applied Travel Demand Model Salt Lake, UT No Network calibration, synthetic Route 1992 All vehicles 20.0 North-Central Texas Council of Governments (NCTCOG), Travel Demand Model Applied for T&R Studies Dallas-Fort Worth, TX Yes Synthetic calibration Route 1999 Autos 10.0 Trucks 12.0 San Diego Association of Governments (SANDAG), Applied Travel Demand Model San Diego, CA No Synthetic calibration Route 1995 All vehicles 21.0 Table 12. (Continued). (continued on next page)

52 different studies relate to different years and can only be com- pared after a scaling of the VOTs to account for inflation and income growth as explained in Section 4.5. It is yet to be fully demonstrated to what extent VOT esti- mates can be transferred in space (i.e., between regions) and in time (i.e., applied to different years). Some general pat- terns and orders of magnitudes, however, are quite clear, and serve as the basis for the set of recommended default VOTs provided in the following section. 4.3.2 Recommended Values for VOT, Travel Time, and Cost Coefficients Based on the review and analysis of the estimated and applied VOTs, we have developed default values that can be recommended for travel demand models and traffic assign- ment procedures. It should be understood that these values represent something like a common denominator across very different regions and model structures. It will always be preferable to estimate VOT (and underlying time and cost coefficients in the utility functions) based on local RP and SP surveys. The suggested values might be helpful as reasonable defaults when a local survey or other supporting data are not available. The recommended default VOTs for travel demand models (specifically mode and occupancy choice) are presented in Table 13. The values are scaled to correspond to the year 2008. The underlying time and cost coefficients are also presented for each VOT value. Following the prevailing modeling prac- tice, we assume that travel time is measured in minutes, and travel cost (including toll) is measured and coded in cents. The values of travel time and cost coefficients intended for use in the (mode) utility functions are scaled accordingly. The VOT, however, is presented in $/hour units, again, to follow the conventional practice. For HOV vehicles, using scale parameters for VOT of 1.75 for HOV2 and 2.5 for HOV3+ is suggested. These multipliers are somewhat lower than the number of travelers in the party. It is believed that it is more realistic than scaling VOT directly proportional to the number of travelers, as was assumed in many applied models. In particular, for intra-household car- pools (many of them with children) it is unrealistic to assume that the willingness of the all passengers to pay will be equal to driver’s willingness to pay. The recommended default VOTs for multi-class traffic assignments are presented in Table 14. Again, following conventional practice, VOT values are presented in $/hour units. However, the coefficient for cost (including toll) is scaled in min/cent units in order to be used as a multiplier for cost in the link generalized cost function. Thus, we assume that link travel time function is coded in minutes and link cost is coded in cents, as in most transportation models. A word of caution is needed before the default VOTs are adopted for network assignments. Whenever possible, a consistency between travel demand model and network assignment procedures should be held. This means that if some travel segments applied in the demand model (like travel purposes or income categories) are to be aggregated for the Table 12. (Continued). Source Location Existing toll facilities Survey type, estimation method Choice context Year of data for estimation Segment (vehicle class) VOT, $/hour Dehghani et al, 2003 Florida Turnpike, Orlando, FL Yes RP/SP Route 2000 All vehicles, peak 12.0 All vehicles, Midday 6.0 All vehicles, Night 4.7 Evaluating the effectiveness of toll strategies on route diversion and travel times for specific OD-pairs in a regional transportation network, 2007, TRB CD (Paper 07-0806) Orlando, FL Yes Synthetic calibration Route 2007 All vehicles 15.0 A Cordon Charge for the District Of Columbia: A Solution for DC’s Fiscal Problems and Region’s Congestion? (2007) TRB CD (Paper 07- 0806) Washington, DC No Synthetic calibration Route 2004 All vehicles 13.8

53 Travel purpose Household income group TOD period SOV HOV2 (scale 1.75) HOV3+ (scale 2.5) VOT, $/h Time coeff, 1/min Cost coeff, 1/cent VOT, $/h Time coeff, 1/min Cost coeff, 1/cent VOT, $/h Time coeff, 1/min Cost coeff, 1/cent Work commute Low (0-$50K) AM peak 8.0 -0.025 -0.00 188 14.0 -0.025 -0.00107 20.0 -0.025 -0.00075 PM peak 7.0 -0.025 -0.00214 12.3 -0.025 -0.00122 17.5 -0.025 -0.00086 Off-peak 6.0 -0.025 -0.00250 10.5 -0.025 -0.00143 15.0 -0.025 -0.00100 Med ($50K-$100K) AM peak 15.0 -0.025 -0.00100 26.3 -0.025 -0.00057 37.5 -0.025 -0.00040 PM peak 13.5 -0.025 -0.00111 23.6 -0.025 -0.00063 33.8 -0.025 -0.00044 Off-peak 11.0 -0.025 -0.00136 19.3 -0.025 -0.00078 27.5 -0.025 -0.00055 High ($100K+) AM peak 22.0 -0.025 -0.00068 38.5 -0.025 -0.00039 55.0 -0.025 -0.00027 PM peak 20.0 -0.025 -0.00075 35.0 -0.025 -0.00043 50.0 -0.025 -0.00030 Off-peak 18.0 -0.025 -0.00083 31.5 -0.025 -0.00048 45.0 -0.025 -0.00033 Business, at- work Low (0-$50K) Peak 12.0 -0.040 -0.00200 21.0 -0.040 -0.00114 30.0 -0.040 -0.00080 Off-peak 10.0 -0.040 -0.00240 17.5 -0.040 -0.00137 25.0 -0.040 -0.00096 Med ($50K-$100K) Peak 20.0 -0.040 -0.00120 35.0 -0.040 -0.00069 50.0 -0.040 -0.00048 Off-peak 17.0 -0.040 -0.00141 29.8 -0.040 -0.00081 42.5 -0.040 -0.00056 High ($100K+) Peak 28.0 -0.040 -0.00086 49.0 -0.040 -0.00049 70.0 -0.040 -0.00034 Off-peak 24.0 -0.040 -0.00100 42.0 -0.040 -0.00057 60.0 -0.040 -0.00040 University, college All Peak 8.5 -0.030 -0.00212 14.9 -0.030 -0.00121 21.3 -0.030 -0.00085 Off-peak 6.5 -0.030 -0.00277 11.4 -0.030 -0.00158 16.3 -0.030 -0.00111 School All All 4.0 -0.035 -0.00525 7.0 -0.035 -0.003 10.0 -0.035 -0.00210 Shopping, escorting, personal business, household maintenance, medical Low (0-$50K) Peak 6.5 -0.035 -0.00323 11.4 -0.035 -0.00185 16.3 -0.035 -0.00129 Off-peak 5.5 -0.035 -0.00382 9.6 -0.035 -0.00218 13.8 -0.035 -0.00153 Med ($50K-$100K) Peak 11.0 -0.035 -0.00191 19.3 -0.035 -0.00109 27.5 -0.035 -0.00076 Off-peak 9.0 -0.035 -0.00233 15.8 -0.035 -0.00133 22.5 -0.035 -0.00093 High ($100K+) Peak 15.0 -0.035 -0.00140 26.3 -0.035 -0.0008 37.5 -0.035 -0.00056 Off-peak 13.0 -0.035 -0.00162 22.8 -0.035 -0.00092 32.5 -0.035 -0.00065 Leisure, sport, entertainment, discretionary, eating out, visiting relatives and friends Low (0-$50K) Peak 5.5 -0.030 -0.00327 9.6 -0.030 -0.00187 13.8 -0.030 -0.00131 Off-peak 4.5 -0.030 -0.00400 7.9 -0.030 -0.00229 11.3 -0.030 -0.00160 Med ($50K-$100K) Peak 10.0 -0.030 -0.00180 17.5 -0.030 -0.00103 25.0 -0.030 -0.00072 Off-peak 8.0 -0.030 -0.00225 14.0 -0.030 -0.00129 20.0 -0.030 -0.00090 High ($100K+) Peak 14.0 -0.030 -0.00129 24.5 -0.030 -0.00073 35.0 -0.030 -0.00051 Off-peak 12.0 -0.030 -0.00150 21.0 -0.030 -0.00086 30.0 -0.030 -0.00060 Table 13. Recommended default VOT for travel demand models.

54 assignment procedure, the VOT for the aggregate segment (vehicle class) should be calculated as a weighted average across all included demand segments. This method derives the assignment VOTs from travel demand model VOTs, and is preferred compared to the default assignment VOTs (or any other assignment VOTs established independently of the demand model VOTs). The default values should be used only if the linkage between the demand model segments and assignment vehicle classes is not unambiguous. It can be ambiguous, for example, if the demand model does not differentiate VOTs by vehicle occupancy and time-of-day period (relying on trip purpose, income, and other variables). It is essential to differentiate VOTs by vehicle occupancy and time-of-day, since the tolls are differentiated by these categories. 4.4 Model Validation, Calibration, and Sensitivity Testing 4.4.1 Dimensions and Data for Model Validation Travel models in the United States (both 4-step and ABM) are subject to certain acceptance criteria established by the FHWA and FTA. Virtually all of this guidance relates to the base year calibration and replication of the most important aggregate targets that are established from data independent of the model. There is, however, a great deal of variation in the practice of travel modeling from region to region. The rigor and completeness of the criteria are normally subject to spe- cific project or policy considerations, and are consequently focused on either highway side (matching traffic counts) or transit side (matching observed ridership and travel times), but rarely both. It should also be considered that the validation and cali- bration of a travel model solely on the highway side, with no attention paid to the transit side, is problematic even though only the highway statistics are the focus of road pricing studies. The need for a reasonable transit validation stems from the fact that mode choice represents one of the four key travel dimen- sions (i.e., first-order travel responses to pricing) along with route choice, time-of-day choice, and car occupancy choice. For pricing studies we suggest a comprehensive approach to model validation that is based on the following system of basic criteria: • Highway validation: – Replication of daily traffic counts and daily AADT/ VMT statistics in the study corridor with 0.95 level of correlation. Vehicle class Household income & purpose sub-class TOD period VOT, $/h Cost/toll coefficient for time equivalent in generalized cost function, min/cent SOV Work trips, medium & high income AM 20.00 0.0300 PM 18.00 0.0333 Off-peak 15.00 0.0400 Other trips and incomes AM 12.00 0.0500 PM 10.00 0.0600 Off-peak 8.00 0.0750 HOV2 (scale 1.75) Work trips, medium & high income AM 35.00 0.0171 PM 31.50 0.0190 Off-peak 26.25 0.0229 Other trips and incomes AM 21.00 0.0286 PM 17.50 0.0343 Off-peak 14.00 0.0429 HOV3+ (scale 2.5) Work trips, medium & high income AM 50.00 0.0120 PM 45.00 0.0133 Off-peak 37.50 0.0160 Other trips and incomes AM 30.00 0.0200 PM 25.00 0.0240 Off-peak 20.00 0.0300 Taxi All All 20.00 0.030 0 Light trucks and commercial vehicles All All 30.00 0.0200 Heavy trucks All All 60.00 0.0100 Table 14. Recommended default VOT for multi-class traffic assignments.

55 – Replication of AM period counts (normally, 6:00–9:00 but can be adjusted to reflect the observed regional con- ditions) with 0.90 level of correlation. – Replication of PM period counts (normally, 3:30–6:30 but can be adjusted to reflect the observed regional con- ditions) with 0.90 level of correlation. – Replication of Midday off-peak period counts (nor- mally, 9:00 AM–3:30 PM but can be adjusted to reflect the observed regional conditions) with 0.80 level of correlation. – Replication of travel speed and LOS/congestion levels (if the data is available) by time-of-day period with 0.80 level of correlation. • Transit validation: – Replication of the daily synthetic trip matrix from the on-board survey (if available) with 0.80 level of correla- tion at the level of aggregate districts for each time-of- day period. – Replication of daily transit line ridership for the most loaded rapid transit lines (commuter rail, LRT), bus lines (grouped by corridors), and major station boarding counts with 0.80 level of correlation. Focusing on transit validation in key corridors where a mode choice shift might be expected due to the pricing projects is suggested. • Modal split validation: – Replication of the observed modal split from the House- hold Travel Survey by purpose, time of day, and aggregate district-to-district OD pairs with 0.80 level of correlation. • Spatial distribution (destination choice) validation: – Replication of the observed daily journey-to-work patterns from the Population Census by mode and aggregate district-to-district OD pairs with 0.90 level of correlation. – Matching average trip distance and trip length frequency distributions extracted from the Household Travel Survey (after expansion) and Census data (CTPP tables) by travel purpose with a good level of statistical confidence. Traffic counts should be prepared for major corridors and screenlines that are relevant for the project under study. The usual practice is to augment the basic set of traffic counts used for the regional model validation with additional counts collected along the project corridor and for feeder and com- peting roads. Currently, most regional agencies set the bar for model validation in terms of the percent root mean square error for highway volumes differently. While the existing regional culture represents a good starting point, it makes sense to discuss and agree upon exact validation criteria at the outset of the project, to ensure that the team understands what will be acceptable for all key stakeholders. For model validation and calibration, it is essential to estab- lish a compact districting system, which will be used for data summaries of mode choice calibration and destination choice calibration. The districting system should ideally have not more than 15–20 districts that would geographically allow for a full capturing of the major traffic flows, corridors, and screenlines. District boundaries used for general regional modeling can be specifically adjusted to the pricing study or project. Remote and irrelevant areas can be combined into large districts while in the vicinity of the study area the district system should be finer. A good replication of the observed journey-to-work flows remains the cornerstone of travel model validation, and is especially important for congestion pricing studies since commuting represents the largest travel segment in peak periods. In 4-step models, this relates to the home-based-work component. In ABMs, this relates to the usual workplace choice model. Before any validation or calibration effort is undertaken with respect to journey-to-work flows, a compar- ison of home-interview and census journey-to-work data sets at a district level is necessary in order to determine whether significant differences exist between datasets. Any differences between datasets should be identified and resolved before beginning the calibration of the model. In particular, prior to a mode choice model calibration, the expanded survey data should be extensively compared with census journey- to-work data in order to understand potential differences in data and develop a reasonable set of district-level model calibration targets. The main sources for model validation relate the observed statistics for the base year. Consequently, the main calibration effort is associated with making the model replicate these statistics by way of adjustment of the parameters. This, how- ever, is not the only important aspect of validation. Another potentially useful way to check the model system’s perfor- mance includes forecasting: either by show ing that the model performs reasonably when future-year scenarios are modeled or by back-casting to an earlier year and comparing results to independent data. These options should be explored and other useful reasonable ness checks should be undertaken and documented. This step should be closely intertwined with the model application. It is not unusual in practice that a model that was well calibrated for the base year without pricing would require some adjustments when the pricing projects are introduced. The main reason for this can be the discovery of an unreasonable sensitivity to pricing that could not be detected if the base year network is characterized by a no or only a limited number of existing priced facilities. 4.4.2 Region-Level Calibration Procedures In general, it is a non-trivial task to identify the sources of discrepancies that manifest in the final model validation against traffic counts and then decide upon the best course

56 of action. The reason for discrepancies can be related to any of the model components applied prior to the assignment stage: population and employment data; car ownership; tour and trip generation; spatial distribution of tours and trips; time-of-day choice; mode choice; as well as in the assignment parameters themselves. It is generally not possible to diag- nose the assignment results and conclude what specific fixes needed based solely on the detected discrepancy between the traffic counts and assigned volumes. The only consistent way to screen out the reasons for discrepancy, and to identify the model components that should be adjusted accordingly is to carefully validate and calibrate (if needed) all sub-models in the sequence in which they are applied in the model system. The sequential validation and calibration of all sub-models may be time-taking compared to such fast fixes as a trip table adjustment to traffic counts. This is the most preferable way, however, to promote consistency and accuracy throughout the entire model system. The following sequence of the major validation and cali- bration steps can be outlined, where each subsequent step can be undertaken only after the previous step has been completed: • The travel generation models (trip and/or tour produc- tion and attraction components) should be validated and calibrated (if needed) to closely match the established aggre- gate targets. The targets should be segmented by household/ person type and travel purpose as well as by geography. Several sources of information on travel generation will be combined and consolidated in order to develop reli- able base-year targets. They include relevant CTPP tables, Household Travel Survey (after expansion), data on actual employment, etc. Trip and tour rates should match those observed in the GPS, traffic generator studies, and other available inventories. Generated trips in combination with the average trip length should match the regional VMT statistics. • The trip distribution (destination choice) models have to be validated and calibrated against the statistics observed in the Household Travel Survey and/or the CTPP journey- to-work tables. Calibration criteria include matching aver- age trip distance, trip length frequency distributions, and district-level flows. • The time-of-day choice (peak-spreading) model should be validated and calibrated across several dimensions and against different sources of information. One routine vali- dation includes structural comparison of aggregate distribu- tions of departure times, arrival times, and tour durations (that latter is relevant for ABMs only) to the observed dis- tributions tabulated from the Household Travel Survey for each travel purpose. Another set of tests involves validation of the resulted trip departure/arrival time distributions for highway modes (after application of destination choice, time-of-day choice, and mode choice models for all types of tours) to the time-of-day distributions observed in traffic counts on major screen-lines and along major corridors. • The mode choice model should be validated and cali- brated against aggregate mode shares developed from the expanded Household Travel Survey, and Transit On-Board Survey data, as well as against other available independent sources of information. In particular, the CTPP tables provide good aggregate estimates of mode shores for work tours, while the Transit On-Board Survey provides the most reliable estimates for the total number and spatial distribution of transit trips. Validation and calibration of all main models should be implemented at county, district, and (if necessary) TAZ levels. In general, it is always preferable to operate with large-unit parameters in model calibration, rather than to introduce parameters specific to a smaller geographic unit that might result in a model over-specification. Despite the fact that the model components are validated and calibrated one by one, it is essential to have the entire model application system in place at this stage, where final (feedback) iteration LOS matrices are used and final trip tables by mode and time-of-day period are tested to ensure that they are consistent with survey data, and also checked against screenline traffic flows in order to determine whether further adjustments are necessary at a geographic level to better match traffic counts. In general, the equilibration procedure itself may introduce significant changes in one of the travel dimen- sions (specifically mode choice) compared to any validation or calibration with static LOS variables. In practical terms, after all model components have been validated and reasonably calibrated, there still can be a residual level of discrepancy with respect to particular traffic counts that is difficult or too time-taking to resolve, either with the counts or with the model. This might require trip table adjustment to traffic counts. The methodological difference between model calibration and trip table adjustment to traffic counts should be well understood. Trip table adjustment to traffic counts can improve the match further but is problem- atic for carrying over into future as discussed below. In general, the adjustment of a trip table to traffic counts is a technically effective procedure with a set of methods available (in some cases, built-in in the transportation soft- ware packages), but it should be taken with a necessary level of cautiousness. First of all, adjustment of a trip table to traffic counts is a fairly mechanical procedure that tends to create unrealistic OD patterns (or unrealistic production and/or attraction marginals) and can significantly change the observed trip-length distribution. While this procedure can be somewhat embedded in the aggregate trip distribution

57 structure of a 4-step model in a form of so-called K-factors, it is more problematic to integrate trip table adjustments with an advanced ABM structure. Two additional aspects of model validation and calibra- tion should be taken into account before adjustment to traffic counts is employed: • The validation criteria can always be matched by mechan- ical adjustment of the trip tables to traffic counts or by over-specification of the model with multiple constants including K-factors for destination choice or trip distribu- tion and area-specific mode choice constants. We recom- mend that these methods of calibration are applied with caution and adjustment of certain model parameters, only if it makes behavioral sense. This calibration process takes longer than mechanical adjustment and over-specification and may result in a lower level of match, but it is prefer- able, since the predictive power of the model will be fully preserved. • The calibration targets themselves are not perfect and nor- mally have numerous internal inconsistencies. All types of surveys have certain built-in biases, including under- reporting of travel. Different data sources are synthetic and relate to different years. By bringing them together to the same reference year, it is impossible to fully ensure inter- nal consistency. For this reason, some discrepancies are inevitable and the model cannot match all targets exactly. The process of model validation and calibration normally includes numerous iterations with improvement of the data itself (for example, re-weighting of the Household Survey by the commuting pattern observed in the Popula- tion Census). It is important to recognize several objective factors that require post-model adjustment of the highway trip tables produced by the core demand model in order to better rep- licate traffic counts. These factors can be aggregated into two meaningful groups that are important in view of the need for application of the procedure for future year forecasts: • Built-in biases in a household survey, like under-reporting of short trips and intermediate stops, and the adjustment factors (ratio of the adjusted trip table to original trip table at the district-to-district level) calculated for the base year for this group should be applied for the future years in a multiplicative way, accounting for residential population growth and assuming that the structural share of the under- reported trips stays the same over years. • Missing non-residential-population components like commercial vehicles’ traffic and tourists’ travel that are not strictly linked to the population growth; the adjustment factors calculated for the base year for this group should be applied for the future years in an additive incremental way, i.e., the same absolute addition calculated for the base year (difference between the adjusted trip table and original trip table at the district-to-district level) is applied for all target years, assuming that the underlying activities do not grow (or decline) significantly. Both procedures (multiplicative and incremental) have been applied in practice frameworks. They both produce rea- sonable results that are not dramatically different for regions with overall stability or moderate growth of land-use char- acteristics in future years. It should be noted that in most cases where a moderate population and employment growth is expected, the additive incremental procedure tends to pro- duce a slightly more conservative forecast, while the multipli- cative procedure usually tends to slightly overestimate traffic. In view of the need to use the model in a real planning envi- ronment for pricing analysis, conservatism of the forecasts is normally preferred. 4.4.3 Corridor-Level and Sub-Area-Level Calibration Procedures Local calibration and adjustments represent a frequent step of regional model application for a particular study. Even if the regional model is well-calibrated and satisfies all the criteria, it may need an additional local calibration for application in a specific corridor or sub-area where more disaggregate level of analysis is undertaken, more detailed data for calibration are available, or smaller-scale differences in pricing project alternatives are under scrutiny. For example, while the basic version of the regional model should generally be applied to identify the main pricing proj- ects and alternatives in terms of the layout, number of lanes, and base toll rates, the subsequent analysis might focus on details of the access ramps or toll discounts by vehicle types (SOV, HOV, taxi, commercial vehicle, truck, bus, etc.). For the modeling of access ramps, the level of calibration of the regional model may not be sufficient to address the details needed for this analysis. In particular a reasonable level of replication of traffic counts on links for broad time-of-day periods like AM, Midday, and PM may not be enough. An additional singling out of peak hours within AM and PM peri- ods, as well as replication of counts on turns, is highly desirable. For the analysis of impacts of different discounts by vehicle types, an additional calibration effort may be needed to ensure a reasonable level of replication of traffic counts by vehicle type rather than just total traffic flow. In particular, the core set of trip tables by vehicle class can be adjusted to the subset of local counts in the sub-area under the study. Taking into account a limited subset of counts and additional network details in the sub-area application, the

58 adjustment can be made to the extent that each traffic count is replicated almost exactly. Then, depending on the pro- portion of the commercial versus residential-based traffic, area-specific decision can be made, using either additive or multiplicative strategy for future years as discussed above. 4.4.4 Sensitivity Tests, Risk Analysis, and Mitigation Survey of Reported T&R Forecast Errors The evaluation of model quality and capabilities is directly related to the degree of accuracy and the identification of likely sources of error. This section discusses the methods developed and applied by rating agencies to eliminate built-in optimistic biases and produce more realistic and conservative forecasts. Uncertainty in demand for tolled roadways compared to free highways is compounded by the introduction of more unknown variables (like willingness to pay). Yet such new understanding can be critical, since private investment gen- erally depends on cost recovery through toll collection. In order to begin to address this clear gap in the literature, Stan- dard & Poor’s (Bain and Wilkins 2002, Bain and Plantagie 2003 and 2004, Bain and Polakovic 2005) and Fitch Ratings (George, et al. 2003 and George, et al. 2007) produced a series of studies that examine the risk and uncertainty of tolled highway projects. Standard & Poor’s (S&P’s) study of traffic forecasts began in 2002 with data from 32 toll road projects around the world. The sample was then increased to 68 and 87 projects in 2003 and 2004, respectively. However, in both updates the conclu- sions remained largely the same. In the first study, Bain and Wilkins (2002) found that traffic forecasts for new toll roads suffered from substantial optimism bias, a finding that was supported in the subsequent studies. The average ratio of actual-to-forecast traffic volumes in the first year of operation was about 0.73 (versus 0.74, 0.76, and 0.77 in the 2003, 2004, and 2005 studies). Figure 12 shows the distribution of forecasting errors in the 2005 update. (Comparisons to non-tolled projects are drawn later in this section.) Of course, due to the nature of averaging ratios such as these, traffic forecasts for toll roads may be over-predicting actual volumes by even more than 33% (implied by an actual- to-forecast ratio of 0.75). A volume-weighted average of ratios (essentially the sum of predicted values over the sum of actual values) yields a much more robust indicator of the average percentage error, reflecting whether an investor will win (average >1) or lose (<1) - on average, across projects. Essentially, the issue is that the ratios are non-negative and bounded by zero, leaving a right-side skew that tends to bias averages to the high side. For instance, if predicted-to-actual ratios for two projects are 0.5 and 2.0, the average is 1.25, suggesting predictions are biased high. If the ratios are first inverted and then averaged, the result is again 1.25, but the interpretation is that predictions are biased low. Thus, one must use caution when dealing with averages of ratios. Moreover, the 2002 study found that 78% of actual-to- forecast traffic volume ratios were less than 0.9 while only 12% were over 1.05. In the 2003 study, 63% of such ratios were less than 0.85 and 12% were over 1.05. Essentially three quarters of first-year traffic forecasts for tolled facilities are overestimated by 10% or more, suggesting that planners, bankers, and com- munities should be wary, and modelers need to improve their methods. One of the main diagnostics to come out of the 2002 study was S&P’s Traffic Risk Index (TRI). While the exact details for its estimation are proprietary in nature (and thus not provided), the index attempts to predict the amount of project risk based 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Actual/Forecast Traffic Figure 12. Distribution of actual-to-forecast traffic volumes (Bain and Polakovic 2005).

59 on many project attributes, as discussed later in this section. Based on the TRI, Bain and Wilkins (2002) determined a risk level (low, average, or high) for each project, and divided its discussion by forecast source: those commissioned by banks versus those commissioned by others. Figures 13 and 14 show the TRI profiles over time. The findings suggest that actual-to-forecast traffic volume ratios in the first year of operation average about 0.9 for low- risk bank-commissioned projects, and 0.8 for low-risk proj- ects commissioned by others. Both types of low-risk projects had average ramp-up durations of about 2 years (after which actual volumes closely match forecasts). For average-risk projects, year one volume ratios were found to be 0.8 and 0.65 for bank- and non-bank-commissioned projects, respectively. Ramp-up duration was about 5 years in both cases. However, those commissioned by banks ramped-up to about 95% of forecast volumes over those first five years, while others ramped-up to only 90%. For high-risk projects, the volume Figure 13. Estimated errors in tolled highway projects commissioned by banks (Bain and Wilkins 2002). Figure 14. Estimated errors in tolled highway projects commissioned by others (Bain and Wilkins 2002).

60 ratios were just 0.7 and 0.45, respectively, and ramp-up dura- tions were about 8 years. After ramp-up, bank-commissioned projects reached about 90% of forecast volumes while other projects reached approximately 80% of forecast. What this sug- gests is that projects with greater uncertainty (and thus risk) underestimate initial traffic volumes by a greater amount, on average, experience a longer ramp-up duration (to reach stable volumes), and stabilize at lower final traffic volumes (versus predictions). Moreover, the magnitude of risk is greater for projects not commissioned by banks, which is not so sur- prising given that banks are much more directly accountable for investors’ monies than are public agencies. Moreover, other project commissioners (public agencies, interest groups, and bidders) may have interests that are best served when predicted traffic volumes are high (Bain and Wilkins 2002). With the 2003 study’s increased sample size, Bain and Plantagie (2003) were able to conduct several less aggregate analyses. Multiple factors were investigated, but only one with significance was found, in distinguishing countries with and without a tolling history. The findings suggest that actual- to-forecast volume ratios in the first year of operations aver- aged 0.81 in countries with a history of tolling, but just 0.58 in other countries. Thus, forecast risks appear much higher in countries without a history of tolling. This is intuitive, given that user adoption will be much faster (thanks to existing toll tag and manual payment experiences) and that contractor and operator familiarity will be higher. In several U.S. regions (e.g., Florida, Southern California, New York, and Houston), flat-rate tolling is already well-established; so, in these regions it may be reasonable to expect first-year ratios in the neighbor- hood of 0.8. However, most other U.S. regions may dramatically under-perform if more appropriate modeling assumptions are not used (particularly for the ramp-up period). In the 2004 update, Bain and Plantagie (2004) traffic fore- casts along new tolled highways were compared to those of new non-tolled facilities. The sample size was increased to 87 highway projects, with all data for non-tolled facilities coming from Flyvbjerg, et al.’s (2005 and 2006) work. The comparisons suggest that new non-tolled roadways exhibit little optimism bias, though the same amount of uncertainty or spread in the distribution (of volume ratios) remains. Figure 15 shows how the two distributions appear similar, but with an added –20% optimism-bias shift in the distribu- tion of tolled road (forecast-to-actual) volume ratios. This suggests that, after controlling for the added optimism bias of tolled projects, there may be little difference in the accuracy of traffic forecasts for tolled and non-tolled projects. In Standard & Poor’s 2005 update (Bain and Polakovic 2005), the uncertainty in project ramp-up years was inves- tigated in greater depth. The expectation is that uncertainty falls slightly from opening year forecasts, since traffic demand would have an opportunity to stabilize, as drivers learn of route alternatives and obtain toll accounts, for example. The sample size was just 25 projects for years 1 through 5, and the hypothesis was not supported (Bain and Polakovic 2005). The mean ratio (of actual-to-forecast traffic volumes) was 0.77 in year 1, and 0.79 (negligibly higher) in Year 5. These results suggest that traffic performance generally remains much less than forecast, even into Year 5 of operation. While Vassallo and Baeza’s (2007) much smaller sample (of Spanish toll roads) identified similar optimism biases, forecast ratios generally improved following year one. So there is room for differences in average results, due to regional economic conditions, marketing campaigns or other factors. Sources of Risk and Uncertainty While significant uncertainty in traffic forecasts clearly exists, the causes of such uncertainty vary, including the sources of forecast error. Numerous studies have identified and examined several sources of forecast error (Flyvbjerg, et al. 2005 and 2006, Bain and Wilkins 2002, George, et al. 2003, George, Figure 15. Distribution of actual-to-forecast traffic volumes for tolled and non-tolled projects (Bain and Plantagie 2004).

61 et al. 2007), and for the most part, these are similar for tolled and non-tolled highways, but differences do exist. Flyvbjerg, et al. (2005 and 2006), interviewed project man- agers who identified a variety of sources, including several travel demand modeling components. Figure 16 provides the percentage of projects, found by Flyvbjerg, et al. (2005 and 2006), with stated sources of traffic forecasting error, for both passenger rail and road projects. The two top-stated sources of error for toll-free road projects are estimates of trip generation-related factors and land development, though trip distribution-factors and the forecasting model (mode choice and route choice) are close runners-up. Zhao and Kockelman (2002) tracked the propagation of uncertainty through a four-step travel demand model. They controlled the uncertainty of model inputs and parameters, and performed 100 simulations of the model. Overall, Zhao and Kockelman’s (2002) work suggests that link-flow estimates enjoy the same level of uncertainty as inputs and parameters, and simple regressions of outputs on inputs (and aggregations of inputs) offer very high predictive power, suggesting that prime sources of forecast uncertainties can be rather quickly deduced (and exploited) for better prediction. Network attributes can also play a key role in forecast reliability. Analysts do not know the actual future network, and coded networks are significant simplifications of actual networks (generally ignoring local streets, signal timing plans, turning lane presence and lengths, etc.). Forecasts that depend on future network changes (such as nearby highway extensions) tend to be less reliable (Bain and Wilkins 2002). Traffic con- gestion is also a key. As noted by Bain and Wilkins (2002) and Zhao and Kockelman (2002), uncongested networks often are more difficult to anticipate flows on, since congestion feedbacks distribute traffic more evenly over space and time while establishing something like an upper bound (due to inherent capacity limitations) on all links. Thus, low-volume corridors tend to have greater uncertainty in their forecasts (Bain and Wilkins 2002). Another key source of error in traffic forecasts comes from uncertainty in land development patterns (Rodier 2003, Flyvbjerg, et al. 2005 and 2006, Land Transport New Zealand 2006). Rodier’s (2003) application of the Sacramento, Cali- fornia, travel demand model for year 2000 conditions found that about half of the 11% overestimation of VMT was due to demographic and employment projections, which serve as inputs to the demand models. The other half was due to the model itself. George, et al. (2007) suggest that user fees make a tolled road more susceptible to changes in demand caused by economic downturns/recessions, toll rate increases, and escalating fuel costs. Other special or relatively rare events (e.g., natural disasters or acts of terrorism among other events) are often key sources of uncertainty as well (George, et al. 2007). Of course, such events are difficult to predict, though HLB Decision Eco- nomics (2004) suggests that the number and duration of reces- sions in the forecast period should be considered in investment grade studies. Another important consideration in understanding project risk is the “tolling culture” of a region (Bain and Wilkins 2002). This is essentially the degree to which tolls have been used in the past. In nations and regions where tolling has not pre- Figure 16. Project manager-stated sources of forecast error for non-tolled facilities (Flyvbjerg, et al. 2005).

62 viously been used, there is greater uncertainty surrounding traffic forecasts. If travelers are accustomed to paying tolls for other road facilities, forecasts tend to be much more reliable. As noted earlier, this appears to result in 20% greater average optimism bias (Bain and Plantagie 2003). Of course, travel demand model imperfections are a key source of error in traffic forecasts. For instance, the robustness and heterogeneity (across travelers and trip types) of value of travel time estimates are generally ignored, but may be crucial in producing accurate forecasts. The use of imported param- eters (calibrated for other regions or even other countries) can also cause much error (Bain and Wilkins 2002). Facilities enjoying a competitive advantage of some sort also tend to offer more reliable forecasts (Bain and Wilkins 2002; George, et al. 2007). For instance, forecasts for projects in dense, urban networks (with many alternative routes) gener- ally will be less certain than those for projects with a clear competitive advantage over alternatives (e.g., a corridor with the only river crossing in a region). Moreover, many privately financed projects rely on protection against competition in the future. If protection is provided (via non-compete clauses, for example), long-run traffic forecasts tend to be more reliable (Bain and Wilkins 2002). Meaningful distinctions can also arise in the context of user attributes. Bain and Wilkins (2002) assert that toll facilities serving mostly a small market segment of travelers allow for more reliable traffic forecasts. This is because smaller markets are easier to model than more heterogeneous populations (Bain and Wilkins 2002). For example, beltways (orbital style facilities) are likely to carry more forecasting risk than radial facilities (which typically carry a high share of commuters into and out of the city center, for work purposes). Overall, Bain and Wilkins (2002) indicate seven top drivers of forecast failure: • Poorly estimated VOTs, • Economic downturns, • Mis-prediction of future land use conditions, • Lower-than-predicted time savings, • Added competition (e.g., improvements to competing roads or the addition of new roads), • Lower than anticipated truck usage, and • High variability in traffic volumes (by time-of-day or day of the year). Bain and Plantagie (2003) added several other top drivers: • Complexity of the tolling regime, • Underestimation of the duration and severity of the ramp-up period, • Reliance on a single VOT (as opposed to segmenting user groups). Another rating agency, Fitch Ratings (George, et al. 2003), also suggested several of these same drivers, but added that the use of a regional travel demand model developed for other planning purposes also can cause great error in traffic forecasts. Relevant Risk Factors and Mitigation Measures for Pricing Projects To review the national and international experience, accom- modating risk and uncertainty in demand and revenue fore- casts is an important component of any toll road study. While a single best statistical forecast is useful, it lacks the information needed for making long-term financial decisions. With the great number of assumptions, inputs, and estimated param- eters entering travel demand models, model outputs can be highly uncertain and inaccurate. Neglecting this uncertainty (or equivalently, assuming determinism) can invite scrutiny from stakeholders, since not all will agree with assumed inputs and parameter values (Duthie 2008). Most analysts, policy makers, and investors agree that it is imperative that modelers quantify forecasting risk in a mean- ingful way (Rodier 2007), and while the financial community has understood the need to address risk in toll road studies, Kriger, et al. (2006) believe that very few practitioners conduct any sort of risk assessment. Some simply verify results by use of reality checks (e.g., comparing to older forecasts and using simple intuition to verify whether results seem reasonable), while others use no verification methods at all. One key component of risk assessment in model outputs lies in explicitly stating all major modeling assumptions (Kriger, et al. 2006), making the model specification as transparent as possible. If modelers and users understand the implications of alternative assumptions, the uncertainty in the forecasting process will be better understood. A relatively common and reasonably effective method for accommodating risk in T&R forecasts is the use of sensitivity analyses or “stress tests” (Kriger, et al. 2006). Most sensitivity analyses rely on the exploration of a very limited set of differ- ent values for key variables, such as a region’s or neighbor- hood’s population growth rate, values of travel time, and planned tolls (Kriger, et al. 2006). Though such analyses can provide key insights, many practitioners and financial analysts feel that they inadequately reveal the range of pos- sible outcomes (HLB Decision Economics 2003, Kriger, et al. 2006). As their name implies, stress tests seek to understand the outcomes of relatively extreme conditions, generally to anticipate worst- and best-case investment scenarios. In this way they help analysts anticipate lower (and upper) bounds on project outcomes, but certainly not a distribution of outcomes, or probability of financial loss. Model validation studies offer another method for quanti- fying uncertainty, by examining how well model forecasts

63 match observed data not used in model calibration (Rodier 2007). Such studies measure forecast uncertainty directly from the observed data and thus require data from two points in time: the older data set is used for model estimation and calibration while the newer one is used for validation. It can be impossible to conduct such tests of models developed from recent data, but at least one obtains a sense of the magni- tudes of errors that can emerge from transferring behavioral parameters calibrated on old data to current-year contexts. Of course, sensitivity testing and model validation studies have their limitations. For example, sensitivity tests are quite constrained, to typically three or four scenarios. In contrast, Monte Carlo simulation techniques more fully explore the range of possible outcomes by defining and drawing from probability distributions for key inputs. Of course, such tech- niques also exhibit limitations: They require assumptions of input distributions (and their covariances), when these are often unknown, and generally more sophisticated program- ming techniques (to ensure rapid run times for testing a high number of scenarios). Monte Carlo techniques are at the heart of the four-step Risk Analysis Process (RAP) used by HLB Decision Economics (2003). In Step 1, HLB defines a structure and logic model, in order to forecast traffic and revenue on the basis of an array of inputs and parameters. In Step 2, central estimates and probability ranges are assigned to each relevant input and parameter. In Step 3, expert opinions regarding the results of Step 2 are obtained, and probability ranges and central esti- mates are revised. In the final step, Monte Carlo simulation techniques are employed, drawing inputs and parameters from their respective probability distributions, and traffic and revenue probability ranges are derived based on the simulation outcomes. This approach allows firms like HLB to determine the likelihood that revenue cannot cover the debt service, an important criteria for issuance of debt. As discussed earlier, Zhao and Kockelman (2002) performed a similar analysis (for a non-tolled case), using a four-step travel demand model for a sub-network of the extensive Dallas-Fort Worth region with 118 variable input and parameter values. They assigned density functions to the 18 random model parameters (13 in trip generation, one in trip distribution, two in mode choice, and two in assignment) and four major model inputs for each of 25 zones (household counts along with basic, retail, and service job counts). This analysis indi- cated that inputs and trip generation parameter values were the most important factors in forecasts of total VMT. Consistent with such analyses, the National Federation of Municipal Analysts (NFMA 2005) formally recommends that a range of possible road project and policy outcomes should be explored based on different scenarios (or assumptions) and varying variables or parameters one at a time is insufficient. By assigning realistic probability distributions to parameter values and inputs, the probability of a given scenario can be understood. The NFMA (2005) guidelines for traffic and revenue studies include several highlights: a no-build traffic forecast should be produced; a baseline traffic and revenue forecast should be produced; sensitivity analyses should be performed on inputs (including population, employment, and income growth, toll elasticity by consumers, and accel- eration of the planned transportation network); and debt ser- vice analysis should be performed. Another approach is reference class forecasting, as described by Flyvbjerg, et al. (2005). This method essentially relies on past experiences with a sample of similar projects in order to estimate outcome distributions and thus the probability of various events occurring. By comparing the forecasts with past experience, judgments can be made regarding the validity of results. Of course, this is difficult to do without good data on a variety of reasonably comparable projects. But it is a useful strategy when such data exist. To determine an investment’s credit rating, credit agencies and financial analysts use varied approaches to account for revenue forecast risk. For example, Fitch Ratings (George, et al., 2003, George, et al. 2007) claims to study the key assump- tions and inputs of the travel demand model used in creating future forecasts, and then considers a range of possible out- comes associated with each factor in order to develop a stress scenario alongside a base scenario (essentially sensitivity test- ing, but with relatively extreme scenarios). The base case is generally more conservative than the base case developed by the project sponsor, eliminating any evident forecast optimism. The stress case is developed to determine the project’s ability to withstand rather severe (but not unreasonable) circumstances in which the ability to pay debt service is stressed. Based on the results of the stress scenario, an investment rating is assigned to the project. For credit analysis of longer-term traffic forecasts, Bain, et al. (2006) suggest taking a conservative approach, reducing growth rate expectations and carefully examining future toll schedule increases. They also suggest that long-term growth rates exceeding 1% and toll increases beyond those suggested by reasonable correction for inflation should be viewed with caution. While these techniques simplify uncertainty testing dramatically and help investors understand the real possibility of loss, they do not illuminate the variety (and likelihood) of futures that truly exist, and associated investment risk cannot be fully understood using such methods. Comparing the most frequently used analytical techniques, sensitivity testing and Monte Carlo simulation, the following difference should be understood. Sensitivity testing allows for greater understanding of the magnitudes of uncertainty in the model. By allowing key model inputs and parameters to vary simultaneously, creating multiple possible scenarios, uncertainty in traffic and revenue forecasts can be better

64 bounded. Indeed, this appears to be the most common method for dealing with uncertainty by credit agencies. However, sensitivity testing generally does not provide a probability of particular outcomes occurring. Therefore, it can be difficult for policy makers to truly understand inherent risks. Monte Carlo simulation may be most appropriate to identify a more probable set of possible futures. By drawing parameters and inputs from reasonable sets of distributions, the probability of particular outcomes can be understood. It should be, of course, taking into account that Monte Carlo simulation requires multiple model runs to build a distribu- tion of the outcomes that is difficult to implement in practice since each run of a full regional travel model normally takes several hours (or even days). A possible way to overcome this technical limitation is to build an auxiliary regression of the model outcomes of interest (for example, total traffic or revenue) to a set of predetermined input parameters (for example, population growth, basic toll rate, capacity of the alternative road, etc.) based on several full-model runs that would serve as pivot points in the Monte Carlo simulation. Then multiple points are added using the simple regression model to interpolate between the pivot points. This interpola- tion is of course very crude and is intended for only estimation of the probability distribution around the true model runs. Secondly, risk mitigation methods are recommended for each specific project type and model. The following general approach is recommended. At first stage, major risk fac- tors are identified for each project depending on the project scale, network topology, affected population, etc. The follow- ing approximate check-list of factors should be considered, although this list should be built for each project specifically: • Population growth in the relevant project corridor. This growth should be compared to the observed tendencies in the past and the entire region and the corridor. If the pro- jected growth is significantly higher than the observed past trends, it should be considered as a high risk factor. Creating optimistic and pessimistic scenarios with estimated prob- ability to occur is recommended. • Employment growth in the relevant project corridor. Sim- ilar to the population growth, the realistic comparisons to the observed trends should be made. Each case of growth rates higher than the observed trends should be carefully substantiated; otherwise high risk is assigned to this factor. Creating optimistic and pessimistic scenarios with esti- mated probability to occur is recommended. • Competing highway and transit projects in the corridor. This factor is relevant for the pricing projects that are located in the corridors where another significant and competing project may take place (including a significant improvement of the existing free road or transit service). If this is a realistic option, the competing projects should be described, coded, and included in the pessimistic network scenarios. • Complementary (feeding) highway projects in the corri- dor and beyond. This factor is relevant for pricing projects that are located in such a way that a substantial share of travelers might use this facility in combination with some other future projects. It specifically affects such projects and policies as HOV/HOT lanes where network connectivity is essential. If this is a real factor, the complementary projects should be described, coded, and included in the optimistic network scenarios. • VOT estimates and related travel time and cost coefficients used in the traffic assignment, mode choice, time-of-day choice and other models. This is a fundamental behavioral parameter in the travel model that always represents a source of uncertainty, simply because of the randomness known to be inherent to travel behavior. It should be determined that the average VOT values applied for each segment are reasonable. A high risk is assigned to this factor if the VOT value was not estimated, but instead was assumed or borrowed. No matter how well structured and segmented the model system, a ±20% variation in VOT can generally be considered within the 99% confidence interval. For sim- ple models with poor segmentation, the range should be extended to at least ±40%. Variation of VOT also incor- porates uncertainty associated with real income growth, possible economic recession, and other related factors (if they are not considered explicitly). • Toll escalation scenarios that may be affected by economic conditions or government intervention. Constraints on the ability to escalate tolls over years represent a risk factor, even if the toll escalation strategy is well defined in the contract between the toll road operator and government. Normally, it is assumed that the toll rates will automati- cally grow every year with the GDP, CPI or other index (with some floor and ceiling thresholds). In reality, tolls may be frozen for several years and reconsidered only inter- mittently. A sensitivity test with tolls updated only every 10 years is recommended. • Ramp-up period, especially for Greenfield projects and policies represents a risk factor that can significantly affect the revenue stream for the first years of the project that are the least discounted. It is recommended, depending on the project type, to establish a realistic ramp-up period, and then run a sensitivity test with a longer ramp-up period by at least two years. The risk factors should first be identified and measured one at a time. For each factor, it is recommended that at least three possible scenarios are formulated (optimistic, average, and pessimistic) and probabilities are assigned to each of them. The optimistic and pessimistic scenarios do not have to be the best and worst possible scenarios. As a matter of fact, the absolutely worst and absolutely best scenarios are not extremely informative for the risk analysis since they are

65 normally characterized by a very low probability. Instead, the optimistic and pessimistic scenarios should capture an average of the forecast region that yields approximately a half of the cumulative probability, i.e., 25th percentile and 75th percentile. With respect to the model parameters, the average scenario should correspond to the model calibrated for the base year with a good level of fidelity. Depending on the number of risk factors and the model run time, two strategies can be applied: • Run the model for each possible combination of the input factors and relate the results (T&R forecast) to the joint probability of the scenario occurring. The joint probability can be calculated as the product of assigned probabilities for each factor, assuming the factors are independent; other- wise a more complicated conditional calculation is needed. This is a theoretically preferable method, but it may result in an infeasible number of scenarios to test. For example, with five factors and three possible states for each of them, the total number of scenarios to test will be 35 = 243. • Run the model for several pivot combinations of the input factors and use auxiliary regression to interpolate the results for the other (non-modeled) combinations as described above. It is important for each particular factor state to appear at least once in the pivot combinations. For exam- ple, with the same example of 5 factors (denoted as A, B, C, D, and E) and 3 possible states for each of them (denoted as 1 = optimistic, 2 = average, 3 = pessimistic), the total number of states to explore will be 5 × 3 = 15. All these states can be covered in three model runs with the following combina- torial logic. The first run would combine A1, B2, C3, D1, E2; the second run would combine A2, B3, C1, D2, E3; the third run would combine A3, B1, C2, D3, E1. These three runs would normally provide enough information about possible interactions between the risk factors versus the base sce- nario of A2, B2, C2, D2, E2. In order to provide more vari- ation for the auxiliary regression the base run and three runs described above could be complemented by two extreme runs: optimistic (A1, B1, C1, D1, E1) and pessimistic (A3, B3, C3, D3, E3). These six combinations are normally enough to approximate all possible 243 combinations. 4.5 Adjustment of Travel Cost Inputs and Coefficients for Future Years 4.5.1 Model Input and Coefficient Consistency for Different Years Long-term T&R forecasts for toll roads have brought to the fore from the general issue of the proper treatment of input cost variables (tolls, parking cost, vehicle operating cost, transit fare), and their associated model coefficients (used in the mode/route choice utilities) as related to the dif- ferent years for which models are applied. There are three dif- ferent general time points relevant to a travel demand model and its applications: • Year of the survey implementation (estimation), • Year of the last model calibration (base year), and • Year of model application (future year that might be any year after the project opening). A full consistency between cost related input data and corresponding coefficients across these years is required. Unfortunately, the current modeling practices tend to obscure this point and/or limit it to an accounting for the monetary inflation only, which is done by escalation/discounting of the cost variables along the time line, while the model coefficients are not changed from when the estimation was done. Very rarely considered is a systematic adjustment of the model param- eters, like time and cost coefficients, as well as the resulting VOT (beyond the inflation factor). For example, model coef- ficients estimated in 1995 are used for base year 2005 and recalibration process frequently includes only adjustment of (mode choice) constants. Additional confusion is associated with using income-related variables or variables, where cost is scaled by income, along with linearly included time and cost. This section outlines a systematic approach to the adjust- ment of cost variables and associated model coefficients (if necessary). 4.5.2 Reasons for Adjustment There are three major reasons that make an adjustment of cost variables and coefficients essential for future years: • Inflation that makes dollars from different years incompa- rable. This factor alone is comparatively easy to incorpo- rate through a proper scaling (escalation/discounting) of all cost inputs of the model including tolls. A commonly used inflation index is CPI and reasonable assumptions can normally be made for future years (2.5-4.0%). By using the inflation index, all input cost variables can be expressed in the base year dollars, which is the preferred practice when the model is run for several future years. Alternatively, if revenue forecasts are requested in expenditure years (to explicitly consider different toll rate escalation agreements), the preferred approach can be adjusted through appropriate (inverse) scaling of the cost coefficients in the model utility expressions. • Real growth in income (above inflation) that affects the model coefficients that should reflect changes in travel behavior with respect to change in wealth. This effect is supposed to be equal to the observed cross-sectional dif- ferences in travel behavior across travelers from different

66 income groups and could have been fully captured if income had been fully included in the utility expressions for all cost variables (or better if income had been considered as an explicit budget constraint in line with the microeconomic theory). However, if the income variable is included as just an additional categorized (mode-specific) dummy along with time and cost coefficients, it means that income does not directly affect VOT (frequently the case with the exist- ing models), and an adjustment of coefficients is needed. There are several commonly used indices for real income growth, like GDP per capita (net of CPI) and again assump- tions can be made for future years (1.5-2.0%). Essentially, assumptions/scenarios for the regional (and even corridor- specific) income growth must be considered for Investment Grade Studies, long recognized in toll road industry as one of the important factors affecting future toll roads. • Trends in behavior and associated policies (beyond inflation and real income growth). This is the most complicated factor and is not normally incorporated in travel models (including the most advanced activity-based models) despite a unanimous agreement among researches and practitio- ners that trends in behavior are quite strong and should be analyzed and eventually included in travel models. How- ever, the larger and more general issue of “longitudinal” or time series analysis is not explored in this research. Instead, assumed that many observed trends (like VMT growth per capita or growing time pressures that result in higher VOT for the same income) can actually be fully or partially reduced to cross-sectional effects and captured by explana- tory variables, as demonstrated with the advanced activity- based models. Also note that policies or projected trends related to fuel and vehicle taxation can be modeled explic- itly through reasonable forecasting of the operating cost variables, as a exogenous inputs to the demand models. If both the inflation rate and real income growth are neg- ligible, the model would be perfectly transferable in time and would not require any adjustments of inputs or parameters. This is probably not true, however, for long-term forecasts associated with most T&R studies where inflation and income growth indices are compounded over 30-40 years into signifi- cant multipliers. 4.5.3 Approaches and Time Horizons for Adjustment If it is assumed that all cost inputs are properly expressed in the base year dollars, then inflation is accounted for. Assume also that there is a standard structure of the mode/route choice utility expression for a certain trip purpose that includes some constants (might be income specific), time, and cost terms. If the cost variables are not scaled by income, then accounting for real growth in income will require adjustment of the model coefficients. Arguably, the most reasonable and most conservative assumption is that the VOT (ratio of time to cost coefficient) would be growing proportionally to real income. With this assumption in mind, the following three adjustment strategies can be considered: • Reduce the absolute value of cost coefficients inversely to the real income growth index. An equivalent formu- lation proposed by Adler and Dehghani and used for the Tampa Toll Model Application to I-4 Connector Study (unpublished draft memo) is based on freezing the model coefficients, but discounting the future toll values by the total index of inflation and income growth. The additional discounting by income growth is just applied to the cost itself rather than to the cost coefficient. The behavioral assumption behind this technique is that travelers with growing income would pay money easier but the sensitivity to time savings would be essentially the same. It means that they would appreciate 10 min savings in the same way today and 30 years from now, but would be ready to pay more for it in real dollars. This is probably not the most behaviorally appealing approach. • Make the absolute value of time coefficient grow propor- tionately to the real income. Form the behavioral standpoint this assumes that travelers would appreciate 10 min savings in the future more than they do today. However, their sensi- tivity to one dollar increase in cost (in the base year dollars) would be the same regardless of the real income growth. This seems behaviorally more appealing compared to the first approach, but is still not fully convincing. • Change both time and cost coefficients in different direc- tions controlling for VOT change to be proportional to the real income growth. This looks like the most behaviorally appealing strategy and can be achieved by the following simple transformations: 1) reduce the absolute value of time coefficient inversely to the square root of real income growth, and 2) make the absolute value of cost coefficient grow proportionally to the square root of real income. We will currently consider the third approach as the base for the subsequent discussion, although the first two approaches are also practical options. Additionally, the third approach can be refined by a more elaborate (weighted) split between the time and cost coefficient changes. 4.5.4 Adjustment Strategies for Different Types of Cost Variables Even before consideration of future year forecasting, it is also important to adjust the model coefficients between the

67 estimation and base year. Ideally, these adjustments should be made first and before model recalibration for the base year, taking into account that the input cost related variables will be in the base year dollars. This means that the model coefficients should be adjusted based on the combined effect of inflation and real income growth between the estimation and base year, more specifically: • Reduce the absolute value of time coefficient inversely to the square root of real income growth. • Make the absolute value of cost coefficient grow pro- portionally to the square route of real income, but also inversely proportional to the inflation index. The subsequent adjustments for future years should be as described in the previous section assuming that all cost inputs are in the base year dollars. The adjustment strategies for different types of variables are summarized in Table 15. 4.6 Evaluation of Pricing Projects This section describes the role for cost-benefit analysis (CBA), and the requirements a comprehensive CBA places on the travel demand modeling of tolling. In order to make informed decisions, policy makers must be aware of the costs and benefits that stem from different projects and policies. Accordingly, analysts must be able to produce solid estimates of metrics relating to key evaluation criteria. This is particu- larly important and challenging for policies involving tolled roadway alternatives, since accurate revenue forecasts can be critical to investor support, and at the same time, traveler behavior is made more complex by the presence of tolls and different tolling plans. To this end, welfare economics can play a central role in identifying and quantifying policy benefits based on travel demand model outputs. CBA is the most common approach for thorough project evaluation. Its primary advantage is that all costs and benefits accruing over a project’s life are transformed into a single measure, facilitating the comparison of distinct policies. In order to perform a CBA, all project costs and benefits are generally converted into present-dollar values (Small 1999, FHWA 2003)]. Most costs are relatively easy to estimate, thanks to past project experiences (e.g., construction and operation expenditures), although significant cost overruns are common—particularly for large public transit projects (Flyvbjerg, et al. 2003). Benefits, however, are often less tan- gible, require application of travel demand models to obtain toll revenue and traffic forecasts, and involve the conversion of travel time savings, improved travel reliability, and other benefits into dollar values. Once the dollar value of all project impacts is estimated, one or more discount rates are used to transform future cash flows into present values (Small and Verhoef 2007). The choice of such discount rates is critical and can have important impli- cations for project viability, since many benefits and costs may not occur for several years after project completion. The U.S. Office of Management and Budget (OMB 2003)] speci- fies a real (as opposed to nominal) discount rate of 7% for all public investments and regulations, which approximates the marginal rate of return on private investments. However, OMB (2003) suggests that sensitivity analyses of the discount rate be performed. Selection of appropriate discount rates is discussed in more detail in a later section. While CBA seeks to place every detail in an economic perspective, the assumption that everything can be measured Variables / Inputs Recommended adjustments to variable Recommended adjustments to coefficient Linearly included cost (toll, parking, operating cost, transit fare) Express in the base year dollars (account for inflation) Change inversely to the square root of real income growth Travel time Change proportionately to the square root of real income growth VOT Change proportionately to the real income growth Cost variable relative to (zonal or individual) income Change inversely to the square root of real income growth Zonal or individual income as a separate linearly included variable Express in the base year dollars (account for inflation) Zonal or individual income relative to the average regional income as a separate linearly included variable Change inversely to the real income growth Income group dummy, income-mode- specific constants, and/or segmentation based on absolute thresholds Progress thresholds proportionally to the real income growth Income group dummy, income-mode- specific constants, and/or segmentation based on a fixed percentile Recalculate percentiles based on the progressing of the underlying thresholds Table 15. Adjustment strategies for different cost-related variables.

68 in monetary terms and that all decision-makers agree on all values may not be entirely realistic (Small 1999). CBA methods should be viewed as a way to objectively inform policy mak- ing, but ultimately cannot totally replace expert judgment (Small 1999). Another issue is equity: can policies that help many individuals by a small amount, and hurt a few a great deal, really be supported simply on the basis that the aggre- gate benefits exceed aggregate costs? Small (1999) argues that if these two objections to CBA methods could be alleviated, policy making could be reduced to a simple mathematical exercise. Despite its limitations, CBA offers a powerful tool for decision makers. The remainder of this section focuses on CBA as a means of connecting the decision-making process to predictive models for pricing applications. The next section describes methods of calculating user benefits and costs, net present values, and discount rates. The subsequent section illustrates different approaches for selecting toll rates. An example application, illustrating the key concepts and meth- ods described in this chapter, is provided in Appendix A, Section A.6. 4.6.1 Benefit and Cost Calculation Traveler Welfare In theory and in practice, traveler benefits can be described using economic terms like consumer surplus, compensating variation, and equivalent variation. While each metric is a measure of something slightly different, the idea behind each is the same: a change in price or quality affects perceived demand and benefits accruing to those already purchasing a good (de Jong, et al. 2005). For instance, if the price of travel increases on one road and the demand for that road is a (decreasing) linear function of price, then the demand curve can be drawn as in Figure 17. Some travelers are willing to pay more than the actual price, and thus they use that route and receive a net benefit equal to the difference between the price they were willing to pay and the actual price. The sum of net benefits over all travelers is the consumer surplus (de Jong, et al. 2005, Small and Verhoef 2007). If the price increases, an overall decrease in consumer surplus results, whereas if the price falls an overall increase in consumer surplus results (this increase corresponds to the two shaded regions in the figure). This is the basis of welfare economics. Generally, there is no simple, single relationship between travel demand and travel cost, but transportation modelers often turn to simplifying techniques in order to produce such estimates. One common technique is the Rule-of-Half (RoH) (de Jong, et al. 2005 and 2007, Small and Verhoef 2007). The basic concept behind the RoH is if a policy reduces the cost of travel, the change in consumer surplus can be estimated as the change in cost multiplied by the number of users under the old policy, plus one half of the change in the cost multiplied by the number of new users. The first part of this is the area shaded in gray in Figure 17 and the second part corresponds to the area shaded in black. More formally, for a single link, the RoH estimate for the change in consumer surplus can be computed as follows: ∆CS c c v v vi i i i i i= −( )× + −( )  , , , , , (0 1 0 1 0 1 2 Equation 10) Here, ci,0 and ci,1 correspond to the cost on link i before and after the policy change, respectively, and vi,0 and vi,1 represent the traffic volumes on link i before and after the policy change. Since transportation policies typically affect travel times on routes, this formula can easily be extended to include changes in travel times by using the value of travel time (VOTT). Moreover, the total change in consumer surplus is simply the sum of changes across all links in the network. Thus, the more complete RoH formulation is as follows: ∆ ∆CS CS c c VOT tttot i i l i l i i i= = −( ) + × ∈ ∈ ∑ ∑ 1 2 0 1 0, , , −( )[ ] × +( ) tt v v i i i , , , ( 1 0 1 Equation 11) Here, tti,0 and tti,1 are the before and after travel times on link i, and ci,0 and ci,1 are the out-of-pocket costs of travel on link i before and after the policy change (where out-of-pocket costs can include vehicle operating costs, transit fares, and link tolls). RoH holds exactly if the demand function is linear with price and cross-demand effects are also linear (i.e., choice alternatives are perfect substitutes). But if the demand func- tion is more complex (as is generally the case in transport sys- tems), the RoH only produces a rough estimate of the actual change in consumer surplus. In addition, the RoH provides the best estimates of consumer surplus for small price changes (Small and Verhoef 2007). Furthermore, RoH estimates cannot address situations where the set of alternatives changes, as when P0 Pnew Price Demand Figure 17. Linear demand curve.

69 new routes/links are added and/or new modes are made avail- able (de Jong, et al. 2007). When a new alternative is present, its demand under the base scenario can easily be assumed to be zero. However, to employ the RoH, one must know the price at which demand becomes zero (i.e., the point at which the demand curve crosses the axis). With a new alternative, this price is unknown, and the assumptions that need to be made about this price heavily affect the RoH estimates. So in some cases, such as a new tolled road where price changes can be dramatic or prior travel costs or times simply do not exist (since the new alternative did not exist), the RoH is inappro- priate and other techniques will be needed. Due to their behavioral basis and computational tracta- bility, discrete choice models such as the multinomial logit (MNL) and nested logit (NL) have become mainstays in travel demand forecasting. With these models, link-level demand curves emerge from the application of these models, and such behavioral specifications allow analysts to more for- mally estimate changes in user benefits. Random utility max- imization (RUM) is the basis for the logit model (McFadden 1978 and 1981), where the utility that individual i associates with alternative a is as follows: U Via ia ia= + ε (Equation 12) Here, Via is the systematic component of the utility, as parameterized by the analyst, and eia is a random error term representing unobserved contributions. In the case of the MNL model, eia values are independent and identically dis- tributed (iid), following a Generalized Extreme Value (GEV) type 1 distribution. For such a model, normalized Logsums of systematic utilities provide the basis for consumer surplus calculations. When divided by the marginal utility of money, the welfare change from one scenario to another can then be computed simply as logsum differences between any two scenarios (Small and Rosen 1981; Ben-Akiva and Lerman 1985; de Jong, et al. 2005; Zhao, et al. 2008)]. The calculation is as follows: ∆CS V Vi ia a A ia a A = ( )  − ( )∈ ∈∑ 1 2 1 γ ln exp ln exp∑    (Equation13) Here, g denotes the marginal utility of money (γ = − dV dc , where c = cost), A represents the set of alternatives, and superscripts 1 and 2 refer to before and after conditions, respectively. Of course, if the marginal utility of money is not constant (i.e., income effects are present), complications will arise and special methods are needed (Karlström 1998 and 2001, Franklin 2006, Small, et al. 2006)] beyond those de - scribed here. Furthermore, the error terms in the two scenar- ios (i.e., before and after) are assumed to be held constant—or can be independent. In other words, an individual’s un - observed affinity for alternatives is assumed to be the same—or uncorrelated—across scenarios. Zhao et al. (2008) examined the consequences of intermediate levels of correlation and simulated welfare differences at the level of individuals, illustrating how highly variable group-level welfare changes can be. While the MNL model is more common in practice, the nested logit has become quite popular as well, since it allows for certain useful forms of correlation across alternatives. With the NL logit model, the utility expression for individual i and alternative a can be formulated as a function of the systematic utility and multiple error terms. , (Equation 14)U V a nia ia in ia= + η + ε ∈ Here, n denotes the set of alternatives that exhibit correlation. And the inclusive value, or expected maximum utility, G, for nest n can be formulated as follows: Γin n n ia a n V= ( )  ∈∑ 1 µ µln exp ( )Equation 15 Here, µn is a scale parameter for nest n’s error component. For a model such as this, the welfare change from one scenario to another can be written as follows: ∆ Γ ΓCSi in n N in n N = ( )   − ( )∈ ∈∑ 1 2 1 γ ln exp ln exp∑     ( )Equation 16 Again, g is the marginal utility of money, superscripts 1 and 2 refer to before and after conditions, and N is the set of all nests in the model specification. This formulation can easily be extended to models with differential effects of users. For instance, if discrete variables in the model relate to travelers with different attributes, welfare can be computed individually for each traveler type. At an extreme, welfare may be computed for each traveler indi- vidually, which is important as region-wide microsimulation has become more widespread. Of course, the more individual traveler types that exist, more and more welfare calculations are required. But in comparison to the computational effort needed to run a complicated model of travel demand, the effort required for such welfare calculations is quite minimal. The use of Logsums in welfare calculations allows for a nearly comprehensive measure of net traveler benefits (or losses, depending on the case) resulting from different transportation policies. While the idea of using Logsums for these purposes is nothing new [equations such as these were first developed by McFadden (1981) and Small and Rosen (1981)], their use in general highway or road pricing project

70 evaluation applications has been somewhat limited [de Jong, et al. 2005 and 2007)]. De Jong, et al. (2005, 2007), suggest that there is no particular reason for this other than inertia in the field. In practice, Logsum measures are not much more difficult to compute than other measures (like the RoH). In reality, they are easier to compute than traffic flows and various other calculations that modelers undertake, and they provide an exact measure of user benefits (as long as logit assumptions hold). Thus, the Logsum would appear to be the most appropriate welfare measure for transportation proj- ects that rely on logit models for traffic forecasting. Such an approach is the basis of current FTA guidance for the assess- ment of transit New Starts project cost-effectiveness. It is also important to differentiate nested choice specifica- tions from downward-conditional/sequential or un-nested/ largely independent model specifications, which are not uncommon in practice. The NL model’s nested choice sets imply that the Logsum term across lower-level choice alter- natives appears in the utility function for upper-level choice alternatives, interacting with an inclusive value coefficient (Ben-Akiva and Lerman 1985). In some models, however, choices are not fully nested and lower-level choices are simply conditioned upon the outcomes of upper-level choices. For instance, many practitioners specify an MNL or gravity-based model for destination choice using simply drive-alone travel costs and model mode choice separately, conditioned on destination choice (recognizing all competing modes’ travel costs for each zone pair). In such cases, the mode and desti- nation choices are not fully integrated; yet it may be tempt- ing to compute Logsum differences for both models and add them to estimate total consumer surplus. Unfortunately, this will generally result in a fair amount of double counting. If only one choice dimension exists (e.g., mode and destination choices are modeled together in a single multinomial specifica- tion), this is not an issue. But for accurate welfare calculations across multiple choice dimensions, Logsums only make sense when welfare calculations are consistent with random utility maximization across all choice dimensions (as opposed to less rigorous, sequential application). Other Costs and Benefits Just as user welfare predictions are an essential part of project evaluation, so are estimates of project costs: design, construction, operations and maintenance. Generally, cost estimates are simpler to develop than user welfare, since the former are based on straightforward engineering practices that apply to all road projects, while the latter depend on systems models of travel behavior in response to pricing and congestion. Nonetheless, costs remain very important. Typically, project costs for a new toll road include right-of- way acquisition, construction, maintenance, technology, and management costs and can average $5 to 10 million per lane- mile (Litman 2006). In addition, other benefits and costs exist, including changes in crash occurrence and crash severity, changes in noise levels, improvements in travel reliability, and emissions impacts. Such costs and benefits are not discussed at length here, mostly because they are generally relevant in the evaluation of most major transportation projects, not just toll roads. However, it may be useful to note that there often are perceived safety and environmental benefits for tolled roads (Perez and Sciara 2003). FHWA (2006) provides several tools for the analysis of these benefits and costs (including the Sketch Planning Analysis Spreadsheet Model (SPASM), the Surface Transpor- tation Efficiency Analysis Model (STEAM), and IMPACTS. Small (1999), Litman (2006) and Small and Verhoef (2007) offer detailed discussions of these. Net Present Value and Discount Rates In any large-scale transportation project, a variety of costs and benefits accrue over a relatively long period of time. Performing a cost-benefit analysis requires converting these into a single measure, based on the present value of each. The present value for any future cash flow is computed by converting future values into an equivalent present value by discounting. As shown by Weisbrod and Weisbrod (1997) and FHWA (2003) the present value of any future cash flow can be found by multiplying the future value by a simple factor, f, based on the following formula: f d n = +( ) 1 1 ( )Equation 17 where n is the number of years in the future that the cost or benefit is observed and d is the discount rate. By summing all present values, one obtains the Net Present Value (NPV) of an investment (FHWA 2003). If the NPV is positive, then the investment is one worth pursuing, but if it is negative, it is not. Alternatively, one may want to calculate the Benefit-Cost (B/C) Ratio as the sum of the present value of all project benefits divided by the sum of the present value of all project costs (FHWA 2003). A B/C ratio of 1.0 or greater is one worth pursuing. Of course, if alternative projects are to be compared using both measures, different results may follow, since a small project with very high B/C ratio may have a small NPV, while a large project with a lower B/C ratio may have a relatively high NPV. Of consequence is how ben- efits and costs are defined, since many costs can be defined as negative benefits (e.g., an increase in noise or crashes). If one defined everything in terms of benefits (some positive and some negative), the B/C ratio would be undefined (since costs would be zero). FHWA (2003) recommends that only

71 an agency’s initial investment be included as costs, while all other gains and losses be tallied as positive and negative ben- efits, respectively. Another useful measure in project evaluation is the Inter- nal Rate of Return (IRR), which measures the discount rate needed in order that a project’s NPV equal zero (Blank and Tarquin 1989). In other words, it answers the question of what discount rate is needed to break even on an investment. Since large infrastructure projects generally have high up-front capital costs and benefits that accrue over many years, a higher IRR generally indicates a good investment, while a lower IRR indicates a poor investment. Of course, since the present value of any future cash flow depends greatly on the chosen discount rate, so do the NPV and B/C ratio, and selection of an appropriate discount rate can be critical for large investments (Small 1999). However, it is not often clear what the appropriate discount rate should be for transportation projects. Small (1999) and Small and Verhoef (2007) consider two specific rates of particular importance: • The first deals with the time preference of individuals in consuming goods, or the social rate of time preference. Small (1999) notes that this is often taken to be the real, after-tax interest rate one would expect to receive on a government bond of about 4%, though Boardman, et al. (2006) suggest a lower real, after-tax rate of 1.5%. (The real interest rate refers to the interest rate after accounting for inflation. This is in contrast to a nominal interest rate, which does not account for inflation.) • The second deals with the rate a private investor may expect to receive on investments before taxes. Small and Verhoef (2007) refer to this as the marginal product of capital. Boardman, et al. (2006) recommend a real rate at 4.5%, while Small and Verhoef (2007) state that most analysts recommend substantially higher real rates closer to 9 or 10%. Many times a single discount rate is chosen by weighting the rates described above ([Small 1999, Boardman, et al. 2006, Small and Verhoef 2007)]. Boardman, et al. (2006) suggest an appropriate weight for the social rate of time preference to be the amount of tax-based financing for the project and a weight equal to the amount of project financing coming from private investors for the marginal product of capital. Other times, however, an analyst may follow U.S. Office of Manage- ment and Budget (OMB 2003) guidelines, which recommend a real discount rate of 7%, reflecting OMB’s estimate of the average before-tax rate of return to private capital, and which suggest a 30-year historical rate of social time preference of 3%. The OMB (2003) guidelines also suggest that sensitivity test- ing of the discount rate always be performed and the chosen discount rate clearly reported. In general, there should be little distinction between choos- ing discount rates in a non-tolled road project versus a tolled one. However, in many tolled projects, project costs are leveraged against expected revenues. In such cases, the proj- ect endures added investment risk, and some literature (see Savvides 1994, Hacura, et al. 2001, Poole 2007) suggests that added risk requires the use of higher discount rates. How- ever, the primary purpose of discounting is not to account for risk. OMB (2003) offers the following reasons for discounting future values: money invested today generally earns a posi- tive real rate of return over time (i.e., the opportunity cost of capital) and people have a time preference for consumption (due to future uncertainties and the obvious nature of near- term gratification). 4.6.2 Criteria for Evaluation of Pricing Projects Three main criteria are applied for evaluation of pricing projects: • Economic welfare, • Generated revenue, and • Vehicular throughput. In many cases, obtaining the maximum social welfare provides a solid basis for toll rate selection since it offers the greatest good for the average road user, although it does not address the costs borne by non-road users. On the other hand, privately operated toll road investors will seek to max- imize profits. When tolls are under consideration for con- gestion relief, throughput maximization is often a focus. In general, these three selection criteria will result in very different toll levels. If all roads in a network can be tolled, the maximization of welfare (as it relates to traveler delay) is actually rather straightforward. In this case, the optimal (congestion-based) tolls will equal the cost each traveler imposes on all other drivers (collectively) on the road or link in question. This is the marginal social cost of such travel and presumes fixed link capacities. (Of course, if one adds in the costs of tailpipe emissions, noise, and crashes, the formulation will differ.) In terms of maximizing social welfare, this is a first-best solution. However, there are many situations that make first-best tolls impractical. When considering tolls on a single road or subset of links, first-best tolls clearly do not apply, since first-best tolls generally require tolling on most (or all) links (at least in a welfare maximizing sense). In general, the marginal cost toll on a single road will be higher than the second-best toll. This is because marginal social cost tolls on all links represent a first-best equilibrium, where net social welfare is maximized. If the marginal social cost toll is applied on only a subset of

72 links, leaving all others untolled, the traffic equilibrium will enjoy too few users on the tolled routes overall (relative to the second-best optimum traffic conditions). Thus, if marginal cost pricing were used for a single road, non-optimal tolls would emerge (from a welfare standpoint). First-best tolls may be impractical for a variety of other reasons as well. For example, it may not be possible to differentiate tolls across users, it may be infeasible to adjust tolls dynami- cally, and tolls may be set before actual demand is realized (Small and Verhoef 2007). Nonetheless, it is still possible to attain a welfare-maximizing toll even when first-best condi- tions do not apply, and much research has been devoted to investigating these circumstances. Small and Verhoef (2007) examine how many issues can be handled in second-best environments. Similar to the case of welfare maximization, maximizing revenues results in distinctions between first- and second-best solutions. For instance, very different tolls will arise if all roads in a network can be tolled, versus tolling a single road. In comparison to an objective of maximizing welfare, Verhoef, et al. (1996) show that revenue-maximizing tolls on all links can be much better (in terms of overall social welfare) than a revenue-maximizing toll on a single link, though it depends on the specific conditions of the network being analyzed. However, by definition, such tolls cannot produce greater welfare gains than when welfare itself is maximized. Of course, throughput (flow) maximization focuses on maximizing traffic flow on the tolled road or along the tolled corridor over a period of time (e.g., over a 24-hour day). Interestingly, this criterion is the same as maximizing net social welfare when the focus is on a single road in isolation and both toll level and capacity of the roadway are chosen opti- mally (Verhoef 2007). In addition, Verhoef (2007) shows that the throughput maximizing toll level and capacity (assuming capacity is a decision variable as well) is identical to the second- best welfare maximizing toll and capacity (in the presence of unpriced complements and substitutes) when zero-profit/ revenue-neutral capacity expansion is considered for a net- work. However, because of its reliance on traffic flow, this criterion can be quite difficult to apply in practice, since most forecasting models rely on static traffic assignment procedures, thus neglecting traffic queuing conditions. In such cases, flow is usually taken to be the same as demand, and maximizing demand on a link in a network can result in crippling conges- tion and dramatically reduced flows (in contrast to maximized flows) upstream of network bottlenecks. While application of this objective does not necessarily require DTA procedures, it will require models with some recognition of travel times and queuing so that reasonable estimates of toll road flows across peak times of day can be evaluated. Overall, it may be best to first evaluate and seek some com- promise across all three toll selection criteria, in order to pro- duce a more robust tolling strategy, sensitive to competing stakeholders’ interests. In general, selected toll levels should be compared to optimal toll estimates under each selection criteria. Ratios of anticipated welfare gains, revenues, and flows to maximized levels are key results meriting consideration and reporting. An example application illustrating the differences between approaches is presented in Appendix A, Section A.6.