Roundabouts in the United States (2007)

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102 This chapter presents a series of interpretations, appraisals, and applications of the major findings of this study. This chapter is organized into the following sections: • Application of intersection-level safety performance models • Estimation of the safety benefit of a contemplated conver- sion of an existing intersection to a roundabout • Application of approach-level safety models • Incorporation of safety models into other documents • Application of operational models Application of Intersection-Level Safety Performance Models The safety models and results presented in Chapter 3 can be used in a number of ways (with appropriate cautions). The intersection-level models can be used to evaluate the safety performance of an existing roundabout and to aid in the estimation of the expected safety changes if a roundabout is contemplated for construction at an existing conventional intersection. The approach-level models are presented as tools for evaluating designs in two optional cases: (1) in direct application or (2) as described in Chapter 3, the models with AADT only can be considered as base models (consistent with anticipated HSM procedures) and allow for the estimated coefficients for geometric features in recommended and other models to be considered in developing CMFs. At both the intersection and approach levels, the potential user should confirm that the models adequately represent the jurisdiction or can be recalibrated using data from the jurisdiction. Details of these applications follow, along with a discussion on how these potential applications might be implemented. The intersection-level models presented in Chapter 3 can be used in an empirical Bayes (EB) procedure to estimate the expected safety performance of an existing roundabout, providing the models can be assumed as representative of the pertinent jurisdiction or can be recalibrated using representative data from that jurisdiction. This result can then be used in a network screening process to examine the performance of that roundabout in relation to other roundabouts or other intersections. For roundabouts performing below par from a safety perspective, diagnostic procedures can then be used to isolate any problems and to develop corrective measures. The EB method provides a procedure to combine model predictions and observed crash frequencies into a single esti- mate of the expected crash frequency, so that the observed crash history of a site can be considered in the estimation process, while recognizing that the observed crash frequency by itself is a poor estimate of expected crash frequency because of the randomness of crash counts. Overview of EB Calculations Step 1 Assemble data including the number of legs, the number of circulating lanes, and the count of total and injury crashes (excludes possible injury) for the roundabout of interest for a period of n (up to 10) years. For the same time period, obtain or estimate a total entering AADT representative of that time period. Step 2 Assuming the model is representative of the jurisdiction, select the appropriate intersection-level model from Table 19 or 20 and then use it to estimate the annual number of crashes that would be expected at roundabouts with traffic volumes and other characteristics similar to the one being evaluated. If the model cannot be assumed to be representative of the jurisdiction, recalibrate it using data (similar to data acquired in Step 1) from a sample of roundabouts representative of that C H A P T E R 6 Interpretation, Appraisal, and Applications

jurisdiction. At a minimum, data for at least 10 roundabouts with at least 60 crashes are needed. The recalibration multi- plier is the sum of crashes recorded in the jurisdiction cali- bration dataset divided by the sum of the crashes predicted by the model for the jurisdiction calibration dataset. Then use the model from Table 19 or 20 including the recalibration multiplier to estimate the annual number of crashes, P. Step 3 Combine the SPF estimate, P, with the count of crashes, x, in the n years of observed data to obtain an estimate of the expected annual number of crashes, m, at the roundabout. This estimate of m is calculated as m  w1x  w2P where the weights w1 and w2 are estimated from the mean and variance of the model estimate as where k is the dispersion parameter for a given model and is estimated from the SPF calibration process with the use of a maximum likelihood procedure. The same procedure is used with the appropriate models for total and injury crashes. Example 1 Consider that the calculations for total crashes are of interest for a given roundabout. Step 1 The assembled data are as follows: • Number of legs  4 • Number of circulating lanes  1 • Years of observed data  n  3 • Total crashes observed  x  12 • Total entering AADT  17,000 Step 2 The appropriate SPF and dispersion factor k from Table 19, given four legs and one circulating lane, are as follows: Total crashes/yr  0.0023(AADT)0.7490, k  0.8986 w P k nP w k k nP 1 2 1 1 1 = + = + Assume for illustration purposes that this model is repre- sentative of intersections in the jurisdiction and that no recalibration is necessary. The estimate of P is then P  0.0023(17,000)0.7490  3.39 crashes/yr Step 3 Calculate the weights and the EB estimate of expected annual crash frequency. Therefore, the prediction model estimate of 3.39 has been refined to an EB estimate of 3.94 after consideration of the observed annual crash frequency of 12 crashes in 3 years. Application to Network Screening Part IV of the Highway Safety Manual will provide proce- dures for network screening. It is anticipated that these will be based on EB estimates since this is currently the state of the art. In screening, EB estimates can be used to assess how well an existing roundabout is performing relative to simi- lar roundabouts and other intersection types. Comparisons may be made to the average expected crash frequency of other sites or to specific sites in particular. If the other sites are also roundabouts, the appropriate models would be selected from Table 19. If the other sites are other intersec- tion types, then similar models specific to those site types need to be assembled. Comparison to the Average Expected Crash Frequency Comparing the expected crash frequency of a particular roundabout to the average expected frequency involves com- paring that site’s EB estimate to the regression model estimate for that average site type. Comparison to Other Specific Sites This comparison involves comparing the site’s EB estimate to the EB estimate for the other sites. A useful application of these estimates is to rank sites in descending order of expected crash frequency to prioritize the sites for a more w P k nP w k k nP 1 2 1 3 39 1 0 8986 3 3 39 0 30 1 1 = + = + × = = + . . . . = + × = = + = × 1 0 8986 1 0 8986 3 3 39 0 10 0 301 2 . . . . .m w x w P 12 0 10 3 39 3 94+ × =. . . crashes/yr 103

detailed investigation of safety performance. An alternative method is to rank sites by the difference between the EB esti- mate and the prediction model estimate. The models and results in Chapter 3 allow for either method to be applied. Estimation of the Safety Benefit of a Contemplated Conversion of an Existing Intersection to a Roundabout To provide designers and planners with a tool to estimate the change in crash frequency expected with the conversion of an intersection to a roundabout, two alternative approaches are proposed: calibrated intersection-level models or before- after studies. For both approaches, an SPF representative of the existing intersection is required; that is, an SPF must exist for the jurisdiction or data must be available to enable recalibra- tion of a model calibrated for another jurisdiction. The SPF of the existing intersection would be used, along with the inter- section’s crash history, in the EB procedure to estimate the expected crash frequency with the status quo in place (the EB esti- mate), which would then be compared to the expected fre- quency should a roundabout be constructed to estimate the benefit of converting the intersection to a roundabout. The two approaches differ in how the expected frequency should a roundabout be constructed is estimated. For the pre- ferred approach (Method 1), this value is estimated from an intersection-level model, which requires that data be available to recalibrate intersection-level models or that existing models be deemed adequate for the jurisdiction.Where there is no rep- resentative intersection-level model for the jurisdiction, an alternative approach (Method 2) can be used. In this approach, the results of the before-after study presented in Chapter 3 (Table 28) can be applied as CMFs to the expected crash fre- quency with the status quo in place to get the expected benefit. The first approach (Method 1) is preferred and most con- venient because a comprehensive set of CMFs (which would be required for a large number of conditions, including AADT levels) is simply not available and is difficult to obtain, although some have been estimated in the disaggregate analy- sis conducted for this project. Overview of the Preferred Approach For presentation purposes it is assumed that a stop- controlled intersection is being considered for conversion to a roundabout. Step 1 Assemble data and crash prediction models for stop- controlled intersections and roundabouts. For the past n years a. Obtain the count of total and injury crashes. b. For the same period, obtain or estimate the average total entering AADTs. c. Estimate the entering AADTs that would prevail for the period immediately after the roundabout is installed. d. Assemble required crash prediction models from Chapter 3 or elsewhere for stop-controlled intersections and round- abouts. If the models cannot be assumed to be representa- tive of the jurisdiction, they must be recalibrated using data (similar to data acquired in Step 1a) from a sample of inter- sections representative of that jurisdiction. At a minimum, data for at least 10 intersections with at least 60 crashes are needed. The recalibration multiplier is simply the number of crashes recorded in the sample divided by the number of crashes predicted for the sample by the model. The multi- plier is applied to the equation selected for predicting crashes. Step 2 Use the EB procedure with the data from Step 1 and the stop-controlled intersection model to estimate the expected annual number of total and injury crashes that would occur without conversion. The EB estimate for PDO crashes is then derived as the EB estimate for total crashes, minus the EB esti- mate for injury crashes. Step 3 Use the appropriate intersection-level model from Table 19 or 20 in Chapter 3 and the AADTs from Step 1 to estimate the expected number of total and injury crashes that would occur if the intersection were converted to a roundabout. The esti- mate for PDO crashes is then derived as the model estimate for total crashes minus the model estimate for injury crashes. Step 4 Obtain for injury and PDO crashes, the difference between the stop-controlled and roundabout estimates from Steps 2 and 3. Step 5 Applying suitable severity weights and dollar values for injury and PDO crashes, obtain the estimated net benefit of converting the intersection to a roundabout. The best source of information for unit crash costs at the time of this writ- ing is a recently published FHWA web document, “Crash Cost Estimates by Maximum Police-Reported Injury Sever- ity within Selected Crash Geometries,” at http://www.tfhrc. gov/safety/pubs/05051/index.htm. The document presents 104

disaggregate unit costs of crashes by severity level, by type of facility (e.g., intersection type), by impact type, and by envi- ronment (urban versus rural). Step 6 Compare the net benefit against the cost, considering other impacts if desired and using conventional economic analysis tools. How this analysis is done, and in fact whether it is done, is very jurisdiction specific, and conventional methods of economic analysis can be applied only after estimates of the economic values of changes in delay, fuel consumption, and other impacts have been obtained. The results of this analysis may indicate that roundabout conversion is justified based on a consideration of safety benefits. This result may be consid- ered in context with other factors, such as the following: • Other improvement measures at the given intersection may have higher priority in terms of cost effectiveness. • The analysts may need to assess the safety benefits and other benefits (delay, fuel consumption, etc.) against the costs and other impacts that may be created by the round- about. • Other locations in a system may be more deserving of a roundabout. In other words, the analyst should feed the results of this analysis into the safety resource allocation process. Example 2 Consider the data for the roundabout in Example 1. Before it was converted to a single-lane roundabout, this site was a four-leg, two-way-stop–controlled intersection in an urban environment. Assume for purposes of this example that before the roundabout was actually constructed, the pro- posed process was used to decide whether to convert this site into a roundabout. Preferred Approach Step P1. The assembled data are as follows: • Number of legs  4 • Control  two-way stop • Years of observed data  3 • Total crashes observed  17 • Injury crashes observed  10 • Average total entering AADT during years of observed data  16,000 • Anticipated AADT at time of conversion  17,000 Step P2. Models for urban, four-leg, two-way-stop– controlled intersections (Table 27) can be used in the EB procedure to predict the expected annual number of crashes if the conversion does not take place. First, the models are used to predict the annual number of crashes by severity: Total crashes/yr  exp(1.62)(AADT)0.220, k  0.45  exp(1.62)(16000)0.220  1.66 Injury crashes/yr  exp(3.04)(AADT)0.220, k  0.45  exp(3.04)(16000)0.220  0.40 Next, the weights and EB estimate are calculated for total crashes: Then, the weights and EB estimate are calculated for injury crashes: Because volumes are expected to increase in the after period, albeit only slightly, an adjustment is made to m to account for this change. This factor is calculated as (AADT after)0.220/(AADT before)0.220  (17000)0.220/(16000)0.220  1.01 The adjusted m is now equal to 4.42  1.01  4.46 for total crashes/yr 2.28  1.01  2.30 for injury crashes/yr The expected number of annual crashes by severity at the site if a conversion does not take place is estimated to be 4.46 total and 2.30 injury crashes/yr. The expected number of annual PDO crashes is calculated as 4.46  2.30  2.16. w P k nP w k k nP 1 2 1 1 40 1 0 45 3 0 40 0 12 1 1 1 = + = + × = = + = . . . . 0 45 1 0 45 3 0 40 0 65 0 12 10 0 61 2 . . . . . . + × = = + = × +m w x w P 5 1 66 2 28× =. . injury crashes/yr w P k nP w k k nP 1 2 1 1 66 1 0 45 3 1 66 0 23 1 1 1 = + = + × = = + = . . . . 0 45 1 0 45 3 1 66 0 31 0 23 17 0 31 2 . . . . . . + × = = + = × +m w x w P 1 1 66 4 42× =. . total crashes/yr 105

Step P3. The intersection-level model (see Example 1) is used to predict the annual number of crashes should the intersection be converted. In this case, the model was deemed adequate and was not recalibrated specifically for the jurisdiction. Total crashes/yr  0.0023(AADT)0.7490  0.0023(17000)0.7490  3.39 Injury crashes/yr  0.0013(AADT)0.5923  0.0013(17000)0.5923  0.42 The expected number of annual crashes by severity at the site if a conversion does take place is 3.39 total and 0.42 injury crashes/yr. The expected number of annual PDO crashes is calculated as 3.39  0.42  2.97. Step P4. The expected change in total crashes is equal to 3.39  4.46  1.07 total crashes/yr, or a 24% reduction. The expected change in injury crashes is equal to 0.42  2.30  1.88 injury crashes/yr, or an 82% reduction. The expected change in PDO crashes is equal to 2.97  2.16  0.81 PDO crashes/yr, or a 38% increase. Alternative Approach Step A1. This step is the same as Step P1 in the preferred approach. Step A2. This step is the same as Step P2 in the preferred approach. The expected number of annual crashes by sever- ity at the site if a conversion does not take place is estimated to be 4.46 total crashes, 2.30 injury crashes, and 2.16 PDO crashes. Step A3. From Table 28 in Chapter 3, the index of effec- tiveness for an urban, two-way-stop–controlled intersection converted to a single-lane roundabout is 0.612 for total crashes and 0.217 for injury crashes. The estimate of crashes per year after conversion is 4.46  0.612  2.73 total crashes/yr 2.30  0.217  0.50 injury crashes/yr 2.73  0.50  2.23 PDO crashes/yr Step A4. The expected change in total crashes is equal to 2.73  4.46  1.73 total crashes/yr, or a 39% reduction. The expected change in injury crashes is equal to 0.50  2.30  1.80 injury crashes/yr, or a 78% reduction. The expected change in PDO accidents is equal to 2.23  2.16  0.07 PDO crashes/yr, or a 3% increase. Difference in Results The results obtained using the preferred and the alternative approaches differ because the preferred method incorporates data calibrated to the jurisdiction. The alternative approach employs CMFs that have not been calibrated to the specific jurisdiction and may not be representative of the situation under consideration. Application of Approach-Level Safety Models There are two sets of possible applications for the approach-level models: (1) they can be used to evaluate the safety performance of an existing roundabout at the approach level, and (2) they can be considered for use in Highway Safety Manual-type applications to estimate the expected safety per- formance at the approach level. Details of these applications are provided in the following sections. Evaluation of Safety Performance at the Approach Level Although the approach-level models have been developed to assist with design decisions, the models presented in Chapter 3 also can be used in an EB procedure to estimate the expected safety performance at an approach or number of approaches to an existing roundabout, provided that the models can be assumed as representative of the pertinent jurisdiction or can be recalibrated using representative data from that jurisdiction. This estimate would be used in screen- ing to compare the performance of the subject roundabout approach to that of other similar approaches. For approaches performing below par from a safety perspective, diagnostic procedures can then be used to isolate any problems and to develop corrective measures. The EB procedure applied at the approach level would be identical to the example intersection-level procedure pre- sented previously. The models to be used would be those indi- cated by the shaded rows of Tables 21 through 23. Consideration of Approach-Level Model Results for HSM-Type Application The prototype chapter of the HSM documents a crash prediction algorithm that enables the number of total inter- section-related crashes per year to be estimated as follows: Nint  Nb (CMF1 CMF2L CMFn) where Nint  predicted number of total intersection-related crashes per year after application of crash modification factors 106

Nb  predicted number of total intersection-related crashes per year for base conditions CMF1 . . . n  crash modification factors for various inter- section features, 1 through n For the prototype chapter, which pertains to two-lane rural roads, a panel of experts selected the base model and CMFs after a review of relevant research findings, including recently calibrated prediction models, the estimated coefficients of geometric variables in these models, and the results of before- after studies. To apply a similar methodology at the approach level of roundabouts, the first models listed in Tables 21 through 23 (with AADT as the only variable) can be considered in devel- oping base models. And, as noted in Chapter 3, the estimated coefficients for geometric features in the recommended and other approach-level models can be considered in developing CMFs. The CMFs directly related to geometry are shown in Table 24. Using the previous equation, the effect of a design change can be identified by applying the appropriate CMF. How- ever, caution is advised because many of the variables are correlated, resulting in model-implied effects that may not reflect reality. The correlations should therefore be consid- ered in making final decisions on the CMFs that are to be used in the HSM. To this end, a correlation matrix is provided as Table 25. Incorporation of Safety Models into Other Documents The models above have the potential for being incorpo- rated into major documents that guide the transportation profession, including FHWA’s Manual on Uniform Traffic Control Devices (MUTCD) and the Highway Safety Manual under development. Potential for Use in MUTCD Intersection Control Evaluations The decision on the form of traffic control for an inter- section is based in part on the satisfaction of various war- rants provided in the 2003 MUTCD (43). As noted in Section 4B.04 of the MUTCD, alternatives to signalized intersection control—including roundabouts (Option K in Section 4B.04)—should be considered, even when one or more signal warrants are met. These alternatives may yield improved safety performance over that of a signalized inter- section. The proposed procedures presented in this report for estimating the likely change in safety and operational performance following the installation of a roundabout at an existing conventional intersection (as previously out- lined) are anticipated to support this type of evaluation. Given the substantial safety and operational benefits that roundabouts appear to provide in a variety of situations, the language in this section of the MUTCD should be strength- ened to further emphasize the need to consider roundabouts as one of these less-restrictive treatments. Potential for Assimilation into the HSM As noted previously, there are two potential HSM applica- tions. First, the intersection-level models can be used to estimate the expected crash frequency for network screening applications that are anticipated for Part IV of the HSM, as long as they are representative, or can be recalibrated to be so, of a jurisdiction’s roundabouts. Second, the approach-level models and implied CMFs can be considered for use in the prototype HSM chapter-type methodology for estimating the expected crash frequency of a roundabout approach (e.g., to estimate the safety implications of a decision to install or improve a roundabout). The first application would be relatively straightforward to implement, depending on how Part IV is written. The imple- mentation process for the second application is somewhat more complex. The research team recommends that a process similar to that followed in developing the prototype chapter of the HSM be undertaken: the HSM developers—through the various chapter contractors, and perhaps expert panels— would consider the models and CMFs suggested in Chapter 3, along with all other relevant information, in finalizing base models and CMFs for roundabouts for application in the pertinent chapters for two-lane and multilane highways. Application of Operational Models The operational models and results presented in Chapter 4 form the basis for a proposed revised operational procedure for inclusion in the Highway Capacity Manual. A draft proce- dure has been prepared and attached as Appendix M. This draft is expected to undergo further refinement beyond this project through the activity of the TRB Committee on High- way Capacity and Quality of Service before publication in the next update to the HCM. The highlights of the proposed HCM procedure include the following improvements over the procedure in the HCM 2000: • Single-lane model based on an expanded field database • Guidance on the capacity of double-lane roundabouts, including an approach that is sensitive to lane use • Procedure for estimating control delay and queues • Guidance for estimating LOS • Explanatory text supporting the recommended models • Sample problems illustrating the use of the procedure 107

Capacity Two capacity models are recommended: a model for esti- mating the capacity of a single-lane entry into a single-lane circulatory roadway and a model for estimating the capacity of the critical lane of a two-lane entry into a two-lane circula- tory roadway. Simple, empirical models were chosen for both for two reasons. First, the simple model fit the data as well as or better than any of the more complicated models used inter- nationally. Second, a detailed analysis of geometric parameters at both the microscopic (critical headway and follow-up head- way) and macroscopic (goodness-of-fit) level did not reveal a strong relationship that would significantly improve the capacity estimate, other than number of lanes. As a result, the data do not support the use of a more complicated model. The following exponential regression form is recom- mended for the entry capacity at single-lane roundabouts: where c  entry capacity (pcu/h) vc  conflicting flow (pcu/h) The exponential model parameters can be calibrated using locally measured parameters as follows: where c  entry capacity (pcu/h) A  3600/tf B  (tc  tf /2)/3600 vc  conflicting flow (pcu/h) tf  follow-up headway (s) tc  critical headway (s) The recommended capacity model for the critical lane of a multilane entry into a two-lane circulatory roadway is as follows: where ccrit  entry capacity of critical lane (pcu/h) vc  conflicting flow (pcu/h) Several influences in the multilane data should be noted: • The critical-lane data mostly comprise observations in the right entry lane. Because of limited critical left-lane obser- vations, the data were inconclusive in supporting a differ- ence in the capacity between the right lane and left lane. • The critical-lane data mostly comprise entering vehicles against two conflicting lanes. One site in the data has a two-lane entry and one conflicting lane but has too few observations to draw any conclusions. c vcrit c= ⋅ − ⋅1130 0 0007exp( . ) ( )6-3 c A B vc= ⋅ − ⋅exp( ) ( )6-2 c vc= ⋅ − ⋅1130 0 0010exp( . ) ( )6-1 The recommended intercept of the critical-lane regression was modified to correspond to field-measured follow-up head- ways in the critical lane. These headways essentially match the follow-up headways for the single-lane approaches and thus result in the same intercept. The slope of the curve represents a least-squares fit to the data given the intercept constraint. Control Delay and Queue Models The recommended control delay model is as follows: where d  average control delay (s/veh) c  capacity of subject lane (veh/h) T  time period (h: T1 for 1-h analysis, T0.25 for 15-min analysis) v  flow in subject lane (veh/h) This model is recommended as a reasonable method for estimating delays at U.S. roundabouts and is consistent with the methods for other unsignalized intersections. Given the low number of U.S. roundabouts currently operating with high delays, there is little ability at the present time to assess the accuracy of this model to predict higher magnitudes of delays. This model should be revisited in the future, where a more reliable estimation technique might become necessary. Because the delay model is the same as is currently used for unsignalized intersections and because the queuing and delay models are related, the current queuing model for unsignalized intersections is recommended for use on roundabout approaches. As discussed in Chapter 4, it may be appropriate to include a “ 5” factor with some modification for volume-to-capacity ratio. This inclusion is to account for the fact that, at higher volume-to-capacity ratios, vehicles may need to come to a stop and thus incur additional decel- eration and acceleration; at low volume-to-capacity ratios, vehicles are more likely to enter without having to come to a complete stop. Level of Service The recommended LOS criteria have been given previously in Chapter 4. The recommended thresholds are the same as for other unsignalized intersections because of the similarity in the task required of the driver (finding a gap) and thus in expectations. The LOS for a roundabout is determined by the computed or measured control delay for each lane. The LOS is not defined for the intersection as a whole. d c T v c v c c v c = + − + − ⎛⎝⎜ ⎞⎠⎟ + ⎛⎝⎜ ⎞⎠⎟3600 900 1 1 3600 4 2 50T ⎡ ⎣ ⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥⎥ ( )6-4 108