Roundabouts: An Informational Guide – Second Edition (2010)

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Chapter 4/Operational Analysis Page 4-1 Roundabouts: An Informational Guide CHAPTER 4 OPERATIONAL ANALYSIS CONTENTS 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 4.2 PRINCIPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 4.2.1 Effect of Traffic Flow and Driver Behavior . . . . . . . . . . . . . . . . . . . . . 4-4 4.2.2 Effect of Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5 4.3 DATA COLLECTION AND ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6 4.3.1 Field Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6 4.3.2 Determining Roundabout Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . 4-6 4.4 ANALYSIS TECHNIQUES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 4.5 HIGHWAY CAPACITY MANUAL METHOD . . . . . . . . . . . . . . . . . . . . . . 4-10 4.5.1 Adjustments for Vehicle Fleet Mix . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11 4.5.2 Entry Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11 4.5.3 Right-Turn Bypass Lanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13 4.5.4 Effect of Pedestrians on Vehicular Operations at the Entry . . . . . . 4-13 4.5.5 Volume-to-Capacity Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 4.5.6 Control Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15 4.5.7 Quality of Service and Level of Service . . . . . . . . . . . . . . . . . . . . . . . 4-16 4.5.8 Geometric Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17 4.5.9 Queue Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17 4.5.10 Reporting of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18 4.6 DETERMINISTIC SOFTWARE METHODS . . . . . . . . . . . . . . . . . . . . . . . . 4-18 4.7 SIMULATION METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19 4.8 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20

Roundabouts: An Informational Guide Page 4-2 Chapter 4/Operational Analysis LIST OF EXHIBITS Exhibit 4-1 Calculation of Circulating Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Exhibit 4-2 Calculation of Exiting Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Exhibit 4-3 Conversion of Turning-Movement Volumes to Roundabout Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Exhibit 4-4 Selection of Analysis Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10 Exhibit 4-5 Passenger Car Equivalencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11 Exhibit 4-6 Entry Lane Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 Exhibit 4-7 Entry Capacity Adjustment Factor for Pedestrians Crossing a One-Lane Entry (Assuming Pedestrian Priority) . . . . . 4-14 Exhibit 4-8 Entry Capacity Adjustment Factor for Pedestrians Crossing a Two-Lane Entry (Assuming Pedestrian Priority) . . . . . 4-14 Exhibit 4-9 Level-of-Service Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16

Chapter 4/Operational Analysis Page 4-3 Roundabouts: An Informational Guide 4.1 INTRODUCTION This chapter presents methods for analyzing the operation of an existing or planned roundabout. The methods allow a transportation analyst to assess the oper- ational performance of a facility, given information about the usage of the facility and its geometric design elements. An operational analysis produces two kinds of estimates: (1) the capacity of a facility (i.e., the ability of the facility to accommodate various streams of users) and (2) the level of performance, often using one or more measures of effectiveness, such as delay and queues. The Highway Capacity Manual (HCM)(1) defines the capacity of a facility as “the maximum hourly rate at which persons or vehicles can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions.” While capacity is a spe- cific measure that can be defined and estimated, level of service (LOS) is a qualitative measure that “characterizes operational conditions within a traffic stream and their perception by motorists and passengers.” To quantify LOS, the HCM defines spe- cific measures of effectiveness for each highway facility type. Control delay is the measure of effectiveness that is used to define level of service at intersections as per- ceived by users. In addition to control delay, all intersections cause some drivers to also incur geometric delay when making turns. A systems analysis of a roadway net- work may include geometric delay because of the slower vehicle paths required for turning through intersections. While an operational analysis can be used to evaluate the performance of an existing roundabout during a base or future year, its more common function in the United States may be to evaluate new roundabout designs. This chapter: • Presents the principles of roundabout operations, • Presents a method to estimate the capacity of five of the six basic round- about configurations presented in this guide, • Describes the measures of effectiveness used to determine the perform- ance of a roundabout and a method to estimate these measures, and • Briefly describes the computer software packages available to implement the capacity and performance analysis procedures. 4.2 PRINCIPLES The operational performance of roundabouts is relatively simple, although the techniques used to model performance can be quite complex. A few features are common to the modeling techniques employed by all analysis tools: • Drivers must yield the right-of-way to circulating vehicles and accept gaps in the circulating traffic stream. Therefore, the operational performance of a roundabout is directly influenced by traffic patterns and gap acceptance characteristics.

Roundabouts: An Informational Guide Page 4-4 Chapter 4/Operational Analysis • As with other types of intersections, the operational performance of a roundabout is directly influenced by its geometry. The extent to which this influence is affected in the aggregate (e.g., number of lanes) or by design details (e.g., diameter) is discussed in more detail in this section. The following sections discuss these principles in more detail. 4.2.1 EFFECT OF TRAFFIC FLOW AND DRIVER BEHAVIOR The capacity of a roundabout entry decreases as the conflicting flow increases. In general, the primary conflicting flow is the circulating flow that passes directly in front of the subject entry. When the conflicting flow approaches zero, the maxi- mum entry flow is given by 3,600 seconds per hour divided by the follow-up headway, which is analogous to the saturation flow rate for a movement receiving a green indication at a signalized intersection. This defines the intercept of the capacity model. A variety of real-world conditions occur that can affect the accuracy of a given modeling technique. The analyst is cautioned to consider these effects and determine whether they are significant for the type of analysis being performed. For example, the level of accuracy needed for a rough planning-level sizing of a roundabout is considerably less than that needed to determine the likelihood of queue spillback between intersections. Some of these conditions include the following (1): • Effect of exiting vehicles. While the circulating flow directly conflicts with the entry flow, the exiting flow may also affect a driver’s decision on when to enter the roundabout. This phenomenon is similar to the effect of the right-turning stream approaching from the left side of a two-way stop-controlled intersection. Until these drivers complete their exit maneuver or right turn, there may be some uncertainty in the mind of the driver at the yield or stop line about the intentions of the exiting or turning vehicle. • Changes in effective priority. When both the entering and conflicting flow volumes are high, limited priority (where circulating traffic adjusts its headways to allow entering vehicles to enter), priority reversal (where entering traffic forces circulating traffic to yield), and other behaviors may occur, and a simplified gap-acceptance model may not give reliable results. • Capacity constraint. When an approach operates over capacity during the analysis period, a condition known as capacity constraint may occur. During this condition, the actual circulating flow downstream of the constrained entry will be less than the demand. The reduction in actual circulating flow may therefore increase the capacity of the affected downstream entries. • Origin–destination patterns. Origin–destination patterns may have an influ- ence on the capacity of a given entry. As noted in the HCM, capacities measured in the United States have been generally lower than observed in other countries. Roundabout design practices and the public’s use of roundabouts are still maturing in the United States. Much

Chapter 4/Operational Analysis Page 4-5 Roundabouts: An Informational Guide of the data available at the time of publication of the 2010 HCM dates to 2003, when fewer roundabouts operating at capacity were available for study in the United States. It is therefore probable that capacities will increase over time as drivers become more familiar and as demands on existing roundabouts force drivers to improve efficiency. The extent to which this increase will occur, and whether this increase will cause capacities in the United States to match international observations, is an open question. It has been argued that capacities in the United States over time may still be different from those observed in other countries due to a variety of factors: • Limited use of turn indicators at roundabout exits, • Differences in vehicle fleet mixes, and • Much more common use of stop-controlled intersections (versus yield- controlled intersections) in the United States. 4.2.2 EFFECT OF GEOMETRY Geometry plays a significant role in the operational performance of a round- about in a number of key ways: • It affects the speed of vehicles through the intersection, thus influencing their travel time by virtue of geometry alone (geometric delay). • It dictates the number of lanes over which entering and circulating vehicles travel. The widths of the approach roadway and entry deter- mine the number of vehicle streams that may form side-by-side at the yield line and govern the rate at which vehicles may enter the circulat- ing roadway. • It can affect the degree to which flow in a given lane is facilitated or con- strained. For example, the angle at which a vehicle enters affects the speed of that vehicle, with entries that are more perpendicular requiring slower speeds and thus longer headways. Likewise, the geometry of multilane entries may influence the degree to which drivers are comfortable entering next to one another. • It may affect the driver’s perception of how to navigate the roundabout and their corresponding lane choice approaching the entry. Improper lane alignment can increase friction between adjacent lanes and thus reduce capacity. Imbalanced lane flows on an entry can increase the delay and queuing on an entry despite the entry operating below its theoretical capacity. Thus, the geometric elements of a roundabout, together with the volume of traffic desiring to use a roundabout at a given time, may determine the efficiency with which a roundabout operates. These elements form the core of commonly used models, including the Kimber model from the United Kingdom (2). Recent U.S.-based research has suggested that while aggregate changes in geometry are statistically significant, minor changes in geometry are masked by the large varia- tion in behavior from driver to driver (3). As a result, the extent to which geome- try is modeled depends on the available data and the modeling technique employed.

Roundabouts: An Informational Guide Page 4-6 Chapter 4/Operational Analysis 4.3 DATA COLLECTION AND ANALYSIS 4.3.1 Field Data Collection Operational analysis of roundabouts requires the collection or projection of peak period turning-movement volumes. For existing conventional inter- sections, these can be determined using standard techniques (4). For existing roundabouts, turning movements can be collected using a variety of techniques: • Live recording of turning-movement patterns using field observers. This is only feasible under low-volume conditions where the entire roundabout is visible from one location. • Video recording of the entire intersection, followed by manual extraction of turning movements from the video. This technique is feasible under any volume condition but usually requires all of the turning movements to be visible from one location. Multiple video locations can be used, but they must be carefully synchronized for successful data extraction. • Field observers at each of the exits, manually recording vehicles approaching the exit. • Link counters placed across each entry, each exit, and the circulatory roadway in front of each splitter island, plus manual counting of right-turn movements. • Origin–destination survey techniques. This is generally more effective when multiple intersections are being studied simultaneously. Operational performance of a roundabout can also be measured directly in the field using a variety of techniques: • Control delay can be estimated by measuring the average time it takes vehicles to travel between a control point upstream of the maximum queue in a lane and a point immediately downstream of the entry. The control delay is the difference between this measured travel time and the travel time needed by an unconstrained vehicle (one that did not queue or need to yield at entry). • Geometric delay can be estimated by comparing the travel time of an unconstrained vehicle passing through a roundabout to that needed by an unconstrained vehicle that does not pass through the geometric features of the roundabout (either measured before construction or estimated). Geometric delay is of particular importance when comparing travel times along a corridor. Note that field measurement of performance measures may require large sample sizes due to the inherent large variability in delay measures. 4.3.2 DETERMINING ROUNDABOUT FLOW RATES The manual technique presented in this document requires the calculation of entering, circulating, and exiting flow rates for each roundabout leg. Although the following sections present a numerical methodology for a four-leg roundabout, this methodology can be extended to any number of legs. The circulating flow rate opposing a given entry is defined as the flow conflicting with the entry flow of that leg. The movements that contribute to the

Chapter 4/Operational Analysis Page 4-7 Roundabouts: An Informational Guide northbound circulating flow rate are illustrated in Exhibit 4-1. In this exhibit, vc,NB is the circulating flow rate in front of the northbound entry, and the contributing movements are the eastbound through (EBT), eastbound left-turn (EBL), eastbound U-turn (EBU), southbound left-turn (SBL), southbound U-turn (SBU), and west- bound U-turn (WBU) movements. Exhibit 4-1 Calculation of Circulating Flow Exhibit 4-2 Calculation of Exiting Flow The exiting flow rate for a given leg is used primarily in the calculation of conflicting flow for right-turn bypass lanes and in determining queuing at exit- side crosswalks. The exiting flow calculation for the southbound exit is illus- trated in Exhibit 4-2. If a bypass lane is present on the immediate upstream entry, the right-turning flow using the bypass lane is deducted from the exiting flow. In this exhibit, vex,SB is the southbound exiting flow rate, and the con- tributing movements are the eastbound right-turn (EBR), southbound through (SBT), westbound left (WBL), and northbound U-turn (NBU) movements.

Roundabouts: An Informational Guide Page 4-8 Chapter 4/Operational Analysis Exhibit 4-3 Conversion of Turning- Movement Volumes to Roundabout Volumes Conversion of Turning-Movement Volumes to Roundabout Volumes Prior to conducting a roundabout analysis, turning-movement volumes must first be converted to roundabout volumes. Turning-Movement Data • Percent heavy vehicles for all movements = 2% • Peak Hour Factor (PHF) = 0.97 Step 1: Convert Movement Demand Volumes to Flow Rates Each turning-movement volume given in the problem is converted to a demand flow rate by dividing by the peak-hour factor. As an example, the northbound left volume is converted to a flow rate in passenger cars per hour as follows: 149 pc/h 0.97 145 === PHF V v NBLNBL Step 2: Adjust Flow Rates for Heavy Vehicles The flow rate for each movement may be adjusted to account for vehicle stream characteristics as follows (northbound left turn illustrated): 0.980 1 + 0.02(2 − 1) 1 1 + PT (ET − 1) 1 ===HVf 152 pc/h 0.980 149 === HV NBL NBL,pce f v v The resulting adjusted flow rates for all movements accounting for Steps 1 and 2 are therefore computed as follows: Exhibit 4-3 provides a sample calculation.

Chapter 4/Operational Analysis Page 4-9 Roundabouts: An Informational Guide Exhibit 4-3 (cont.) Conversion of Turning- Movement Volumes to Roundabout Volumes Conversion of Turning-Movement Volumes to Roundabout Volumes Step 3: Determine Entry Flow Rates by Lane The entry flow rate is calculated by summing up the movement flow rates that enter the roundabout. For single-lane roundabouts, all approach volumes are summed together. Additional lane-use calculations are required for multilane roundabouts. The entry flow rates are calculated as follows for the south leg (northbound entry): pc/h451792201520 ,,,,,,, =+++= +++= pceeNBRpceNBTpceNBLpceNBUpceNBe vvvvv Step 4: Determine Circulating Flow Rates The circulating flow is calculated for each leg. The circulating volumes are the sum of all volumes that will conflict with entering vehicles on the subject approach. For the south leg (northbound entry), the circulating flow is calculated as follows: pc/h841025831502680 ,,,,,,,, =+++++= +++++= pceEBUpceEBLpceEBTpceSBUpceSBLpceWBUpceNBc vvvvvvv Step 5: Determine Exiting Flow Rates The exiting flow is calculated for each leg by summing all flow that will be exiting the roundabout on a particular leg. For the south leg (northbound entry), the exiting volume is calculated as follows: pc/h3151101001050 ,,,,,,, =+++= +++= pceeEBRpceSBTpceWBLpceNBUNBpceex vvvvv Result The following figure illustrates the final volumes converted into roundabout entering, exiting, and circulating flow rates.

Roundabouts: An Informational Guide Page 4-10 Chapter 4/Operational Analysis 4.4 ANALYSIS TECHNIQUES A variety of methodologies are available to analyze the performance of roundabouts. All are approximations, and the responsibility is with the analyst to use the appropriate tool for conducting the analysis. The decision on the type of operational analysis method to employ should be based on a number of factors: • What data are available? • Can the method satisfy the output requirements? Exhibit 4-4 presents a summary, rather than an exhaustive list, of common applications of operational analysis tools, along with the outcome typically desired and the types of input data usually available. Note that the outcome desired is dis- tinct from the output of the analysis tool. For example, the lane configuration is commonly determined through an iterative process of assigning lane configura- tions as inputs to the analysis tool and then assessing the acceptability of the resultant performance measures. Application Typical Outcome Desired Input Data Available Potential Analysis Tool Planning-level sizing Number of lanes Traffic volumes Section 3.5 of this guide, HCM, deterministic software Preliminary design of roundabouts with up to two lanes Detailed lane configuration Traffic volumes, geometry HCM, deterministic software Preliminary design of roundabouts with three lanes and/or with short lanes/flared designs Detailed lane configuration Traffic volumes, geometry Deterministic software Analysis of pedestrian treatments Vehicular delay, vehicular queuing, pedestrian delay Vehicular traffic and pedestrian volumes, crosswalk design HCM, deterministic software, simulation System analysis Travel time, delays and queues between intersections Traffic volumes, geometry HCM, simulation Public involvement Animation of no- build conditions and proposed alternatives Traffic volumes, geometry Simulation Exhibit 4-4 Selection of Analysis Tool In addition to the planning method in Section 3.5 of this guide, three basic types of analysis are suggested in the above table: HCM method, deterministic software, and simulation. These are presented in detail in the following sections. 4.5 HIGHWAY CAPACITY MANUAL METHOD The analytic method presented in the 2010 HCM represents a major update of the method presented in the 2000 edition. It is largely based on a recent study of roundabout operations for U.S. conditions based on a study of 31 sites (1, 3). The

Chapter 4/Operational Analysis Page 4-11 Roundabouts: An Informational Guide procedures allow the assessment of the operational performance of an existing or planned one-lane or two-lane roundabout given traffic-demand levels. This section presents an overview of key elements but not a complete represen- tation of the HCM method; details and sample problems can be found in the HCM (1). The HCM method and subsequent interpretations, corrections, and changes approved by the Transportation Research Board’s Committee on Highway Capacity and Quality of Service should take precedence over the content in this chapter. 4.5.1 ADJUSTMENTS FOR VEHICLE FLEET MIX The flow rate for each movement may be adjusted to account for vehicle stream characteristics using factors given in Exhibit 4-5. Note that the capacity equations given in this chapter implicitly incorporate these factors. As a result, adjustments to these factors should be done only in conjunction with reviewing the effect of those adjustments on others factors (e.g., critical headway and follow-up time). The calculation to incorporate these values is given in Equation 4-1 and Equation 4-2 (HCM): where vi,pce = demand flow rate for movement i, pc/h; vi = demand volume for movement i, veh/h; fHV = heavy vehicle adjustment factor; PT = proportion of demand volume that consists of heavy vehicles; and ET = passenger car equivalent for heavy vehicles. 4.5.2 ENTRY CAPACITY Based on national research, the HCM employs a number of simple, empirical regression models to reflect the capacity of roundabouts with up to two lanes. The capacity of an entry lane opposed by one circulating lane [e.g., a one-lane entry to a one-lane roundabout, or either lane of a two-lane entry conflicted by one circulating lane (for example, Exhibit A-3 of Appendix A)] is based on the conflict- ing flow. The equation for estimating the capacity is given as Equation 4-3. where ce,pce = lane capacity, adjusted for heavy vehicles, pc/h; and vc,pce = conflicting flow, pc/h. c ee pce vc pce , . ,,= − × −( )1 130 1 0 10 3 f P E HV T T = + −( ) 1 1 1 v v f i pce i HV , = Vehicle Type Passenger Car Equivalent, ET Passenger Car 1.0 Heavy Vehicle 2.0 Bicycle 0.5 Exhibit 4-5 Passenger Car Equivalencies Equation 4-1 Equation 4-2 Equation 4-3

Roundabouts: An Informational Guide Page 4-12 Chapter 4/Operational Analysis The capacity of the left lane of a roundabout approach is lower than the capacity of the right lane. Equation 4-4 gives the capacity of a one-lane roundabout entry opposed by two conflicting lanes as follows: where all variables are as given previously. Equation 4-5 and Equation 4-6 give the capacity of the right and left lanes, respectively, of a two-lane roundabout entry opposed by two conflicting lanes: where ce,R,pce = capacity of the right entry lane, adjusted for heavy vehicles, pc/h; ce,L,pce = capacity of the left entry lane, adjusted for heavy vehicles, pc/h; and vc,pce = conflicting flow, pc/h. Exhibit 4-6 presents a plot showing Equation 4-3, Equation 4-5, and Equa- tion 4-6. The dashed lines represent portions of the curves that lie outside the range of observed field data. c ee L pce vc pce , , . ,,= − × −( )1 130 0 75 10 3 c ee R pce vc pce , , . ,,= − × −( )1 130 0 7 10 3 c ee pce vc pce , . ,,= − × −( )1 130 0 7 10 3 Each of the capacity models given above reflects observations made at U.S. roundabouts in 2003. As noted previously, it is probable that U.S. roundabout capacity will increase to some degree over time with increased driver familiarity. In addition, communities with higher densities of roundabouts and/or generally more aggressive drivers may experience higher capacities. Therefore, local calibra- tion of the capacity models is recommended to best reflect local driver behavior. This is discussed further in the HCM. Exhibit 4-6 Entry Lane Capacity Equation 4-4 Equation 4-5 Equation 4-6 0 200 400 600 800 1,000 1,200 1,400 0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 Conflicting Flow Rate (pc/h) Ca pa ci ty (p c/h ) Dashed regression extrapolated beyond the data Capacity of one-lane entry or right lane of two-lane entry against two conflicting lanes Capacity of left lane of two-lane entry against two conflicting lanes Capacity of one-lane or either lane of two- lane entry against one conflicting lane

Chapter 4/Operational Analysis Page 4-13 Roundabouts: An Informational Guide 4.5.3 RIGHT-TURN BYPASS LANES Right-turn bypass lanes are right-turn lanes that do not share the same entrance line with the lanes designated for through and left-turning vehicles. Two common types of right-turn bypass lanes are used at single-lane and multilane roundabouts: (1) where bypass traffic yields to conflicting exiting vehicles (sometimes referred to as a partial bypass lane), and (2) where the bypass lane joins the intersecting road- way as an additional lane or in a downstream merging operation. The capacity for a yielding bypass lane opposed by one exiting lane can be approximated using Equation 4-7. The capacity for a yielding bypass lane opposed by two exiting lanes can be approximated using Equation 4-8. where cbypass,pce = capacity of the bypass lane, adjusted for heavy vehicles, pc/h; and vex,pce = conflicting exiting flow, pc/h. The capacity of a bypass lane that merges at a low angle with exiting traffic or forms a new lane adjacent to exiting traffic (non-yielding bypass lane) has not been assessed in the United States. Its capacity is expected to be relatively high due to a merging operation between two traffic streams at similar speeds. 4.5.4 EFFECT OF PEDESTRIANS ON VEHICULAR OPERATIONS AT THE ENTRY Pedestrian traffic can reduce the vehicular capacity of a roundabout entry if sufficient pedestrians are present and they assert the right-of-way typically granted pedestrians in most jurisdictions. Under high vehicular conflicting flows, pedestrians typically pass between queued vehicles on entry, resulting in negligi- ble additional impact to vehicular entry capacity. However, under low vehicular conflicting flows, pedestrians can function effectively as additional conflicting vehicles and reduce the vehicular capacity of the entry. The effect of pedestrians is more pronounced with increased pedestrian volume. For roundabout entries opposed by one circulating lane, the model shown in Exhibit 4-7 can be used to approximate this effect (2); for entries opposed by two circulating lanes, the model shown in Exhibit 4-8 can be used. These equations are based on the assumption that pedestrians have absolute priority. Supporting equations can be found in the HCM. Regardless of the analysis method used, vehicular yielding rates vary depending on crossing treatment, number of lanes, posted speed limit, and within individual sites (5). This makes modeling of pedestrian interactions imprecise. As a result, models to analyze pedestrian effects on vehicular capacity or vehicular effects on pedestrian travel should recognize the approximate nature of the adjustment. For locations with high pedestrian volumes or where more precise estimates of capacity effects are desired, a comparison to other analysis methods may be appropriate. c ebypass pce vex pce , . ,,= − × −( )1 130 0 7 10 3 c ebypass pce vex pce , . ,,= − × −( )1 130 1 0 10 3 Equation 4-7 Equation 4-8

Roundabouts: An Informational Guide Page 4-14 Chapter 4/Operational Analysis 4.5.5 VOLUME-TO-CAPACITY RATIO The volume-to-capacity ratio is a comparison of the demand at the roundabout entry to the capacity of the entry and provides a direct assessment of the sufficiency of a given design. For a given lane, the volume-to-capacity ratio, x, is calculated by dividing the lane’s calculated capacity into its demand flow rate, as shown in Equa- tion 4-9. Both input values are in vehicles per hour. While the HCM does not define a standard for volume-to-capacity ratio, inter- national and domestic experience suggests that volume-to-capacity ratios in the range of 0.85 to 0.90 represent an approximate threshold for satisfactory operation. When the degree of saturation exceeds this range, the operation of the roundabout x v c = 0.80 0.85 0.90 0.95 1.00 0 100 200 300 400 500 600 700 800 900 1,000 Conflicting circulating flow (pc/h) En tr y ca pa ci ty a dju stm en t f ac to r, f pe d 0.80 0.85 0.90 0.95 1.00 0 200 400 600 800 1,000 1,200 1,400 1,8001,600 Conflicting circulating flow (pc/h) En tr y ca pa ci ty a dju stm en t f ac to r, f pe d Exhibit 4-7 Entry Capacity Adjustment Factor for Pedestrians Crossing a One-Lane Entry (Assuming Pedestrian Priority) Exhibit 4-8 Entry Capacity Adjustment Factor for Pedestrians Crossing a Two-Lane Entry (Assuming Pedestrian Priority) Equation 4-9

Chapter 4/Operational Analysis Page 4-15 Roundabouts: An Informational Guide enters a more unstable range in which conditions could deteriorate rapidly, particu- larly over short periods of time. Queues that carry over from one 15-minute period to the next may form, and delay begins to increase exponentially. A volume-to-capacity ratio of 0.85 should not be considered an absolute threshold; in fact, acceptable operations may be achieved at higher ratios. Where an operational analysis finds the volume-to-capacity ratio above 0.85, it is encour- aged to conduct additional sensitivity analysis to evaluate whether relatively small increments of additional volume have dramatic impacts on delay or queues. The analyst is also encouraged to take a closer look at the assumptions used in the analysis (i.e., the accuracy of forecast volumes). A higher volume-to-capacity ratio during peak periods may be a better solution than the potential physical and envi- ronmental impacts of excess capacity that is unused most of the day. 4.5.6 CONTROL DELAY Delay is a standard parameter used to measure the performance of an inter- section. The HCM identifies control delay as the primary service measure for sig- nalized and unsignalized intersections, with level of service determined from the control delay estimate. Delay data collected for roundabouts in the United States suggest that control delays can be predicted in a manner similar to that used for other unsignalized intersections. Equation 4-10 shows the model that should be used to estimate average control delay for each lane of a roundabout approach. The HCM only includes control delay, which is the delay attributable to the control device. Control delay is the time that a driver spends decelerating to a queue, queu- ing, waiting for an acceptable gap in the circulating flow while at the front of the queue, and accelerating out of the queue. where: d = average control delay, s/veh; x = volume-to-capacity ratio of the subject lane; c = capacity of subject lane, veh/h; and T = time period, h (T = 1 for a 1-h analysis, T = 0.25 for a 15-min analysis). Average control delay for a given lane is a function of the lane’s capacity and degree of saturation. The analytical model used above to estimate average con- trol delay assumes that there is no residual queue at the start of the analysis period. If the degree of saturation is greater than about 0.9, the average control delay is significantly affected by the length of the analysis period. In most cases, the recommended analysis period is 15 min. If demand exceeds capacity during a 15-min period, the delay results calculated by the procedure may not be accurate due to the likely presence of a queue at the start of the time period. In addition, the conflicting demand for movements downstream of the movement operating over capacity may not be fully realized (in other words, the flow cannot get past the d c T x x c x T = + − + −( ) + ⎛⎝⎜ ⎞⎠⎟ ⎡ ⎣ 3 600 900 1 1 3 600 450 2, ,⎢⎢⎢⎢ ⎤ ⎦ ⎥⎥⎥⎥ + [ ]5 1i min ,x Equation 4-10

Roundabouts: An Informational Guide Page 4-16 Chapter 4/Operational Analysis oversaturated entry and thus cannot conflict with a downstream entry). In these cases, an iterative approach that accounts for this effect and the carryover of queues from one time period to the next, such as the Kimber–Hollis formulation documented elsewhere (6), may be used. To make comparisons to other intersection types, it may be useful to compute the average control delay for the roundabout approach or the intersection as a whole. The control delay for an approach is calculated by computing a weighted average of the delay for each lane on the approach, weighted by the volume in each lane. The calculation is shown in Equation 4-11. Note that the volume in the bypass lane should be included in the delay calculation for the approach. The control delay for the intersection as a whole is similarly calculated by computing a weighted average of the delay for each approach, weighted by the volume on each approach. This is shown in Equation 4-12. where: dintersection = control delay for the entire intersection, s/veh; di = control delay for approach i, s/veh; and vi = flow rate for approach i, veh/h. 4.5.7 QUALITY OF SERVICE AND LEVEL OF SERVICE The HCM defines quality of service as how well a transportation facility or service operates from a traveler’s perspective (1, Chapter 5). Furthermore, the HCM defines LOS as a quantitative stratification of a performance measure or measures that represent that quality of service. For roundabouts, LOS has been defined using control delay (see Section 4.5.6) with criteria given in Exhibit 4-9. As the exhibit notes, LOS F is assigned if the volume-to-capacity ratio of a lane exceeds 1.0 regardless of the control delay. For assessment of LOS at the approach and intersection levels, LOS is based solely on control delay. The thresholds given in Exhibit 4-9 are the same as defined in the HCM for stop-controlled intersections. All HCM methodologies for unsignalized intersections share a similar equation form for estimating control delay, and thus similar volume-to-capacity ratios produce similar control delays. In addition, drivers at d d v v i i i intersection = ∑ ∑ d d v d v d v v v approach LL LL RL RL bypass bypass LL = + + + RL bypassv+ Level of Service by Volume-to-Capacity Ratio* Control Delay (s/veh) v/c 1.0 v/c >1.0 0–10 A F >10–15 B F >15–25 C F >25–35 D F >35–50 E F >50 F F * For approaches and intersection-wide assessment, LOS is defined solely by control delay. Exhibit 4-9 Level-of-Service Criteria Equation 4-11 Equation 4-12

Chapter 4/Operational Analysis Page 4-17 Roundabouts: An Informational Guide roundabouts must make judgments about entering gaps similar to those experi- enced at two-way stop-controlled intersections; these judgments become more challenging at higher volume-to-capacity ratios. As a result, drivers may not per- ceive the same amount of control delay the same way at roundabouts as they do at signalized intersections. As with any intersection evaluations, LOS is one of several measures (along with volume-to-capacity ratios, control delay, queue length, and other measures) that should be used in the comparison of roundabouts to other intersection types. 4.5.8 GEOMETRIC DELAY Geometric delay is a component of delay that is present at roundabouts but is not taken into consideration under typical HCM procedures. Geometric delay is the additional time that a single vehicle with no conflicting flows spends slowing down to the negotiation speed, proceeding through the intersection, and accelerating back to normal operating speed. Geometric delay may be an important consideration in network planning (possibly affecting route travel times and choices) or when com- paring operations of alternative intersection types. While geometric delay is often negligible for through movements at a signalized or stop-controlled intersection, it can be more significant for turning movements at those intersections and all move- ments through a roundabout. Calculation of geometric delay requires knowledge of the roundabout geometry as it affects vehicle speeds during entry, negotiation, and exit. Procedures are given in the Australian design guide (7). For LOS calculations, geometric delay is not needed, as the HCM defines LOS solely on the basis of control delay. However, if deterministic software or simula- tion tools are used to estimate travel time along a corridor, geometric delay is inherently included in the estimate of travel time. Care is needed when comparing results between models. 4.5.9 QUEUE LENGTH Queue length is important when assessing the adequacy of the geometric design of the roundabout approaches. The estimated length of a queue can also provide additional insight into the operational performance of a roundabout in comparison to other intersection types. Queue interaction with adjacent intersec- tions or driveways is another important consideration. The 95th-percentile queue for a given lane on an approach is calculated using Equation 4-13: where: Q95 = 95th-percentile queue, veh; x = volume-to-capacity ratio of the subject lane; c = capacity of subject lane, veh/h; and T = time period, h (T = 1 for a 1-h analysis, T = 0.25 for a 15-min analysis). Q T x x c x T 95 2900 1 1 3 600 150 = − + −( ) + ⎛⎝⎜ ⎞⎠⎟ ⎡ ⎣ ⎢⎢⎢⎢ ⎤, ⎦ ⎥⎥⎥⎥ ⎛⎝⎜ ⎞⎠⎟ c 3 600, Equation 4-13

Roundabouts: An Informational Guide Page 4-18 Chapter 4/Operational Analysis The queue length calculated for each lane should be checked against avail- able storage. The queue in each lane may interact with adjacent lanes in one or more ways: • If queues in adjacent lanes exceed available storage, the queue in the sub- ject lane may be longer than anticipated due to additional queuing from the adjacent lane. • If queues in the subject lane exceed the available storage for adjacent lanes, the adjacent lane may be starved by the queue in the subject lane. Should one or more of these conditions occur, the analyst can conduct a sensi- tivity analysis using the methodology by varying the demand in each lane. The analyst may also use an alternative tool that is sensitive to lane-by-lane effects, as discussed in Section 4.6 of this chapter. 4.5.10 REPORTING OF RESULTS Each of the performance measures described above provides a unique per- spective on the quality of service at which a roundabout will perform under a given set of traffic and geometric conditions. Whenever possible, the analyst should estimate as many of these parameters as possible to obtain the broadest possible evaluation of the performance of a given roundabout design. In all cases, a capacity estimate must be obtained for an entry to the roundabout before a spe- cific performance measure can be computed. The analyst should be particularly careful not to mask deficient performance characteristics of individual approaches or lanes by using potentially misleading aggregated measures. The reader is encouraged to refer to the HCM for further discussion on this important topic. 4.6 DETERMINISTIC SOFTWARE METHODS A variety of deterministic software methods are available that are anchored to international research and practice. These methods model vehicle flows as flow rates and are commonly sensitive to various flow and geometric features of the roundabout, including lane numbers and arrangements and/or specific geometric dimensions (e.g., entry width, inscribed circle diameter). Some software implemen- tations may include more than one model and employ extensions beyond the origi- nal fundamental research. Since 1990, the most commonly employed deterministic software methods in the United States have been based on Australian and British research and practice, although methods developed in France and Germany have seen some limited use. For example, British research suggests a much stronger correlation between capacity and fine gradations of geometry than research in some other countries, including the United States (2). For example, the research indicates that approach width, entry width, and the effective flare length have the most significant effects on capacity. In addition, the British research found that entry angle and entry radius have a combined significant effect and that diameter has a small effect, only becoming significant with high circulating volumes. Conversely, Australian research has found more significant effects related to traffic flow, including lane- Key performance measures for roundabouts include volume- to-capacity ratio, delay, and queue length.

Chapter 4/Operational Analysis Page 4-19 Roundabouts: An Informational Guide by-lane assessments and sensitivity to origin–destination patterns. Even though research in the United States has not necessarily confirmed these findings at American roundabouts, the principles embodied in these tools can be useful to guide a designer in making decisions about potential trade-offs in operational performance due to changes in traffic flows or geometric modifications. As with any analysis procedure, care should be taken to ensure that the proce- dure is being appropriately applied. Common items to check for include the fol- lowing: • Calibration to local driver behavior. For analytical-based models, this may involve using locally measured values for gap acceptance parameters or applying global factors that shape the capacity model. For regression- based models, this may involve adjusting the intercept to match field- measured values of follow-up times. • Calibration to effective geometry. For regression-based models that employ continuous variables for key dimensions (e.g., entry width in feet/meters rather than in number of lanes), adjustments for effective geometry should be considered. This is particularly true for single-lane entries that have large curb-to-curb widths to accommodate large vehicles. Regression- based models do not recognize that a large single-lane entry has only one lane and thus may be modeled as a two-lane entry. A common adjustment used in these cases is to assume that a single-lane entry has a maximum entry width of 15 ft (4.5 m) regardless of the actual curb-to-curb width. • Lane use and assignment. Some models are sensitive to lane use and assign- ment; others are not. Adjustments should be made to account for lane configurations or system effects (e.g., downstream destinations) that might cause traffic to favor one lane over another, thus influencing capac- ity and performance measures. 4.7 SIMULATION METHODS A variety of simulation software packages are available to model transporta- tion networks. Several of these are capable of modeling roundabouts, and features change frequently. These models display individual vehicles and thus are sensitive to factors at that level: car-following behavior, lane-changing behavior, and decision-making at junctions (e.g., gap acceptance). Since 1990, the most commonly employed simulation methods in the United States are based on U.S., British, and German research and practice. As with the deterministic software methods described previously, care should be taken to ensure that the simulation model is being appropriately applied. Com- mon items to check for include the following: • Calibration to local driver behavior. Calibration of stochastic models is more challenging than for deterministic models because some calibration fac- tors, such as those related to driver aggressiveness, often apply globally to all elements of the network and not just to roundabouts. In other cases,

Roundabouts: An Informational Guide Page 4-20 Chapter 4/Operational Analysis the specific coding of the model can be fine-tuned to reflect localized driver behavior, including look-ahead points for gap acceptance and locations for discretionary and mandatory lane changes. • Volume pattern checking. For network models with dynamic traffic assign- ment, traffic volumes on a given link may not match what has been measured or projected. Further guidance on the application of simulation models can be found in the FHWA Traffic Analysis Toolbox (8). 4.8 REFERENCES 1. 2010 Highway Capacity Manual. Transportation Research Board of the National Academies, Washington, D.C., forthcoming. 2. Kimber, R. M. The Traffic Capacity of Roundabouts. TRRL Laboratory Report LR 942. Transport and Road Research Laboratory, Crowthorne, England, 1980. 3. Rodegerdts, L., M. Blogg, E. Wemple, E. Myers, M. Kyte, M. Dixon, G. List, A. Flannery, R. Troutbeck, W. Brilon, N. Wu, B. Persaud, C. Lyon, D. Harkey, and D. Carter. NCHRP Report 572: Roundabouts in the United States. Transporta- tion Research Board of the National Academies, Washington, D.C., 2007. 4. Robertson, H. D., J. E. Hummer, and D. C. Nelson, eds. Manual of Transportation Engineering Studies. ITE, Washington, D.C., 2000. 5. Fitzpatrick, K., S. Turner, M. Brewer, P. Carlson, B. Ullman, N. Trout, E. S. Park, J. Whitacre, N. Lalani, and D. Lord. TCRP Report 112/NCHRP Report 562: Improving Pedestrian Safety at Unsignalized Crossings. Transportation Research Board of the National Academies, Washington, D.C., 2006. 6. Kimber, R. M. and E. M. Hollis. Traffic Queues and Delays at Road Junction. Labo- ratory Report LR 909, TRRL, Crowthorne, England, 1979. 7. Guide to Traffic Engineering Practice, Part 6: Roundabouts. Austroads, Sydney, Australia, 1993. 8. FHWA. Traffic Analysis Toolbox. ops.fhwa.dot.gov/trafficanalysistools/index. htm. Accessed August 2009.