Accelerating Roundabout Implementation 

in the United States – Volume II of VII 

Assessment of Roundabout Capacity Models 

for the Highway Capacity Manual 

SEPTEMBER 2015 

Updated October 2020 PUBLICATION NO. FHWA-SA-15-070 

 

 

 

 

 

 

 

 

 

 

 

 

 

FOREWORD 

Since the Federal Highway Administration (FHWA) published the first Roundabouts 

Informational Guide in 2000, the estimated number of roundabouts in the United States has 

grown from fewer than one hundred to several thousand. Roundabouts remain a high priority for 

FHWA due to their proven ability to reduce severe crashes by an average of 80 percent. They are 

featured as one of the Office of Safety Proven Safety Countermeasures and were included in the 

Every Day Counts 2 campaign for Intersection & Interchange Geometrics. 

As roundabouts became more common across a wide range of traffic conditions, specific 

questions emerged on how to further tailor certain aspects of their design to better meet the needs 

of a growing number and diversity of stakeholders. The substantial work performed for this 

project – Accelerating Roundabout Implementation in the United States – sought to address 

several of the most pressing issues of National significance, including enhancing safety, 

improving operational efficiency, considering environmental effects, accommodating freight 

movement and providing pedestrian accessibility. This work represents yet another notable step 

forward in advancing roundabouts in the United States. 

The electronic versions of each of the seven report volumes that document this project are 

available on the Office of Safety website at http://safety.fhwa.dot.gov/. 

Michael S. Griffith 

Director 

Office of Safety Technologies 

NOTICE 

This document is disseminated under the sponsorship of the U.S. Department of Transportation 

in the interest of information exchange. The U.S. Government assumes no liability for the use of 

the information contained in this document. This report does not constitute a standard, 

specification, or regulation. 

The U.S. Government does not endorse products or manufacturers. Trademarks or 

manufacturers’ names appear in this report only because they are considered essential to the 

objective of the document. 

QUALITY ASSURANCE STATEMENT 

The Federal Highway Administration (FHWA) provides high-quality information to serve 

Government, industry, and the public in a manner that promotes public understanding. Standards 

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its 

information. FHWA periodically reviews quality issues and adjusts its programs and processes to 

ensure continuous quality improvement. 

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TECHNICAL REPORT DOCUMENTATION PAGE 

1. Report No. 

FHWA-SA-15-070 

2. Government Accession No. 3. Recipient’s Catalog No. 

4. Title and Subtitle 

Accelerating Roundabouts in the United States: Volume II of VII -

Assessment of Roundabout Capacity Models for the Highway 

Capacity Manual 

5. Report Date 

September 2015 

6. Performing Organization Code: 

7. Author(s) 

Lee A. Rodegerdts, Anais Malinge, Patrick S. Marnell, Scott G. 

Beaird, Matt J. Kittelson, and Yuri S. Mereszczak 

8. Performing Organization Report No. 

11861 Task 3 

9. Performing Organization Name and Address 

Kittelson & Associates, Inc. 

610 SW Alder St., Suite 700 

Portland, OR 97205 

10. Work Unit No. (TRAIS) 

11. Contract or Grant No. 

DTFH61-10-D-00023-T-11002 

12. Sponsoring Agency Name and Address 

Office of Safety 

Federal Highway Administration 

United States Department of Transportation 

1200 New Jersey Avenue SE 

Washington, DC 20590 

13. Type of Report and Period Covered 

Technical Report 

August 2011 through September 2015 

14. Sponsoring Agency Code 

FHWA HSA 

15. Supplementary Notes 

The Contracting Officer’s Technical Manager (COTM) was Jeffrey Shaw, HSST Safety Design Team 

16. Abstract 

This volume is second in a series of seven. The other volumes in the series are: Volume I - Evaluation of Rectangular RapidFlashing Beacons (RRFB) at Multilane Roundabouts, Volume III – Assessment of the Environmental Characteristics of 

Roundabouts, Volume IV – A Review of Fatal and Severe Injury Crashes at Roundabouts, Volume V – Evaluation of 

Geometric Parameters that Affect Truck Maneuvering and Stability, Volume VI – Investigation of Crosswalk Design and 

Driver Behaviors, and Volume VII – Human Factor Assessment of Traffic Control Device Effectiveness. These reports 

document a Federal Highway Administration (FHWA) project to investigate and evaluate several important aspects of 

roundabout design and operation for the purpose of providing practitioners with better information, leading to more 

widespread and routine implementation of higher quality roundabouts. 

This report presents an assessment and development of updated roundabout capacity models for implementation in the major 

update of the HCM 2010. The roundabout capacity models in the HCM 2010 are based on data collected in 2003 as part of 

NCHRP Report 572; this task is based on a new set of capacity data collected in 2012. A total of 819 usable minutes of data 

at single-lane roundabouts, 711 minutes of usable data were obtained for the multilane case for two entry lanes conflicting 

with two circulating lanes, and 519 minutes of usable data were obtained for the multilane case for two entry lanes 

conflicting with one circulating lane. Parametric analyses were conducted to extract and review critical headway, follow-up 

time, and key geometric parameters. The new data confirmed that the HCM 2010 generally underestimates capacity. The 

most promising models involve recalibrating the HCM 2010 models with an intercept that is calibrated to follow-up time 

and a slope parameter based on regression of the data. Additional calibration factors such as critical headway or geometric 

parameters beyond number of lanes were not found to add significant improvement. 

17. Key Words 

Roundabouts, capacity, operational performance, 

calibration, HCM 

18. Distribution Statement 

No restrictions. This document is available to the public at 

http://safety.fhwa.dot.gov/ 

19. Security Classif. (of this report) 

Unclassified 

20. Security Classif. (of this page) 

Unclassified 

21. No. of Pages 

94 

22. Price 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized 

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TABLE OF CONTENTS 

FOREWORD.................................................................................................................................. i 

NOTICE.......................................................................................................................................... i 

QUALITY ASSURANCE STATEMENT ................................................................................... i 

TABLE OF CONTENTS ............................................................................................................ iii 

LIST OF FIGURES ...................................................................................................................... v 

LIST OF TABLES..................................................................................................................... viii 

CHAPTER 1. INTRODUCTION............................................................................................... 1 

SCOPE OF STUDY............................................................................................................... 2 

RESEARCH APPROACH ................................................................................................... 2 

Summarize Existing Relationships ............................................................................... 2 

Site Inventory and Data Collection............................................................................... 2 

Operational Model Development .................................................................................. 3 

CHAPTER 2. LITERATURE REVIEW................................................................................... 5 

NCHRP REPORT 572 METHOD ....................................................................................... 5 

HCM 2010 METHOD ........................................................................................................... 6 

HCM 2010 ROUNDABOUT MODEL CALIBRATION................................................... 7 

Bend, OR ......................................................................................................................... 9 

California......................................................................................................................... 9 

Carmel, IN..................................................................................................................... 10 

Wisconsin....................................................................................................................... 11 

Kansas............................................................................................................................ 11 

OTHER CAPACITY INFLUENCES................................................................................ 12 

ALTERNATIVE ROUNDABOUT CAPACITY MODELS............................................ 12 

CHAPTER 3. DATA CHARACTERISTICS.......................................................................... 15 

SITE INVENTORY............................................................................................................. 15 

Single-Lane Sites........................................................................................................... 21 

Multilane Sites .............................................................................................................. 23 

DATA COLLECTION AND REDUCTION..................................................................... 26 

CHAPTER 4. PARAMETRIC ANALYSES ........................................................................... 31 

CRITICAL HEADWAY..................................................................................................... 31 

Single-Lane Critical Headway..................................................................................... 31 

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Multilane Critical Headway ........................................................................................ 32 

FOLLOW-UP TIME........................................................................................................... 35 

Single-Lane Follow-Up Times ..................................................................................... 35 

Multilane Follow-Up Time........................................................................................... 36 

GEOMETRIC PARAMETRIC ANALYSIS .................................................................... 38 

CHAPTER 5. MODEL DEVELOPMENT.............................................................................. 45 

ASSESSMENT OF HCM 2010 MODEL .......................................................................... 45 

Single-Lane Model........................................................................................................ 45 

Multilane Models.......................................................................................................... 46 

DEVELOPMENT OF SINGLE-LANE MODELS........................................................... 50 

Regression ..................................................................................................................... 50 

Calibration .................................................................................................................... 51 

Localized Regression.................................................................................................... 53 

Regression Model Form ............................................................................................... 55 

DEVELOPMENT OF MULTILANE MODELS ............................................................. 61 

Regression ..................................................................................................................... 62 

Calibration .................................................................................................................... 65 

INFLUENCE OF EXITING VEHICLES ......................................................................... 69 

ANALYSIS OF CAPACITY TRENDS OVER TIME..................................................... 75 

SUMMARY OF MODEL DEVELOPMENT................................................................... 79 

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS .......................................... 83 

REFERENCES............................................................................................................................ 85 

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LIST OF FIGURES 

Figure 1. Equation. Capacity model for single lane roundabouts from NCHRP Report 

572................................................................................................................................................... 5 

Figure 2. Equation. Capacity model for critical lane of multilane roundabouts from 

Figure 4. Equation. HCM 2010 capacity model for one-lane entry conflicting with one 

Figure 5. Equation. HCM 2010 capacity model for right lane of two-lane entry conflicting 

Figure 6. Equation. HCM 2010 capacity model for left lane of two-lane entry conflicting 

Figure 7. Equation. HCM 2010 capacity model for each lane of a two-lane entry conflicting 

Figure 8. Equation. HCM 2010 capacity model for one-lane entry conflicting with two 

Figure 20. Scatter Plot. Assessment of HCM 2010 model for single-lane roundabout sites.46 

Figure 21. Scatter Plot. Assessment of HCM 2010 model for 2x2 multilane roundabout sites 

Figure 22. Scatter Plot. Assessment of HCM 2010 model for 2x2 multilane roundabout sites 

Figure 23. Scatter Plot. Assessment of HCM 2010 model for 2x1 multilane roundabout sites 

Figure 24. Scatter Plot. Assessment of HCM 2010 model for 2x1 multilane roundabout sites 

NCHRP Report 572. .................................................................................................................... 5 

Figure 3. Equation. Siegloch capacity model.............................................................................. 6 

circulating lane.............................................................................................................................. 6 

with two circulating lanes............................................................................................................. 7 

with two circulating lanes............................................................................................................. 7 

with one circulating lane. ............................................................................................................. 7 

circulating lanes. ........................................................................................................................... 7 

Figure 9. Equation. Capacity model for single-lane roundabouts in Bend, OR.(5) ................ 9 

Figure 10. Equation. Capacity model for multilane roundabouts in Bend, OR.(5) ................. 9 

Figure 11. Equation. Capacity model for single-lane roundabouts in California.(6).............. 9 

Figure 12. Equation. Capacity model for multilane roundabouts in California.(6).............. 10 

Figure 13. Equation. Capacity model for single-lane roundabouts in Carmel, IN.(7).......... 10 

Figure 14. Image. Example of nonvisible back of queue. ........................................................ 26 

Figure 15. Image. Example of rolling queues. .......................................................................... 27 

Figure 16. Scatter Plot. Follow-up time vs. inscribed circle diameter. .................................. 39 

Figure 17. Scatter Plot. Follow-up time vs. entry lane width.................................................. 40 

Figure 18. Scatter Plot. Follow-up time vs. entry angle. ......................................................... 41 

Figure 19. Scatter Plot. Follow-up time vs. splitter island width. .......................................... 42 

and right entry lane. ................................................................................................................... 47 

and left entry lane. ...................................................................................................................... 48 

and right entry lane. ................................................................................................................... 49 

and left entry lane. ...................................................................................................................... 50 

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Figure 25. Scatter Plot. Regression models for single-lane roundabout sites........................ 51 

Figure 26. Equation. Follow-up headway as a field-observable parameter to calibrate the 

y-intercept.................................................................................................................................... 51 

Figure 27. Scatter Plot. Regression models for single-lane roundabout sites with calibration 

to follow-up time. ........................................................................................................................ 52 

Figure 28. Scatter Plot. Regression models for single-lane roundabout sites, normalized by 

follow-up time.............................................................................................................................. 53 

Figure 31. Scatter Plot. Regression models for Carmel, IN data. 

Figure 33. Scatter Plot. Exponential regression of group means, predicted vs. measured 

.......................................... 55 

Figure 32. Scatter Plot. Regression of group means for single-lane sites. ............................. 56 

entering flow, for single-lane sites. ............................................................................................ 57 

Figure 34. Scatter Plot. Linear regression of group means, predicted vs. measured entering 

flow for single-lane sites.............................................................................................................. 58 

Figure 35. Scatter Plot. Regression of group means for Carmel-only single-lane 

roundabout sites.......................................................................................................................... 59 

Figure 36. Scatter Plot. Regression of group means for non-Carmel single-lane roundabout 

sites. .............................................................................................................................................. 60 

Figure 37. Scatter Plot. Regression models for two approaches at a single roundabout in 

Carmel, IN. .................................................................................................................................. 61 

Figure 38. Scatter Plot. Regression models for multilane, 2x2 roundabout sites, right entry 

lane. .............................................................................................................................................. 62 

Figure 39. Scatter Plot. Regression models for multilane, 2x2 roundabout sites, left entry 

lane. .............................................................................................................................................. 63 

Figure 40. Scatter Plot. Regression models for multilane, 2x1 roundabout sites, right entry 

lane. .............................................................................................................................................. 64 

Figure 41. Scatter Plot. Regression models for multilane, 2x1 roundabout sites, left entry 

lane. .............................................................................................................................................. 65 

Figure 42. Scatter Plot. Regression models for multilane 2x2 roundabout sites, right entry 

lane with calibration to follow-up time. .................................................................................... 66 

Figure 43. Scatter Plot. Regression models for multilane 2x2 roundabout sites, left entry 

lane with calibration to follow-up time. .................................................................................... 67 

Figure 44. Scatter Plot. Regression models for multilane 2x1 roundabout sites with 

calibration matching the y-intercept to the 2x2 roundabout, right entry lane. .................... 68 

Figure 45. Scatter Plot. Regression models for multilane 2x1 roundabout sites, combined 

right and left entry lanes with calibration to combined follow-up time. ............................... 69 

Figure 46. Equation. Equation incorporating constant exiting vehicles flow to calculate 

effective conflicting flow............................................................................................................. 70 

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Figure 47. Scatter Plot. Regression models for single-lane sites with calibration to follow-up 

time and constant effects of exiting vehicles............................................................................. 71 

Figure 48. Equation. Equation incorporating variable exiting vehicle flow to calculate 

effective conflicting flow............................................................................................................. 72 

Figure 49. Scatter Plot. Regression models for single-lane sites with calibration to follow-up 

time and variable effects of exiting vehicles. ............................................................................ 73 

Figure 50. Scatter Plot. Regression models for 2x2 multilane roundabout sites and left 

entry lane with calibration to follow-up time and constant effects of exiting vehicles......... 74 

Figure 51. Scatter Plot. Regression models for 2x2 multilane roundabout sites and left 

entry lane with calibration to follow-up time and variable effects of exiting vehicles. ........ 75 

Figure 52. Scatter Plot. Comparison of 2003 and 2012 flow data for single-lane roundabout 

site (WA04 North Leg)................................................................................................................ 76 

Figure 53. Scatter Plot. Comparison of 2003 and 2012 flow data for multilane roundabout 

site VT03 east leg, right lane. ..................................................................................................... 77 

Figure 54. Scatter Plot. Comparison of 2003 and 2012 flow data for multilane roundabout 

site VT03 south leg, right lane. .................................................................................................. 78 

Figure 55. Scatter Plot. Comparison of 2003 and 2012 flow data for multilane roundabout 

site VT03 west leg, right lane. .................................................................................................... 79 

Figure 56. Equation. Model Summary, Exponential Model Form......................................... 80 

Figure 57. Equation. Model Summary, Linear Model Form.................................................. 80 

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LIST OF TABLES 

Table 1. Critical headway and follow-up headways for single-lane roundabouts. ................. 8 

Table 2. Critical headway and follow-up headways for multilane roundabouts. ................... 8 

Table 3. Roundabout sites where video data were collected................................................... 16 

Table 4. Summary of single-lane roundabout data.................................................................. 22 

Table 5. Summary of multilane 2x2 roundabout configuration data. ................................... 24 

Table 6. Summary of multilane 2x1 roundabout configuration data. ................................... 25 

Table 7. Summary of multilane 1x2 roundabout configuration data. ................................... 25 

Table 8. Example of data binning, where shaded rows representing arrival times of 

12:01:46 to 12:02:47 are a valid one-minute data point. ......................................................... 28 

Table 16. RMSE for data sets applied to the HCM 2010 model for single-lane roundabout 

Table 17. RMSE for data sets applied to the HCM 2010 model for multilane roundabout 

Figure 29. Equation. Revised exponential model based on single-lane data from Carmel, 

Table 9. Example of coded events, where coded events (5, 6, 13-16) are shaded. ................. 29 

Table 10. Critical headway estimates for single-lane sites. ..................................................... 32 

Table 11. Results for critical headways in multilane roundabouts. ....................................... 33 

Table 12. Summary of results for critical headway in multilane roundabouts..................... 34 

Table 13. Follow-up time estimates for single-lane roundabout sites. ................................... 36 

Table 14. Follow-up time estimates for multilane roundabout sites. ..................................... 37 

Table 15. Results of the geometric parameter correlation analysis ....................................... 39 

sites. .............................................................................................................................................. 45 

sites. .............................................................................................................................................. 46 

IN. ................................................................................................................................................. 54 

Figure 30. Equation. Revised linear model based on single-lane data from Carmel, IN. .... 54 

Table 18. Regression analysis of the Carmel-based model. .................................................... 54 

Table 19. Comparison of single-lane roundabout models....................................................... 80 

Table 20. Comparison of multilane roundabout models......................................................... 81 

Table 21. Recommended models for roundabout types, configuration, and entry lanes..... 83 

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CHAPTER 1. INTRODUCTION 

The debate over the best way to model the operational performance of roundabouts in the United 

States has had a colorful history over the past twenty years. In the early days of practice in the 

United States, there were no models available that were developed and/or calibrated to 

conditions found in the United States. Practitioners used models from other countries, primarily 

Australia (i.e., SIDRA) and the United Kingdom (i.e., RODEL or ARCADY), to analyze 

roundabouts and make design decisions. 

In 2002, the National Cooperative Highway Research Program (NCHRP) initiated NCHRP 

Project 03-65, of which one objective was to collect operational data (collected during 2003) and 

develop performance models based on observed conditions in the United States. The outcomes of 

this study were published in NCHRP Report 572,(1) which included an early draft chapter 

intended for the Highway Capacity Manual (HCM) on the analysis of roundabouts. The 

Transportation Research Board (TRB) Committee on Highway Capacity and Quality of Service 

evaluated the results of the NCHRP Report 572 work, made modifications based on committee 

and subcommittee member input, and adopted two new chapters on roundabouts into the 

Highway Capacity Manual 2010.(2) These chapters, Chapter 21 and Chapter 33, form the main 

chapters and supplemental information on roundabout operational analysis, respectively. The 

adoption of this methodology into the HCM was significant in that it established a model in an 

industry-accepted document that can be applied consistently alongside methodologies for 

conventional intersection forms. 

The NCHRP Report 572 study was significant in being the first major study of roundabout 

operational performance in the United States. However, it uncovered significant differences 

between observed operational performance of roundabouts in the United States and what had 

been observed in other countries. Some of the key observations from that study are directly 

applicable to the development of updated capacity models performed for this project. Those 

observations include: 

Driver-to-driver variation within a given site. The data observed showed considerable variation 

from minute to minute for a given site (in this document, “site” refers to a single approach within 

a roundabout), and this variation when aggregated across all sites creates a variance in capacity 

that appears to be intrinsic to the operation of the roundabout. From a practical standpoint, this 

means that any capacity estimates have an uncertainty associated with them that is inherently 

part of estimating the performance of an unsignalized intersection where capacity is a function of 

individual driver decisions. This led to the recommendation of a simple model where only 

aggregate geometric parameters in terms of number of lanes were found to be statistically 

significant. 

Perception that capacity will increase over time. The number and diversity of sites available to 

the researchers in 2003 was constrained to approximately 300 roundabouts known to exist at that 

time. Most of these were recently constructed and thus were not necessarily operating to their 

design condition, or under saturated conditions. An underlying hypothesis in this study is that an 

increase in capacity would be realized over time as drivers become more familiar with 

roundabouts. 

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Use of turn signals on exit. This factor, looked at in the more general context of the effect of 

exiting vehicles on entry capacity, has been evaluated in previous research and is worth 

examining in this study (for example, Mereszczak et al. 2005). 

Suboptimal design. Some have speculated that sites operating with some degree of queuing may 

have had design features which caused them to operate less optimally than would be desired, 

particularly for multilane roundabouts. Example design features included poor entry path 

alignment (path overlap) that caused poor lane utilization. Under these design conditions, while 

the right lane of the entry was operating under queued conditions and thus could be measured, 

the left lane often would have either intermittent or no queues. 

Other factors that may influence capacity but are not likely to be of significance for this study. 

These include a fleet of larger vehicles relative to other countries, which affects acceleration and 

following distance, and the general dominance of stop control versus yield control in the United 

States, which is believed to contribute to a tendency to stop or nearly stop even when faced with 

yield control and no conflicting vehicles. 

SCOPE OF STUDY 

The scope of this study includes the following activities and products: 

• Develop an updated site inventory of selected roundabouts accessible to the 

transportation profession. 

• Update and expand on a comprehensive database of operational data of selected 

roundabouts for use in the research. 

• Develop an updated operational analysis procedure for the HCM, including capacity 

estimates for single-lane and multilane roundabouts. 

RESEARCH APPROACH 

The detailed approaches for each of the major components of this study are described in the 

following sections. 

Summarize Existing Relationships 

A literature review, presented in chapter 2, focuses on efforts to analyze the capacity of 

roundabouts in the United States, building upon the research and methodologies in NCHRP 

Report 572 and HCM 2010. This review is targeted on identifying calibration or new modeling 

efforts within the U.S. For a more holistic review of roundabout capacity models used 

throughout the world, refer to NCHRP Report 572. 

Site Inventory and Data Collection 

A major element of the study included updating and expanding the inventory of U.S. 

roundabouts compiled for NCHRP Report 572. At selected sites, the research team collected and 

summarized data on operational performance and geometric parameters. Specific data collection 

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methods included extensive video recording during peak and off-peak periods. These methods 

are described in detail in chapter 3. 

Operational Model Development 

Operational model development included the following tasks: 

• Estimate critical headway and follow-up headway for each site and for the population of 

sites studied. 

• Examine geometric parameters. 

• Compare field data to the HCM 2010 model and regression. 

• Perform an empirical regression of observed capacity as a function of circulating flow. 

• Develop a draft revised HCM procedure that incorporates the findings from this study. 

These are discussed in detail in chapters 4 and 5, with conclusions and recommendations 

presented in chapter 6. 

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CHAPTER 2. LITERATURE REVIEW 

To support the research approach documented herein, an extensive literature review was 

completed to identify calibration or new modeling efforts within the United States, building upon 

the research and methodologies in NCHRP Report 572(1) and the HCM 2010.(2) The following 

section provides a summary of the literature review and documents key findings 

NCHRP REPORT 572 METHOD 

The NCHRP Report 572 models show less capacity than many international models, because 

data has suggested that U.S. drivers do not use roundabouts as aggressively as other countries, 

including many European countries and Australia. Further, NCHRP Report 572 found that while 

aggregate geometric details such as number and assignment of lanes was significant in 

determining capacity, the fine details of geometric design, such as lane width, could not be 

distinguished due to considerable variation within driver behavior at a given location. 

From the research conducted in NCHRP Report 572, the following capacity models were 

developed for U.S. roundabouts. For single-lane roundabouts, the equation in figure 1 applies. 

Figure 1. Equation. Capacity model for single lane 

roundabouts from NCHRP Report 572. 

Where c = entry capacity (pc/h) and vc = conflicting flow (pc/h). 

For multilane roundabouts, the equation in figure 2 applies. 

Figure 2. Equation. Capacity model for critical lane of multilane 

roundabouts from NCHRP Report 572. 

Where ccrit = entry capacity of critical lane (pc/h) and vc = conflicting flow (pc/h). 

In the case of multilane roundabouts, per NCHRP Report 572, the capacity is calculated for the 

critical lane. 

The NCHRP Report 572 researchers developed the analysis methodologies such that the capacity 

models could be updated to reflect local conditions or changing national conditions. This allows 

the assumed capacity to be increased or decreased depending upon two key parameters related to 

driver behavior: critical headway and follow-up headway. The analytical model form that most 

closely matches the regression model form is the Siegloch model. (See reference 3, as presented 

in 4.) As such, the exponential model parameters can be calibrated using locally measured 

parameters in the Siegloch model as shown in figure 3. 

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Figure 3. Equation. Siegloch capacity model. 

Where C = entry capacity (pcu/h), vc = conflicting flow (pcu/h), tf = follow-up headway (s), and 

tc = critical headway (s). 

The calibration factors may differ between geographical areas based on driver familiarity with 

roundabouts and/or overall aggressiveness. In addition, calibration factors may change within a 

geographical area over time after roundabouts are introduced and drivers become more familiar 

with roundabout operations. 

HCM 2010 METHOD 

The roundabout procedure included in the HCM 2010 is based on the method described in 

NCHRP Report 572, but with a number of modifications. For example, in HCM 2010, 

circulating flow is converted to passenger-car-equivalents (PCEs) to determine capacity and is 

then converted back to vehicles for use in volume-to-capacity, control delay, and queue 

calculations. The control delay equation presented in NCHRP Report 572 is modified in the 

HCM 2010 to adapt the stop-controlled control delay equation for two-way stop-controlled 

(TWSC) intersections for use in the yield-controlled environment at a roundabout. The final term 

of the control delay equation for roundabouts includes a “+ 5 * min[v/c,1]” term. At v/c=0, the 

term is zero (reflecting a low likelihood of coming to a complete stop); at v/c>=1, the term is five 

(reflecting a high likelihood of coming to a complete stop); and it is linear between v/c=0 and 

one. Additionally, in the HCM 2010, on multilane approaches, a lane utilization factor of 0.53 

was assumed for the lane deemed to be dominant. Level of Service (LOS) is determined for the 

intersection as a whole, all approaches, and all lanes, not just the critical lane as in NCHRP 

Report 572. The control delay thresholds to determine LOS are based on what is currently used 

for other unsignalized intersections. For consistency with other methods in HCM 2010, LOS F 

includes the condition where v/c exceeds 1.0. These modifications result in minor differences 

from the original procedure proposed by NCHRP Report 572. 

As a result of these modifications, the HCM 2010 presents a larger set of capacity models to 

cover a variety of lane configurations, including hybrid combinations of one-lane and two-lane 

entries and circulatory roadways. For a one-lane entry conflicting with one circulating lane (such 

as at single-lane roundabouts), the equation in figure 4 applies. 

Figure 4. Equation. HCM 2010 capacity model for one-lane entry conflicting with one 

circulating lane. 

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Where ce,pce = entry capacity (pc/h) and vc,pce = conflicting flow (pc/h). 

For multilane roundabouts, the choice of equation depends on the number of entry lanes and the 

number of conflicting circulating lanes. For a two-lane entry conflicting with two circulating 

lanes, the equation in figure 5 applies to the right entry lane, and the equation in figure 6 applies 

to the left entry lane. For a two-lane entry conflicting with one circulating lane, the equation in 

figure 7 applies to each entry lane. For a one-lane entry conflicting with two circulating lanes, 

the equation in figure 8 applies. 

Figure 5. Equation. HCM 2010 capacity model for right lane 

of two-lane entry conflicting with two circulating lanes. 

Figure 6. Equation. HCM 2010 capacity model for left lane 

of two-lane entry conflicting with two circulating lanes. 

Figure 7. Equation. HCM 2010 capacity model for each lane 

of a two-lane entry conflicting with one circulating lane. 

Figure 8. Equation. HCM 2010 capacity model for one-lane entry 

conflicting with two circulating lanes. 

Where ce,pce = entry capacity (pc/h) and vc,pce = conflicting flow (pc/h). 

HCM 2010 ROUNDABOUT MODEL CALIBRATION 

Based on the recommendations outlined in NCHRP Report 572 and HCM 2010, several 

jurisdictions have developed and documented local calibration efforts of the capacity models in 

NCHRP Report 572 and HCM 2010. These efforts provide an opportunity to distinguish local 

driving conditions from a more generalized national model. Most notably, the following studies 

were found: Bend, OR;

(5) California;(6) Carmel, IN;(7) Wisconsin;(8) Maryland;(9) and Kansas.(10) 

Table 1 and table 2 below show the critical headways and follow-up headways reported in the 

studies discussed for single-lane and multilane roundabouts, respectively. The table suggests a 

wide range of potential observations. Further commentary on some of these studies, included 

recommended models, is provided below. 

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Table 1. Critical headway and follow-up headways for single-lane roundabouts. 

Gap 

Acceptance 

Parameters 

NCHRP 

Report 572(1) 

(s) 

Bend, OR(5) 

(s) 

California(6) 

(s) 

Carmel, IN(7)

(s) 

Wisconsin(8) 

(s) 

Maryland(9) 

(s) 

Kansas(10) 

(s) 

Critical 

Headway 5.1 4.1 4.5-5.3 3.4-3.8 4.8-5.5 2.5-2.6 

No change 

from NCHRP 

Report 572 

Follow-up 

Headway 3.2 2.7 2.3-2.8 2.1-2.4 2.6-3.8 Not studied 

No change 

from NCHRP 

Report 572 

Table 2. Critical headway and follow-up headways for multilane roundabouts. 

Gap 

Acceptance 

Parameters 

NCHRP 

Report 572(1)

(s) 

Bend, OR(5) 

(s) 

California(6)

(s) 

Carmel, IN(7)

(s) 

Wisconsin(8) 

(s) 

Maryland(9)

(s) Kansas(10) (s) 

Critical 

Headway, 

Right Lane 

4.2 Not studied 4.0-4.8 Not studied 3.4-4.4 Not studied Not studied 

Critical 

Headway, 

Left Lane 

4.5 Not studied 4.4-5.1 Not studied 4.1-4.8 Not studied Not studied 

Follow-up 

Headway, 

Right Lane 

3.1 Not studied 2.1-2.3 Not studied 2.2-3.0 Not studied Not studied 

Follow-up 

Headway, 

Left Lane 

3.4 Not studied 1.8-2.7 Not studied 2.5-3.1 Not studied Not studied 

8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Bend, OR 

The effort conducted for Bend, OR, specifies a variety of analysis parameters, including LOS 

thresholds, queuing analysis procedures, and other such considerations.(5) In addition, data were 

collected at existing roundabouts within Bend to determine local driver characteristics. Based on 

that effort, the capacity model in figure 9 was recommended for use for single-lane roundabout 

analyses within the city, and the capacity model in figure 10 was recommended for use in 

multilane roundabout analyses. 

Figure 9. Equation. Capacity model for 

single-lane roundabouts in Bend, OR.(5) 

Figure 10. Equation. Capacity model for 

multilane roundabouts in Bend, OR.(5) 

Where cpe = capacity, adjusted for heavy vehicles (pc/h), and vc,pce = conflicting circulating flow 

rate, adjusted for heavy vehicles (pc/h). 

In this case, the single-lane model was calibrated to produce a higher capacity then the national 

average. However, no multilane roundabouts existed within the city limits at the time of the 

calibration study. As such, the national model was included in an unmodified form. 

It should be noted that Bend has a large number of roundabouts and, as a result, a driver 

population that is likely more familiar with roundabouts than the average U.S. citizen. Based on 

this, Bend, OR’s finding that the roundabouts within Bend operate at a higher capacity that what 

was shown in NCHRP Report 572 suggests the possibility that driver population familiarity with 

roundabouts can increase the observed capacity. 

California 

Tian et al. developed a set of calibrated roundabout analysis equations for use by Caltrans 

throughout the state of California.(6) These analyses were based on data collected at nine 

representative roundabouts locations throughout the state. Based on the data collected, the 

calibrated equation in figure 11 was developed for single-lane roundabouts, and the equations in 

figure 12 was developed for multilane roundabouts. 

Figure 11. Equation. Capacity model for 

single-lane roundabouts in California.

(6) 

9 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 12. Equation. Capacity model for 

multilane roundabouts in California.(6) 

Where Cpe = capacity, adjusted for heavy vehicles (pc/h), and vc,pce = conflicting circulating 

flow rate, adjusted for heavy vehicles (pc/h). 

California results were able to make predictions about the capacity of multilane roundabouts by 

lane. As such, the resultant capacity equations are more consistent with the procedures outlined 

in HCM 2010. 

Of particular note, the critical headways observed by the Caltrans calibration effort were not 

found to be statistically different from what was developed for NCHRP Report 572. However, 

the follow-up headways, which were found to be considerably lower than what was produced by 

NCHRP Report 572, were determined to be statistically different. 

Further, conflicting flow rate and speed were found to have moderate to low negative correlation 

with both critical headway and follow-up headway. With an increase in conflicting flow and/or 

speed, the critical headway and follow-up headway tend to decrease. The results from the 

correlation analyses indicate that the correlation between speed and follow-up headway is the 

strongest, and the correlation between conflicting flow and follow-up headway is the weakest. 

Carmel, IN 

While some jurisdictions have focused on calibrating the existing NCHRP Report 572 model, 

others have developed new models altogether due to poor fit with a calibrated HCM 2010 model. 

This approach was taken in Carmel, IN, which is known to have one of the largest concentrations 

of roundabouts in the United States. Wei, Grenard and Shah(7) developed a method to derive a 

simplified and calibrated linear equation based on observations made at three single-lane 

roundabouts within Carmel. The developed method is shown in figure 13. 

Figure 13. Equation. Capacity model for 

single-lane roundabouts in Carmel, IN.

(7) 

Where c = capacity of the approach (veh/h), and vc = conflicting flow (veh/h). 

Based on this procedure, the research team found that roundabouts in Carmel operate with a 

higher capacity than what was predicted by NCHRP Report 572. 

In the case of Carmel, the developed model cannot easily be calibrated to other jurisdictions. 

Rather, the developers of this model suggest that other locations develop similar local models by 

enacting a similar process. While this approach likely produces reasonable results for the local 

area, producing a similar model for other jurisdictions would require that the area have 

10 
 

 

 

 

 

 

 

 

 

 

 

 

 

roundabouts at which to collect data. Until that time, national models would likely have to be 

relied upon. 

Wisconsin 

The Wisconsin DOT analysis of roundabouts within the state of Wisconsin collected data for 14 

roundabouts including both single and multilane varieties.(8) Of these, two single-lane and two 

multilane roundabouts were analyzed in depth to determine operational characteristics of 

roundabouts specifically related to Wisconsin drivers. 

The findings of this analysis showed that the critical and follow-up headways observed were 

within the data ranges reported by NCHRP Report 572. Also, consistent with current thinking, 

the critical and follow-up headways were observed to decrease as congestion increased. In 

addition, larger vehicles, such as trucks, were found to have higher critical and follow-up 

headways while smaller vehicles, such as motorcycles, were found to have lower critical and 

follow-up headways than was observed for traditional passenger cars. 

Kansas 

The Kansas DOT commissioned a study to look at calibrating the HCM 2010 equations for use 

in Kansas. The roundabout calibration effort collected data for 10 roundabouts within the 

state.

(10) Of those, three were analyzed in more detail. Specifically, critical headway and followup headway were calculated for the purpose of producing calibrated roundabout analysis models 

for single-lane roundabouts. 

During the calculation of critical headway, the researchers identified an issue when using the 

critical headway calculation method used by NCHRP Report 572 (which is based on the twoway stop-controlled model included in the HCM). Specifically, they attempted to calculate 

critical headway by statistically estimating the minimum headway between circulating vehicles 

that an entering driver would most likely accept based on the gap or gaps the entering driver was 

observed to reject and the gap the entering driver actually accepted. 

This method averages all accepted gap times as recorded, which is well suited for high volume 

sites where there is a somewhat consistent stream of circulating traffic. However, as circulating 

volume decreases and headways between circulating vehicles increase, this method tends to 

produce large estimate critical headway values. For example, if a series of circulating vehicles 

pass and there is a full minute gap before the next circulating vehicle arrives, this method would 

produce an accepted gap time of 60 s. A driver clearly would not require a 60 s gap under normal 

conditions. As such, this method can produce results that higher critical headway values than one 

would expect. 

To address this issue, the Kansas researchers also used the method employed by the researchers 

of the California roundabout calibration effort described earlier. Specifically, this modified 

approach caps all accepted gap values at 8.0 s, meaning any recorded gap longer than 8.0 s is 

modified and a value of 8.0 s is used for critical headway calculations. 

Based on using the modified method originally used by the California researchers, the Kansas 

research team produced critical headway and follow-up headway results that were not 

11 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

statistically different than NCHRP Report 572 results. As such, the team concluded that the 

national models produced by NCHRP Report 572 were adequate for roundabout analysis in 

Kansas without further modification. 

OTHER CAPACITY INFLUENCES 

Recent research has shown that roundabout characteristics not currently accounted for in analysis 

models may have a positive impact on the ability to calculate capacities. Specifically, the 

Wisconsin DOT report(10) and Mereszczak, et al.(11) each quantified the effects of exiting vehicles 

on overall roundabout capacity. For example, if a vehicle is exiting, a driver might be more 

willing to enter the roundabout than if the roundabout were not exiting. Mereszczak, et al.(11) 

expanded on Hagring’s research(12) that showed the capacity of a given approach will increase 

when the proportion of exiting vehicles increases even when the major street flow remains the 

same. Wisconsin researchers evaluated the effect that exiting vehicles have on the calculation of 

critical and follow-up headway calculations, which also directly affect the calculation of 

capacities at roundabouts, as described previously. As shown, the consideration of exiting 

vehicles reduced the calculated critical headway and follow-up headway in all scenarios 

presented. The researchers attribute this to the observation that when entering drivers rejected 

long headways in the circulating stream, there usually was a vehicle exiting during that period. 

By accounting for exiting vehicles, those long headways were able to be reduced. 

ALTERNATIVE ROUNDABOUT CAPACITY MODELS 

Although HCM 2010 uses the research in NCHRP Report 572 as the basis of the procedure 

included in the manual, other methods are identified in the manual as alternatives where the 

HCM method might not be applicable. In reality, the application of HCM 2010 appears to be 

uneven around the United States, likely because software programs are in the process of 

incorporating the new or updated methodologies into their respective platforms, and because 

other software packages implementing international methods(13,14) have been in use for many 

years. 

Evaluations of HCM 2010 methods to other roundabout capacity models may yield strikingly 

different results for certain movements. The discrepancies highlighted a key concern facing 

roundabout analysis procedures in the United States today: with the number of analysis 

procedures being applied to roundabout analyses, results may indicate both favorable and 

unfavorable operational results for the same analysis scenario depending upon what 

methodology is used. Further, favorable or unfavorable results may be dictated by the 

availability of local calibration factors. For the case of roundabouts where a number of 

deterministic models can be applied, analysts may be expected to interpret the reasonableness of 

very technical models and their applicability to a specific project. 

Methods other than traditional gap acceptance or empirical regression techniques have been used 

outside the United States. Specifically, the additive conflict flow (ACF) method was evaluated in 

Germany for use in estimating the performance of mini-roundabouts.(15) The ACF method was 

developed as a new technique for TWSC intersection analysis as an alternative to the theory of 

gap acceptance, on which the current TWSC and roundabout methodologies in HCM 2010 are 

based. Researchers argue that this method is more intuitive than the priority system currently 

12 
 

 

 

applied to TWSC because movement priority rankings do not always make sense when 

considering pedestrian interactions. A distinct advantage of the ACF method is the ability to 

calculate in a single step the capacity for any stream of traffic as a function of traffic volumes of 

other streams. This reality highlights the ACF methods as a substitute to gap acceptance theory, 

especially when pedestrian movements have an effect on normal intersection operations. In the 

case of mini-roundabouts, the ACF method makes it possible to calculate the capacities of miniroundabout entries and exits while taking crossing pedestrian streams into account.

(16) 

13 

 

 

 

 

 

 

 

 

 

 

CHAPTER 3. DATA CHARACTERISTICS 

The following section describes the process by which an updated inventory of roundabouts in the 

United States was developed, including site selection, data collection, and data reduction. 

SITE INVENTORY 

One of the products of this research is an updated site inventory that contains information on 

selected roundabouts. A range of site characteristics is vital to the successful development of 

models with sensitivity to a range of influencing factors. These characteristics are that the sites: 

• Have a high likelihood of queued conditions for some portion of the day, preferably at 

least fifteen minutes, on at least one approach. 

• Have a range of approach versus circulatory roadway lane configurations (e.g., singlelane approach vs. two-lane circulatory roadway, etc.). 

• Include multiple sites within approximately one hour drive time to maximize data 

collection resources. 

• Include diversity in geography and driver type. 

• Have a range of geometric conditions, such as splitter island widths. 

• Include overlapping sites with those in NCHRP Report 572 to demonstrate potential 

change in performance over time. 

• Are overlapped with or in close proximity to NCHRP Project 03-100 sites for data 

collection efficiency. 

Table 3 displays a summary of sites observed as part of this study. 

15 
Table 3. Roundabout sites where videodata were collected. 

Community Intersection Intersection 

Code 

Leg No. of 

Entering 

Lanes 

No. of 

Circulating 

Lanes 

No. of 

Exiting 

Lanes 

Eagle, CO Eby Creek Road/US 6 (Grand Avenue) CO01 S 1 1 1 

Eagle, CO Eby Creek Road/US 6 (Grand Avenue) CO02 W 1 1 1 

Eagle, CO Eby Creek Road/US 6 (Grand Avenue) CO03 N 2 1 1 

Eagle, CO Eby Creek Road/US 6 (Grand Avenue) CO04 E 1 1 2 

Golden, CO Golden Road/Johnson Road/16th Street CO02 N 1 2 1 

Golden, CO Golden Road/Johnson Road/16th Street CO03 W 2 2 2 

Golden, CO Golden Road/Johnson Road/16th Street CO04 E 2 2 2 

Golden, CO Golden Road/Johnson Road/16th Street CO05 S 2 2 2 

Golden, CO Golden Road/Ulysses Street CO38 N 1 1 1 

Golden, CO Golden Road/Ulysses Street CO39 E 1 1 1 

Golden, CO Golden Road/Ulysses Street CO40 S 1 1 1 

Golden, CO Golden Road/Ulysses Street CO41 W 1 1 1 

Avon, CO Beaver Creek Boulevard/Avon Road CO06 N 3 2 2 

Avon, CO Beaver Creek Boulevard/Avon Road CO07 E 3 2 1 

Avon, CO Beaver Creek Boulevard/Avon Road CO08 S 3 2 2 

Avon, CO Beaver Creek Boulevard/Avon Road CO09 W 3 2 1 

Avon, CO Benchmark Road/Avon Road CO07 N 2 2 2 

Avon, CO Benchmark Road/Avon Road CO08 E 2 2 1 

Avon, CO Benchmark Road/Avon Road CO09 S 2 2 2 

Avon, CO Benchmark Road/Avon Road CO10 W 1 2 1 

Avon, CO I-70 EB/Avon Road CO08 S 2 2 2 

Avon, CO I-70 EB/Avon Road CO08 W 2 2 0 

Avon, CO I-70 WB/Avon Road CO09 N 2 2 1 

Avon, CO I-70 WB/Avon Road CO09 E 3 1 0 

Avon, CO US 6/Avon Road/Village Road CO10 N 2 2 2 

Avon, CO US 6/Avon Road/Village Road CO10 E 2 2 1 

Avon, CO US 6/Avon Road/Village Road CO10 S 2 2 2 

Avon, CO US 6/Avon Road/Village Road CO10 W 2 2 1 

16 
Community Intersection Intersection 

Code 

Leg No. of 

Entering 

Lanes 

No. of 

Circulating 

Lanes 

No. of 

Exiting 

Lanes 

Vail, CO I-70 EB/Chamonix Road CO49 SW 2 1 0 

Vail, CO I-70 EB/Chamonix Road CO49 NW 1 1 1 

Vail, CO I-70 EB/Chamonix Road CO49 S 1 1 1 

Vail, CO I-70 EB/Chamonix Road CO49 N 1 1 1 

Vail, CO I-70 EB/Chamonix Road CO49 E 1 1 1 

Vail, CO I-70 WB/Chamonix Road CO50 W 2 2 1 

Vail, CO I-70 WB/Chamonix Road CO50 S 2 2 1 

Vail, CO I-70 WB/Chamonix Road CO50 N 2 1 

Vail, CO I-70 WB/Chamonix Road CO50 NE 2 2 0 

Vail, CO I-70 WB/Chamonix Road CO50 SE 2 2 1 

Vail, CO I-70 EB/Vail Road CO51 N 2 2 1 

Vail, CO I-70 EB/Vail Road CO51 E 3 2 2 

Vail, CO I-70 EB/Vail Road CO51 S 2 2 1 

Vail, CO I-70 EB/Vail Road CO51 NW 2 2 0 

Vail, CO I-70 EB/Vail Road CO51 SW 3 2 1 

Vail, CO I-70 WB/Vail Road CO52 SE 2 1 0 

Vail, CO I-70 WB/Vail Road CO52 NE 2 1 1 

Vail, CO I-70 WB/Vail Road CO52 W 2 1 1 

Edwards, CO Miller Ranch Road/Edwards Access Road CO54 N 2 1 2 

Edwards, CO Miller Ranch Road/Edwards Access Road CO54 W 1 2 1 

Edwards, CO Miller Ranch Road/Edwards Access Road CO54 E 2 2 1 

Edwards, CO Miller Ranch Road/Edwards Access Road CO54 S 2 1 2 

Edwards, CO I-70 EB On-Ramp/Edwards Access Road CO55 S 2 1 1 

Edwards, CO I-70 EB On-Ramp/Edwards Access Road CO55 N 1 1 2 

Edwards, CO I-70 EB On-Ramp/Edwards Access Road CO55 W 2 2 0 

Edwards, CO I-70 WB On-Ramp/Edwards Access Road CO56 N 2 2 1 

Edwards, CO I-70 WB On-Ramp/Edwards Access Road CO56 E 2 2 0 

Edwards, CO I-70 WB On-Ramp/Edwards Access Road CO56 S 2 1 2 

Carmel, IN 126th Street/Hazel Dell Parkway IN02 N 2 2 2 

17 
Community Intersection Intersection 

Code 

Leg No. of 

Entering 

Lanes 

No. of 

Circulating 

Lanes 

No. of 

Exiting 

Lanes 

Carmel, IN 126th Street/Hazel Dell Parkway IN02 S 2 1 2 

Carmel, IN 126th Street/Hazel Dell Parkway IN02 E 2 2 1 

Carmel, IN 126th Street/Hazel Dell Parkway IN02 W 2 2 1 

Carmel, IN 116th Street/Illinois Street IN06 S 2 2 2 

Carmel, IN 116th Street/Illinois Street IN06 N 2 2 2 

Carmel, IN 116th Street/Illinois Street IN06 E 2 2 2 

Carmel, IN 116th Street/Illinois Street IN06 W 2 2 2 

Carmel, IN 96th Street/Ditch Road IN07 S 1 1 1 

Carmel, IN 96th Street/Ditch Road IN07 N 1 1 1 

Carmel, IN 96th Street/Ditch Road IN07 E 1 1 1 

Carmel, IN 96th Street/Ditch Road IN07 W 1 1 1 

Carmel, IN 96th Street/Westfield Boulevard IN08 S 2 1 1 

Carmel, IN 96th Street/Westfield Boulevard IN08 N 1 1 1 

Carmel, IN 96th Street/Westfield Boulevard IN08 E 1 1 1 

Carmel, IN 116th Street/Spring Mill Road IN09 S 1 1 1 

Carmel, IN 116th Street/Spring Mill Road IN09 N 1 1 2 

Carmel, IN 116th Street/Spring Mill Road IN09 E 2 1 1 

Carmel, IN 116th Street/Spring Mill Road IN09 W 1 1 1 

Carmel, IN 106th Street/Spring Mill Road IN10 N 1 1 1 

Carmel, IN 106th Street/Spring Mill Road IN10 S 1 1 1 

Carmel, IN 106th Street/Spring Mill Road IN10 E 1 1 1 

Carmel, IN 106th Street/Spring Mill Road IN10 W 1 1 1 

Carmel, IN 136th Street/Keystone Parkway SB IN11 S 0 1 1 

Carmel, IN 136th Street/Keystone Parkway SB IN11 N 1 1 0 

Carmel, IN 136th Street/Keystone Parkway SB IN11 W 2 1 1 

Carmel, IN 136th Street/Keystone Parkway NB IN12 S 1 1 0 

Carmel, IN 136th Street/Keystone Parkway NB IN12 N 0 1 1 

Carmel, IN 136th Street/Keystone Parkway NB IN12 E 1 1 1 

Malta, NY SR 67 (Dunning Street)/US 9 NY06 N 2 2 2 

18 
Community Intersection Intersection 

Code 

Leg No. of 

Entering 

Lanes 

No. of 

Circulating 

Lanes 

No. of 

Exiting 

Lanes 

Malta, NY SR 67 (Dunning Street)/US 9 NY06 E 2 2 1 

Malta, NY SR 67 (Dunning Street)/US 9 NY06 S 2 2 2 

Malta, NY SR 67 (Dunning Street)/US 9 NY06 W 2 2 1 

Glens Falls, NY US 9/Warren Street/Hudson Avenue/Glen Street NY07 W 1 1 1 

Glens Falls, NY US 9/Warren Street/Hudson Avenue/Glen Street NY07 S 1 1 1 

Glens Falls, NY US 9/Warren Street/Hudson Avenue/Glen Street NY07 NE 1 1 1 

Glens Falls, NY US 9/Warren Street/Hudson Avenue/Glen Street NY07 NW 1 1 1 

Glens Falls, NY US 9/Warren Street/Hudson Avenue/Glen Street NY07 E 1 1 1 

Rotterdam, NY Curry Road (SR 7)/Hamburg Street (SR 146) NY08 W 1 1 1 

Rotterdam, NY Curry Road (SR 7)/Hamburg Street (SR 146) NY08 S 1 1 1 

Rotterdam, NY Curry Road (SR 7)/Hamburg Street (SR 146) NY08 N 1 1 1 

Rotterdam, NY Curry Road (SR 7)/Hamburg Street (SR 146) NY08 E 1 1 1 

Slingerlands, NY Lagrange Road (SR 85)/New Scotland Road NY09 N 2 1 2 

Slingerlands, NY Lagrange Road (SR 85)/New Scotland Road NY09 E 2 2 2 

Slingerlands, NY Lagrange Road (SR 85)/New Scotland Road NY09 S 2 1 2 

Slingerlands, NY Lagrange Road (SR 85)/New Scotland Road NY09 W 2 2 2 

Gilbert’s Corner, VA US 50/ US 15 VA01 N 2 1 1 

Gilbert’s Corner, VA US 50/ US 15 VA01 E 1 2 1 

Gilbert’s Corner, VA US 50/ US 15 VA01 S 2 1 1 

Gilbert’s Corner, VA US 50/ US 15 VA01 W 1 2 1 

Brattleboro, VT SR 9/US 5 VT03 W 2 2 1 

Brattleboro, VT SR 9/US 5 VT03 E 2 2 1 

Brattleboro, VT SR 9/US 5 VT03 N 2 2 1 

Port Orchard, WA SR 166/Mile Hill Drive/Bethel Avenue WA04 N 1 1 1 

Port Orchard, WA SR 166/Mile Hill Drive/Bethel Avenue WA04 E 1 1 1 

Monroe, WA 164th Street/SR 522 NB Ramp/Tester Road WA06 E 2 1 2 

Monroe, WA 164th Street/SR 522 NB Ramp/Tester Road WA06 SW 2 2 0 

Monroe, WA 164th Street/SR 522 NB Ramp/Tester Road WA06 S 1 2 1 

Gig Harbor, WA SR 16 NB/Burnham Drive NW/Borgen Boulevard WA09 N 2 2 1 

19 
Community Intersection Intersection 

Code 

Leg No. of 

Entering 

Lanes 

No. of 

Circulating 

Lanes 

No. of 

Exiting 

Lanes 

Gig Harbor, WA SR 16 NB/Burnham Drive NW/Borgen Boulevard WA09 SE 2 2 1 

Gig Harbor, WA SR 16 NB/Burnham Drive NW/Borgen Boulevard WA09 SW 2 2 0 

Gig Harbor, WA SR 16 NB/Burnham Drive NW/Borgen Boulevard WA09 E 2 1 2 

Gig Harbor, WA 4th Avenue/Olympic Street WA31 N 2 1 2 

Gig Harbor, WA 4th Avenue/Olympic Street WA31 S 2 1 1 

Gig Harbor, WA 4th Avenue/Olympic Street WA31 E 2 2 1 

Gig Harbor, WA SR 16 SB/Burnham Drive NW WA32 N 2 2 0 

Gig Harbor, WA SR 16 SB/Burnham Drive NW WA32 W 2 2 1 

Olympia, WA 14th Avenue/Jefferson Street WA30 N 2 2 1 

Olympia, WA 14th Avenue/Jefferson Street WA30 S 2 2 1 

Olympia, WA 14th Avenue/Jefferson Street WA30 E 2 1 2 

Olympia, WA 14th Avenue/Jefferson Street WA30 W 2 2 2 

Lake Stevens, WA Lundeen Park Way/Callow Road WA33 E 1 1 1 

Lake Stevens, WA Lundeen Park Way/Callow Road WA33 W 1 1 1 

Anacortes, WA SR 20 Spur/Commercial Avenue WA34 N 1 1 1 

Anacortes, WA SR 20 Spur/Commercial Avenue WA34 E 1 1 1 

Bellingham, WA Pole Road/SR 539 WA35 N 2 2 2 

Bellingham, WA Pole Road/SR 539 WA35 S 2 2 2 

Bellingham, WA Pole Road/SR 539 WA35 E 1 1 1 

Bellingham, WA Pole Road/SR 539 WA35 W 1 1 1 

20 
 

 

 

 

Single-Lane Sites 

This section summarizes the sites for each roundabout that yielded single-lane data sets. The data 

are summarized in table 4. A total of 819 usable minutes of data were usable for the capacity 

modeling exercise after excluding minutes without queuing and minutes with pedestrian events. 

This is nearly three times as much data as was available in the NCHRP Report 572 study (318 

minutes). 

21 
Table 4. Summary of single-lane roundabout data. 

Subarea Site Site Code Usable Data Points 

Carmel, IN 136th Street/Keystone Parkway NB IN12-E 4 

Carmel, IN 136th Street/Keystone Parkway NB IN12-S 71 

Carmel, IN 96th Street/Ditch Road IN07-E 31 

Carmel, IN 96th Street/Ditch Road IN07-S 10 

Carmel, IN 96th Street/Westfield Boulevard IN08-N 13 

Carmel, IN 116th Street/Spring Mill Road IN09-S 54 

Carmel, IN 116th Street/Spring Mill Road IN09-W 139 

Carmel, IN 106th Street/Spring Mill Road IN10-E 51 

Carmel, IN 106th Street/Spring Mill Road IN10-N 32 

Carmel, IN 106th Street/Spring Mill Road IN10-W 32 

Carmel, IN Subtotal n/a 437 

New York State US 9/Warren Street/Hudson Avenue/Glen Street NY07-S 71 

New York State US 9/Warren Street/Hudson Avenue/Glen Street NY07-W 92 

New York State US 9/Warren Street/Hudson Avenue/Glen Street NY07-E 65 

New York State US 9/Warren Street/Hudson Avenue/Glen Street NY07-NW 13 

New York State US 9/Warren Street/Hudson Avenue/Glen Street NY07-NE 1 

New York State Curry Road (SR 7)/Hamburg Street (SR14) NY08-N 9 

New York State Curry Road (SR 7)/Hamburg Street (SR14) NY08-W 21 

New York State Subtotal n/a 272 

Washington State SR 166/Mile Hill Drive/Bethel Avenue WA04-E 26 

Washington State SR 166/Mile Hill Drive/Bethel Avenue WA04-N 16 

Washington State Lundeen Park Way/Callow Road WA33-E 4 

Washington State Lundeen Park Way/Callow Road WA33-W 13 

Washington State SR 20 Spur/Commercial Avenue WA34-E 7 

Washington State SR 20 Spur/Commercial Avenue WA34-N 5 

Washington State Subtotal n/a 71 

Colorado Eby Creek Road/US 6 (Grand Avenue) CO01-W 39 

All Sites Total Data Points n/a 952 

All Sites Data Points with One or More Pedestrian Events n/a 133 

All Sites Total Usable Data Points n/a 819 

22 
 

 

 

Multilane Sites 

This section summarizes the sites that yielded multilane data set for different multilane 

roundabout configurations. The data from sites with two entering lanes and two circulating lanes 

(hereafter 2x2 sites) are summarized in table 5; data from sites with two entering lanes and one 

circulating lane (hereafter 2x1 sites) are summarized in table 6; and data from sites with one 

entering lane and two circulating lanes (hereafter referred to as 1x2 site) are summarized in table 

7. The data sample for the 1x2 sites is too small to use for model development. However, 711 

minutes of usable data were obtained for the 2x2 case, representing 366 minutes of right-lane 

data and 345 minutes of left-lane data, and 519 minutes of usable data were obtained for the 2x1 

case, representing 231 minutes of right-lane data and 288 minutes of left-lane data. This total of 

1,230 minutes of lane-specific data compares favorably to the NCHRP Report 572 study, where 

a total of 383 minutes of approach data and 473 minutes of lane-specific data were collected. 

23 
Table 5. Summary of multilane 2x2 roundabout configuration data. 

Subarea Site Site Code Usable Data Points -

Right Lane 

Usable Data Points -

Left Lane 

Colorado Golden Road/Johnson Road/16th Street CO02-E n/a 1 

Colorado Golden Road/Johnson Road/16th Street CO02-S 1 1 

Colorado US 6/Avon Road/Village Road CO10-W n/a 4 

Colorado US 6/Avon Road/Village Road CO10-E 0 15 

Colorado I-70 EB/Chamonix Road CO49-E 2 n/a 

Colorado I-70 WB/Chamonix Road CO50-S 1 n/a 

Colorado I-70 EB/Vail Road CO51-N 70 73 

Carmel, IN 126th Street/Hazel Dell Parkway IN02-N 9 n/a 

Carmel, IN 116th Street/Illinois Street IN06-E 0 0 

Carmel, IN 116th Street/Illinois Street IN06-N 7 2 

New York SR 67 (Dunning Street)/US 9 NY06-S 23 20 

New York SR 67 (Dunning Street)/US 9 NY06-W 15 2 

New York SR 67 (Dunning Street)/US 9 NY06-E 5 0 

New York Lagrange Road (SR 85)/New Scotland Road NY09-N n/a 5 

New York Lagrange Road (SR 85)/New Scotland Road NY09-E 23 0 

New York Lagrange Road (SR 85)/New Scotland Road NY09-W 21 3 

Vermont SR 9/US 5 VT03-E 11 5 

Vermont SR 9/US 5 VT03-S 35 4 

Vermont SR 9/US 5 VT03-W 66 4 

Washington State 164th Street/SR 522 NB Ramp/Tester Road WA06-SW 4 2 

Washington State SR 16 NB/Burnham Drive NW/Borgen Blvd WA09-SE n/a 20 

Washington State 14th Avenue/Jefferson Street WA30-N 4 4 

Washington State 14th Avenue/Jefferson Street WA30-S 12 7 

Washington State 14th Avenue/Jefferson Street WA30-W 7 16 

Washington State 4th Avenue/Olympic Street WA31-E 48 21 

Washington State SR 16 SB/Burnham Drive NW WA32-W n/a 6 

Washington State SR 16 SB/Burnham Drive NW WA32-N 2 130 

All 2x2 Sites Total Data Points n/a 366 345 

24 
 

 

Table 6. Summary of multilane 2x1 roundabout configuration data. 

Subarea Site Site Code Usable Data Points -

Right Lane 

Usable Data Points -

Left Lane 

Colorado Eby Creek Road/US 6 (Grand Avenue) CO01-N 1 0 

Carmel, IN 126th Street/Hazel Dell Parkway IN02-S 75 106 

Carmel, IN 136th Street/Keystone Parkway SB IN11-W 8 26 

Washington State SR 16 NB/Burnham Drive NW/Borgen Blvd WA09-E 87 86 

Washington State 14th Avenue/Jefferson Street WA30-E 12 n/a 

Washington State 4th Avenue/Olympic Street WA31-S 29 60 

Washington State 4th Avenue/Olympic Street WA31-N 0 10 

Virginia SR 50/SR 15 VA01-S 19 n/a 

All 2x1 Sites Total Data Points n/a 231 288 

Table 7. Summary of multilane 1x2 roundabout configuration data. 

Subarea Site Site Code Usable Data Points 

Virginia SR 50/SR 15 VA01-W 37 

Virginia SR 50/SR 15 VA01-E 7 

All 1x2 Sites Total Data Points n/a 44 

25 
 

 

 

 

 

DATA COLLECTION AND REDUCTION 

The data set consists of one-minute bins, as described in the following section, of data defined by 

one of two criteria: a minimum queue or a maximum move-up time. The minimum queue 

criterion requires an observed standing queue for a full minute. A standing queue is defined as at 

least two vehicles in queue (i.e., at least one vehicle behind the vehicle at the yield line). Because 

the back of queue is not always visible in the video and therefore was not coded for some sites, a 

second criterion, maximum move-up time, was used to identify data points that most likely 

represented queued conditions (including rolling queues). 

Figure 14 displays an example of a camera angle where the back of the queue is not clearly 

visible and could not be accurately recorded. Figure 15 displays two images of a rolling vehicle 

queue take eight seconds apart (note the red sport utility vehicle as a common element in both 

images). No conflicting vehicles are present during this time period and no vehicles in the rolling 

queue stop before entering the roundabout. The rolling queues clearly represent conditions near 

saturation but would not be captured using a minimum queue criterion. These represent an 

important set of data for low conflicting flows. 

Figure 14. Image. Example of nonvisible back of queue. 

26 
 

 

 

 

 

 

 

 

 

 

 

Figure 15. Image. Example of rolling queues. 

A maximum move-up time of six seconds was used to identify valid data points. If the time 

interval between each vehicle departing from and the next vehicle arriving at the yield line was 

six seconds or less for a full minute, the data point was considered valid for the maximum moveup time data set. 

Table 8 shows an example of the one-minute data bins that were developed from a single lane 

site. The data binning was executed by importing the raw, time-stamped event codes into a 

spreadsheet. A macro routine within the spreadsheet evaluated each arrival time code to 

determine if one of the two criteria (i.e., a queue of at least two vehicles or a move-up time of six 

seconds or less) was met. The spreadsheet considered each of the two criteria independently. If 

one of the criteria was met, the routine continued to look down the data set until a full minute 

had elapsed between the original arrival event and the last arrival event that constituted a full 

minute of valid data. 

Once a full minute had elapsed, a bin of data was created. The number of entering and 

circulating events associated with this bin, inclusive of those circulating and entering events 

associated with the last arrival event, was counted. For example, in table 8, the departure time of 

12:02:56 is associated with the last arrival event of 12:02:47 and was therefore included in the 

entering vehicle count. 

As shown in table 8, this method results in data bins that are at least a minute but vary in 

duration based on the actual arrival and departure times. The data bins were normalized by using 

the actual duration (e.g., 1.17 minutes) to calculate entering and circulating flow rates for the 

individual data bins. 

27 
 

 

 

 

Table 8. Example of data binning, where shaded rows representing arrival times of 

12:01:46 to 12:02:47 are a valid one-minute data point. 

Arrival Time Departure 

Time 

Move-up Time 

(s) 

12:01:41 12:01:44 0.25 

12:01:46 12:01:48 1.56 

12:01:49 12:01:51 0.39 

12:01:51 12:01:53 0.375 

12:01:54 12:01:56 0.749 

12:01:58 12:01:58 2.148 

12:01:58 12:02:02 0.468 

12:02:03 12:02:08 0.406 

12:02:08 12:02:11 0.64 

12:02:11 12:02:18 0.061 

12:02:18 12:02:20 0.437 

12:02:20 12:02:22 0.358 

12:02:22 12:02:26 0.39 

12:02:26 12:02:38 0.327 

12:02:38 12:02:40 0.39 

12:02:41 12:02:47 0.64 

12:02:47 12:02:56 0.6 

12:02:56 12:03:01 0.312 

Multilane data was extracted in the same manner as above using a macro routine within a 

spreadsheet to first separate multilane date into left and right lane data sets. 

Upon completing the two-day video collection for all sites, the research team pre-screened all 

video segments to ensure reduction of time periods with saturated conditions. The screened time 

periods were then reduced to extract time stamps. Table 9 lists the events and respective codes 

used to reduce single-lane roundabout data. The shaded rows (5, 6, 13, 14, 15 and 16) represent 

those codes that have a direct input in calculating the maximum move-up times. The codes for 

multilane roundabout data accounts for multiple entry and circulating lanes, but is otherwise 

consistent with single-lane roundabout codes. 

For all sites, pedestrian events were recorded for the purpose of identifying minutes of data that 

might be influenced by pedestrian activity. Any minutes of data that included pedestrian events 

were excluded from the analysis. 

28 
 

 

Table 9. Example of coded events, where coded events (5, 6, 13-16) are shaded. 

Code Event Name 

1 Entry Leg: Pedestrian Arrival 

2 Entry Leg: Pedestrian Enters Crosswalk 

3 Entry Leg: Pedestrian Completes Crossing 

4 Exit Leg: Pedestrian Enters Crossing 

5 Right Lane: Circulating Vehicle 

6 Right Lane: Exiting Vehicle 

7 Bypass Lane: Entering Vehicle Position 1 

8 Bypass Lane: Entering Vehicle Departure 

9 Exit Leg: Pedestrian Arrival 

10 Exit Leg: Pedestrian Completes Crossing 

11 Next vehicle is a heavy (1 press indicates that a Position 

1 + Departure are both heavy movements) 

12 Next vehicle is a bicycle (1 press indicates that a Position 

1 + Departure are both bike movements) 

13 Right Lane: Entering Vehicle Departure (Right Turn) -

Indicates most recent right lane departure was a right turn 

14 Right Lane: Entering Vehicle Back of Queue 

15 Right Lane: Entering Vehicle Departure (Through) 

16 Right Lane: Entering Vehicle Position 1 

29 

 

 

 

 

 

 

 

 

 

CHAPTER 4. PARAMETRIC ANALYSES 

The model development for this project examined two key sets of potential parameters for use in 

model descriptions: driver behavior parameters, including critical headway and follow-up 

headway, and geometric parameters. These are discussed further in the following sections. 

CRITICAL HEADWAY 

Per the HCM 2010, the critical headway, tc, is defined as “The minimum headway in the major 

traffic stream that will allow the entry of one minor-street vehicle.”(2) In theory, the driver rejects 

any headway within the circulating stream that is less than the critical headway and accepts any 

such headway greater than the critical headway. As such, the largest rejected headway will be 

less than the critical headway, and all accepted headways will be greater than the critical 

headway. Such theory assumes that drivers’ behaviors are consistent and rational. 

The critical headway was evaluated using the Maximum Likelihood Technique as was 

documented in NCHRP Report 572. In accordance with the critical headway methodology tested 

and recommended in NCHRP Report 572, only observations that contained a rejected gap were 

evaluated. The probabilistic distribution for the critical headways is assumed to be log-normal. 

Critical headway data were reduced only during periods of known or estimated queuing (based 

on a maximum move-up time of six seconds), making the data collection effort similar to that 

described as Method 3 in NCHRP Report 572. 

Single-Lane Critical Headway 

Table 10 lists the critical headways for single-lane sites. The critical headways vary between 3.3 

s and 6.5 s with a weighted average of 4.7 s and a standard deviation of 1.6 s. Some sites have 

fewer than 100 critical headway observations. While the average critical headway of these sites 

may change with a larger sample size, the result is indicative of the average behavior of the site 

during those minutes when queuing was observed. 

31 
 

 

 

 

 

 

Table 10. Critical headway estimates for single-lane sites. 

Site Number of 

Observations, n 

Mean Std. 

Dev. 

CO01-W 15 6.5 3.4 

IN07-E 52 4.5 2 

IN07-S 5 4 1.5 

IN08-N 50 4.3 1.3 

IN09-S 93 3.5 1.5 

IN09-W 203 3.6 1 

IN10-E 10 3.7 2.3 

IN10-N 85 3.8 1 

IN10-W 51 3.3 1.8 

IN12-E 67 4 1 

NY07-E 272 4.8 1.4 

NY07-N 263 5 1.4 

NY07-S 273 5.1 1.5 

NY07-W 768 4.6 1.7 

NY08-N 51 5.5 1.9 

NY08-W 102 4.9 1 

WA04-E 65 5.1 1.9 

WA04-N 299 5.6 2.2 

WA34-E 18 5.6 2 

Total 2,742 n/a n/a 

Average n/a 4.7 1.6 

Multilane Critical Headway 

For a multilane roundabout, the critical headway was calculated in a similar way to single-lane 

roundabouts, and is consistent with the NCHRP Report 572 methodology. For multilane 

roundabouts, this method combines circulating volumes into a single conflicting stream. For each 

entry lane, this methodology assumes that all conflicting vehicles have an influence on the 

entering driver’s behavior, which will be true in some cases and generally conservative. 

Table 11 lists the critical headways for multilane sites by roundabout lane configuration and 

entry lane, with a summary provided in table 12. Some sites have fewer than 50 critical headway 

observations. While the average critical headway of these sites may change with a larger sample 

size, the result is indicative of the average behavior of the site during those minutes when 

queuing was observed. 

32 
 

 

Table 11. Results for critical headways in multilane roundabouts. 

Site Configuration Entry 

Lane 

Number of 

Observations, n 

Mean Std. Dev. 

IN02-N 2x2 right 174 5.5 2.1 

IN06-N 2x2 right 23 4.1 1.4 

NY06-N 2x2 right 99 4.9 1.3 

NY06-W 2x2 right 408 4.5 1.6 

NY09-W 2x2 right 157 4.3 1.2 

VT03-E 2x2 right 153 5 1.6 

VT03-S 2x2 right 251 4.6 1.6 

VT03-W 2x2 right 573 5.4 2.3 

WA06-SW 2x2 right 72 4.1 1.4 

WA09-N 2x2 right 59 4.2 1.4 

WA09-SE 2x2 right 228 4.5 2 

WA09-SW 2x2 right 78 4.4 1.2 

WA30-S 2x2 right 214 3.8 1.6 

WA30-W 2x2 right 130 5 1.4 

WA31-E 2x2 right 227 4.5 1.1 

WA32-N 2x2 right 184 4 1.8 

CO10-S 2x2 right 66 5.1 1.5 

CO49-E 2x2 right 76 8.6 4.4 

CO50-E2 2x2 right 56 6 1.1 

CO51-N 2x2 right 12 12.9 6.5 

CO51-S 2x2 right 88 5.6 2.5 

CO51-W 2x2 right 72 5.1 2.1 

Total 2x2 right 3,400 n/a n/a 

Average 2x2 right n/a 4.9 1.8 

IN02-N 2x2 left 207 5.2 1 

IN06-E 2x2 left 2 4 0.4 

IN06-N 2x2 left 79 11.1 12 

NY09-W 2x2 left 121 4.4 0.9 

VT03-E 2x2 left 118 5.8 1.8 

VT03-S 2x2 left 125 6.1 1.7 

VT03-W 2x2 left 437 5.1 2.1 

WA06-SW 2x2 left 53 4.8 2.2 

WA09-N 2x2 left 88 4.4 1.4 

WA09-SE 2x2 left 143 4.7 2.3 

WA09-SW 2x2 left 113 4.6 1.1 

WA30-S 2x2 left 35 4.5 1.4 

WA30-W 2x2 left 142 5.2 1.3 

WA31-E 2x2 left 181 5.3 2 

WA32-N 2x2 left 309 4.9 2.6 

CO01-N 2x2 left 65 4.9 2.5 

CO10-S 2x2 left 50 5.6 1.9 

33 
 

 

Site Configuration Entry 

Lane 

Number of 

Observations, n 

Mean Std. Dev. 

CO10-W 2x2 left 53 6.5 2.5 

CO49-E 2x2 left 87 8.3 3 

CO51-N 2x2 left 12 13.2 3.8 

CO51-S 2x2 left 51 6.3 2.1 

C051-W 2x2 left 32 4.8 1.7 

Total 2x2 left 2,503 n/a n/a 

Average 2x2 left n/a 5.5 2.2 

VA01-S 2x1 right 193 5 1.2 

IN02-S 2x1 right 327 4.4 1.2 

IN11-W 2x1 right 74 3.8 1 

WA09-E 2x1 right 505 4.2 1.3 

WA30-E 2x1 right 11 4.9 2.8 

WA31-N 2x1 right 42 6.1 0.6 

WA31-S 2x1 right 168 4 0.9 

CO01-N 2x1 right 128 4.2 4.2 

Total 2x1 right 1,448 n/a n/a 

Average 2x1 right n/a 4.3 1.5 

VA01-S 2x1 left 53 4.6 0.9 

IN02-S 2x1 left 366 4.6 1.1 

IN11-W 2x1 left 77 4.2 1.1 

WA09-E 2x1 left 448 4.5 1.1 

WA31-N 2x1 left 85 6.6 2.2 

WA31-S 2x1 left 99 4.1 0.8 

Total 2x1 left 1,128 n/a n/a 

Average 2x1 left n/a 4.6 1.1 

VA01-W 1x2 n/a 260 5.3 1.8 

VA01-E 1x2 n/a 185 4.9 1 

Total 1x2 n/a 445 n/a n/a 

Average 1x2 n/a n/a 5.2 1.5 

Table 12. Summary of results for critical headway in multilane roundabouts. 

Lane configuration 

and entry lane 

Range (s) Weighted Average (s) 

2x2, right lane 3.8-12.9 4.9 

2x2, left lane 4.0-13.2 5.5 

2x1, right lane 3.8-6.1 4.3 

2x1, left lane 4.1-6.6 4.6 

1x2 4.9-5.3 5.2 

34 
 

 

 

 

FOLLOW-UP TIME 

Per the HCM 2010, the follow-up time, or follow-up headway, tf, is defined as “the time between 

the departure of one vehicle from the minor street and the departure of the next vehicle using the 

same major-street headway, under a condition of continuous queuing on the minor street”.(2) In 

addition, the follow-up headway methodology was further refined from the technique used for 

NCHRP Report 572 to exclude the effect of exiting vehicles. This was done by identifying and 

excluding any consecutive entering vehicle events with one or more intervening exiting vehicle 

events, even if there were no intervening conflicting vehicles. The resulting follow-up headway 

measurement is therefore a pure measurement of two consecutive entering vehicles with no 

intervening real or perceived conflicts. 

Single-Lane Follow-Up Times 

Table 13 lists the follow-up times for single-lane sites. The follow-up times vary between 1.7 s. 

and 3.0 s. with a weighted average of 2.6 s. and a standard deviation of 1.0 s. 

35 
Table 13. Follow-up time estimates for single-lane roundabout sites. 

Site Number of 

Observations, n 

Mean Std. 

Dev. 

CO01-W 83 2.8 1 

CO49-W2 4 2.9 0.9 

IN07-E 40 2.5 1.1 

IN07-S 38 2 0.8 

IN08-N 69 1.7 0.7 

IN09-E 433 2.9 1.3 

IN09-S 136 2.2 1.1 

IN09-W 192 2.3 0.7 

IN10-E 189 2.1 0.8 

IN10-N 26 2.2 0.9 

IN10-W 49 2 0.6 

IN12-E 45 1.9 0.9 

NY07-E 243 2.9 1 

NY07-NW 141 2.8 0.9 

NY07-NE 115 3 1.1 

NY07-S 271 2.9 1 

NY07-W 327 2.7 1.1 

NY08-N 37 2.4 0.6 

NY08-W 296 2.5 0.8 

WA04-E 251 2.4 0.9 

WA04-N 369 2.9 1.1 

WA33-E 71 2.2 0.8 

WA33-W 14 2.2 0.7 

WA34-E 140 2.4 0.8 

WA34-N 20 2.8 0.8 

WA35-E 23 2.4 1.1 

Total 2,647 n/a n/a 

Average n/a 2.6 1 

Multilane Follow-Up Time 

Table 14 lists the follow-up headways for multilane sites by roundabout lane configuration and 

entry lane. 

36 
 

 

Table 14. Follow-up time estimates for multilane roundabout sites. 

Site Configuration Entry 

Lane 

Number of 

Observations, n Mean Std. Dev. 

CO02-E 2x2 right 8 2.7 0.8 

CO10-S 2x2 right 27 2.5 0.9 

CO10-W 2x2 right 5 4.1 1.7 

CO49-E 2x2 right 26 3.1 0.9 

CO50-E2 2x2 right 33 2.3 0.8 

CO51-W1 2x2 right 33 3.1 1.4 

CO51-N 2x2 right 20 2.6 1.5 

CO51-S 2x2 right 22 2.7 1 

NY06-E 2x2 right 44 2.6 1.2 

NY06-N 2x2 right 72 2.6 1 

NY06-W 2x2 right 235 2.5 1 

NY09-W 2x2 right 114 2.2 0.8 

VT03-E 2x2 right 51 2.8 1 

VT03-S 2x2 right 346 2.3 1 

VT03-W 2x2 right 324 2.8 1.2 

WA06-SW 2x2 right 30 2.8 1.6 

WA09-N 2x2 right 9 2.2 0.5 

WA09-SE 2x2 right 4 2.3 0.5 

WA09-SW 2x2 right 105 2.9 1.5 

WA30-S 2x2 right 14 2.7 1.3 

WA30-W 2x2 right 93 2.6 1.2 

WA31-E 2x2 right 192 2.7 1 

IN02-N 2x2 right 148 2 0.9 

IN06-N 2x2 right 9 2 0.9 

Total 2x2 right 1,964 n/a n/a 

Average 2x2 right n/a 2.5 1 

CO02-E 2x2 left 7 3.2 1.3 

CO10-S 2x2 left 8 2.5 1 

CO10-W 2x2 left 81 2.9 1.2 

CO49-E 2x2 left 163 3 1.1 

CO51-W1 2x2 left 8 2.5 0.8 

CO51-N 2x2 left 2 1.6 0.9 

CO51-S 2x2 left 13 2.7 1.1 

NY06-E 2x2 left 10 3.7 2.3 

NY06-N 2x2 left 57 3.3 1.6 

NY06-W 2x2 left 279 3.4 1.7 

NY09-W 2x2 left 71 2 0.7 

VT03-E 2x2 left 33 2.6 1.3 

VT03-S 2x2 left 110 2.1 0.9 

VT03-W 2x2 left 57 2.4 0.8 

WA06-SW 2x2 left 25 2.7 1.8 

37 
 

 

Site Configuration Entry 

Lane 

Number of 

Observations, n Mean Std. Dev. 

WA09-N 2x2 left 12 2.4 0.4 

WA09-SE 2x2 left 28 2.5 1 

WA09-SW 2x2 left 126 2.4 1 

WA30-S 2x2 left 27 2.6 1 

WA30-W 2x2 left 162 2.4 1 

WA31-E 2x2 left 92 2.5 0.8 

WA32-W 2x2 left 6 2.2 1 

IN02-N 2x2 left 148 1.9 1 

IN06-E 2x2 left 36 3.2 1.8 

IN06-N 2x2 left 2 3.2 0.7 

Total 2x2 left 1,563 n/a n/a 

Average 2x2 left n/a 2.7 1.2 

VA01-S 2x1 right 215 2.3 0.9 

CO01-N 2x1 right 79 2.8 1.2 

WA09-E 2x1 right 188 2.4 0.8 

WA30-E 2x1 right 16 2.4 0.6 

WA31-N 2x1 right 52 2.4 0.7 

WA31-S 2x1 right 96 2.5 1.1 

IN02-S 2x1 right 214 2 0.8 

IN11-W 2x1 right 26 2.2 0.6 

Total 2x1 right 886 n/a n/a 

Average 2x1 right n/a 2.3 0.9 

VA01-S 2x1 left 11 1.5 0.7 

CO01-N 2x1 left 19 2.3 0.8 

WA09-E 2x1 left 263 2.2 0.6 

WA30-E 2x1 left 2 2.9 0.1 

WA31-N 2x1 left 357 2.2 0.5 

IN02-S 2x1 left 271 1.8 0.6 

IN11-W 2x1 left 25 2.2 0.4 

Total 2x1 left 948 n/a n/a 

Average 2x1 left n/a 2.1 0.6 

VA01-W 1x2 n/a 221 2.5 0.8 

VA01-E 1x2 n/a 91 2.5 0.9 

Total 1x2 n/a 318 n/a n/a 

Average 1x2 n/a n/a 2.5 0.9 

GEOMETRIC PARAMETRIC ANALYSIS 

For predictive purposes, it would be desirable to determine whether follow-up time, in particular, 

can be predicted using geometric parameters. The following geometric parameters were 

examined for their relationship to follow-up time: inscribed circle diameter, entry lane width 

(equal to entry width divided by the number of lanes), entry angle, and splitter island width. The 

correlations between follow-up headway and each of these parameters is presented in table 15. 

38 
 

 

 

 

 

The correlations observed in table 15 are generally not significant, as can be seen in the 

correlation and coefficient of determination (R2

) calculations. 

Table 15. Results of the geometric parameter correlation analysis 

Geometric Parameter Correlation to Follow-up Time tf Coefficient of 

Determination R2 

Inscribed Circle Diameter 

(ft) 

-0.051 0.0026 

Average Lane Width (ft) -0.186 0.0345 

Entry Angle (degree) 0.242 0.0586 

Splitter Island Width (ft) -0.158 0.025 

Follow-up time is plotted against each of these geometric parameters in figure 16 through figure 

19 in the order in which they are listed in table 15. 

Follow-Up Time vs. Inscribed Circle Diameter 

Follow-Up Time, tf (s)

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

R2 = 0.0026 

20 30 40 50 60 70 80 90 

Inscribed Circle Diameter, D (m) 

Figure 16. Scatter Plot. Follow-up time vs. inscribed circle diameter. 

39 
 

 

Follow-Up Time vs. Entry Lane Width 

Follow-Up Time, tf (s)

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

R2 = 0.0345 

2 3 4 5 6 7 

Entry Lane Width (m) 

Figure 17. Scatter Plot. Follow-up time vs. entry lane width. 

40 

8 
Follow-Up Time vs. Entry Angle 

Follow-Up Time, tf (s)

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

R2 = 0.0586 

0 10 20 30 40 50 60 70 

Entry Angle (degrees) 

Figure 18. Scatter Plot. Follow-up time vs. entry angle. 

41 
 

 

 

 

Follow-Up Time vs. Splitter Island Width 

4.5 

4 

3.5 

(s)ft

3 

,eim2.5 TpU

R2 = 0.025 -

2 

wlloo1.5 F 

1 

0.5 

0 

0 5 10 15 20 25 

Splitter Island Width (m) 

Figure 19. Scatter Plot. Follow-up time vs. splitter island width. 

In reviewing the figures and correlation table, a number of observations can be made. First, each 

of the geometric parameters tested in this study trends in the direction that is intuitively expected. 

Increases in inscribed circle diameter, entry lane width, and splitter island width cause a decrease 

in follow-up time and thus an increase in capacity. Conversely, an increase in entry angle causes 

an increase in follow-up time and thus a decrease in capacity. 

Second, entry angle shows the strongest correlation of any of the geometric parameters. 

However, the magnitude of the correlation is relatively weak (0.24), and the R2 value is very 

small (<0.06). As can be seen visually, there is significantly more variation in the observed 

follow-up time for a given entry angle than there is in the mean follow-up time over the range of 

observed entry angles. This indicates that while entry angle may have some effect on follow-up 

time, the unexplained variation from site to site (presumed to be from driver behavior) is more 

dominant. 

Last, it may be possible to derive geometric effects on capacity if a baseline value of follow-up 

time is known, as in through localized calibration. This level of detailed analysis was not 

explored further, however, because it does not appear to improve the quality of the fit of the 

model in predicting capacity across all sites. The variations from site to site appear to make it 

unlikely that the base value of follow-up time could be predicted accurately enough for the 

additional precision of geometric fine-tuning to be significant. 

42 
 

 

Based on these observations and given the constraints of budget and schedule, geometric 

parameters were not pursued further in this study. Further research in these areas is 

recommended to determine whether modeling power can be increased with their inclusion. 

43 

 

 

Single-Lane Model 

 

HCM 2010 Model (from figure 14) RMSE reported for NCHRP RMSE with TOPR

Report 572 Data Set 34 Data Set 

ce,pce = 1130 exp (-0.0010 * vc,pce) 155 217

CHAPTER 5. MODEL DEVELOPMENT 

To develop the model for this project, the team followed the below general steps: 

• Assessed the fit of the HCM 2010 models to the new set of data.

• Developed new regression models fitted to the data.

• Explored calibration of models to localized driver behavior and/or geometric parameters.

• Verified the form of regression model—exponential or linear.

• Evaluated the effects of exiting vehicles on entry capacity.

• Analyzed capacity trends over time.

The following sections discuss these steps in more detail. 

ASSESSMENT OF HCM 2010 MODEL 

The single-lane data were compared to the existing HCM 2010 capacity model using the rootmean-square error (RMSE) as the primary goodness-of-fit measurement, consistent with the 

methodology used in NCHRP Report 572. As seen in table 16, the RMSE for the HCM 2010 to 

the new data is 217, which is notably higher than the fit of the model reported in NCHRP Report 

572 to the 2003 data. 

Table 16. RMSE for data sets applied to the HCM 2010 model 

for single-lane roundabout sites. 

Figure 20 shows the HCM 2010 capacity model plotted against the data. Visual inspection of 

figure 20 demonstrates that the bulk of the observed data points lie above the HCM 2010 model, 

thus confirming that the HCM 2010 underpredicts observed capacity. 

45 
1800 

Single-Lane Sites: HCM 2010 Model 

1600 

1400 

1200 

Entering Flow (pc/h) 1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 

Conflicting Flow (pc/h) 

SL Data HCM 2010 Model 

1400 1600 1800 

Figure 20. Scatter Plot. Assessment of HCM 2010 model for single-lane roundabout sites.

Multilane Models

Table 17 summarizes the RMSEs for each multilane configuration. Due to insufficient sample 

size, no comparison was made for the 1x2 configuration. 

Table 17. RMSE for data sets applied to the HCM 2010 model 

for multilane roundabout sites.

HCM 2010 Model RMSE reported for NCHRP RMSE with TOPR 

Report 572 Data Set 34 Data Set 

2x2 Right Lane: ve =1130 exp(-0.0007 vc) 145* 183

(from figure 5)

2x2 Left Lane: ve =1130 exp(-0.00075 vc) N/A 218

(from figure 6)

2x1 Right Lane: ve =1130 exp(-0.0007 vc) N/A 255

(from figure 5)

2x1 Left Lane: ve =1130 exp(-0.0007 vc) N/A 224

(from figure 5)

46 
 

Figure 21, figure 22, figure 23, and figure 24 show the HCM 2010 capacity models plotted 

against the data collected in this study for each roundabout configuration and entry lane in the 

order listed in table 17. The multilane capacity models in the HCM were developed using a 

combination of NCHRP Report 572 findings and post-NCHRP Report 572 analysis by the 

HCQS Committee in the development of HCM 2010. Note that the methodology used for 

NCHRP Report 572 focused on the critical lane of a two-lane approach, which in most cases was 

the right lane of a two-lane entry against two circulating lanes. The other cases included in the 

HCM 2010 were not directly reported in NCHRP Report 572. 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

Entering Flow (pc/h) 

Conflicting Flow (pc/h) 

2x2 Right Lane: HCM 2010 

2x2 right lane data HCM 2010 

Figure 21. Scatter Plot. Assessment of HCM 2010 model for 2x2 multilane roundabout sites 

and right entry lane. 

47 
 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 

Entering Flow (pc/h) 

Circulating Flow (pc/h) 

2x2 Left Lane: HCM 2010 

2x2 Left Lane Data HCM 2010 

Figure 22. Scatter Plot. Assessment of HCM 2010 model for 2x2 multilane roundabout sites 

and left entry lane. 

48 
 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

0 200 400 600 800 1000 1200 1400 1600 

Entering Flow (pc/h) 

Conflicting Flow (pc/h) 

2x1 Right Lane: HCM 2010 

2x1 Right Lane Data HCM 2010 

Figure 23. Scatter Plot. Assessment of HCM 2010 model for 2x1 multilane roundabout sites 

and right entry lane. 

49 
 

 

 

 

 

0 

200 

400 

600 

800 

1000 

1200 

1400 

1600 

1800 

0 200 400 600 800 1000 1200 1400 1600 

Entering Flow (pc/h) 

Conflicting Flow (pc/h) 

2x1 Left Lane: HCM 2010 

2x1 Left Lane Data HCM 2010 

Figure 24. Scatter Plot. Assessment of HCM 2010 model for 2x1 multilane roundabout sites 

and left entry lane. 

Visual inspection of the figures demonstrates that the HCM 2010 model for the right lane in the 

2x2 case somewhat underpredicts the observed capacities and has the best RMSE of the four 

cases tested. Also, the HCM 2010 model for the left lane in the 2x2 case lies within the data, but 

the spread of data is considerable, leading to a higher RMSE. Finally, the HCM 2010 models for 

the 2x1 case significantly underpredict the observed capacities for both the right and left lanes, 

leading to the highest RMSEs of the cases tested. 

DEVELOPMENT OF SINGLE-LANE MODELS 

This section presents the development of single-lane models. The section presents regression, 

calibration, and localized modeling approaches, followed by a summary. 

Regression 

Linear and exponential regression models were developed using all single-lane data. Figure 25 

shows these models plotted on the data. The regression analysis improves the fit of the capacity 

model considerably compared to the HCM 2010 model, with the exponential and linear models 

performing approximately the same (RMSE of 182 and 186, respectively). However, there is still 

considerable spread to the data, particularly for low circulatory flows. 

50 
1800 

Single-Lane Sites: Regression of All Data 

1600 

1400 

c/h)ow (p 

1200 

ng Fl 

1000 

800 

nteriE 

600 

400 

200 

0 

0 200 400 

SL Data 

600 800 1000 1200 1400 1600 

Conflicting Flow (pc/h) 

Exp Regr Linear Regr HCM 2010 

1800 

Figure 25. Scatter Plot. Regression models for single-lane roundabout sites.

Calibration

The generalized regression models shown previously are consistent in philosophy with those 

explored in NCHRP Report 572. However, it is desirable to determine whether a fieldobservable parameter can be used to anchor the regression models and thus enable their 

calibration to local conditions.

The primary field-observable parameter explored is the follow-up headway (tf), which is directly 

related to the y-intercept as shown in figure 26. 

Figure 26. Equation. Follow-up headway as a 

field-observable parameter to calibrate the y-intercept.

Where A = y-intercept and tf = follow-up headway. 

Using the data presented previously for follow-up time, a regression model was developed that 

fixes the y-intercept by the relationship above and allows the slope parameter to float to achieve 

the minimum RMSE. The resulting RMSE for the exponential model increases only slightly with 

51 
Entering Flow (pc/h) 

the fixed intercept, from 182 to 190; the resulting RMSE for the linear model increases more, 

from 186 to 223. As a result, the exponential model anchored to global follow-up time is a 

considerably better fit than its linear counterpart, as shown in figure 27. 

Single-Lane Sites: Calibration to tf 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 

Conflicting Flow (pc/h) 

Data Exp Regr - tf only Linear Regr - tf only HCM 2010 

Figure 27. Scatter Plot. Regression models for single-lane roundabout sites with calibration 

to follow-up time. 

In addition to using a global value of tf to set the intercept, a second regression analysis was 

conducted using individual tf values for each site. The best fit of the exponential model uses sitespecific intercept values and a slope value of -0.00104 and results in a RMSE value of 171. This 

is shown graphically in figure 28, where the observed capacities are normalized by the calculated 

intercept for each site as the observed value of ve divided by the result of 3600 divided by the 

measured tf for that site.

As can be seen in figure 28, the normalization by follow-up time reduces the spread of the data 

around the model, with the data clustering more tightly around the model. This visually 

demonstrates that localized calibration to follow-up time improves the predictive fit of the 

model. The resulting RMSE of the normalized model is 0.115, which when multiplied by the 

mean follow-up time of 1380 results in an effective RMSE of 158. This numerically 

demonstrates a stronger fit when using localized calibration.

52 
Single-Lane Sites: Normalized by tf 

Entering Flow Normalized by tf 

1 

0.8 

0.6 

0.4 

0.2 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 

Conflicting Flow (pc/h) 

Data Exp Regr Linear Regr 

Figure 28. Scatter Plot. Regression models for single-lane roundabout sites, normalized by 

follow-up time. 

A similar calibration was conducted using field-measured values for both follow-up time and 

critical headway, following the full procedure given in the HCM 2010, which applies only to the 

exponential model form (the Siegloch model). The resulting model slightly increased the RMSE 

from 190 to 193. Due to these findings and prioritization of study resources, further use of 

critical headway for model calibration was not pursued further in this study. 

Localized Regression

To further test the notion of localized modeling, a separate regression analysis was conducted for 

the subset of single-lane data from Carmel, IN. By inspection of the data by geographic area, it is 

evident that the Carmel sites exhibit a higher capacity than the other geographic subareas. Figure 

29 and figure 30 are the equations for the revised exponential and linear models, respectively, 

and table 18 summarizes the results of these regression analyses. 

53 
 

Figure 29. Equation. Revised exponential model based on single-lane data from Carmel, 

IN. 

Figure 30. Equation. Revised linear model based on single-lane data from Carmel, IN. 

Table 18. Regression analysis of the Carmel-based model. 

Revised Model Figure 

Number 

Data Set Model 

Method 

RMSE for 

Carmel 

Data Only 

RMSE 

for All 

Data 

ve = 1380 exp (-0.00081 * vc) Figure 29 Best fit to 

Carmel 

sites only 

Exponential 153 212 

ve = 1270 - 0.64 * vc Figure 30 Best fit to 

Carmel 

sites only 

Linear 152 219 

As can be seen from table 18, the fit of the revised Carmel models improves considerably when 

applied only to the Carmel data, in effect matching the goodness of fit (RMSE) of the original 

NCHRP Report 572 model to its data. 

Figure 31 shows these models plotted against the Carmel data subset, with the full dataset 

included in the background. 

54 
Entering Flow (pc/h) 

Single-Lane Sites: Regression of Carmel, IN Data 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 

Conflicting Flow (pc/h) 

All Data Carmel Data Carmel Exp Regr Carmel Linear Regr 

Figure 31. Scatter Plot. Regression models for Carmel, IN data. 

When the Carmel model is applied to all sites, the goodness of fit degrades considerably. The 

intercept is considerably higher than for the regression to all data (for the exponential model, 

1,380 for Carmel sites only versus 1,200 for all sites). The Carmel-specific model is clearly the 

best result for Carmel sites, but the generalized fit of the Carmel-specific model to national 

conditions is worse than other models explored. 

Regression Model Form

The choice of model form—exponential or linear—has been of particular interest. To help clarify 

the choice of model, the data were sorted by conflicting flow, clustered into groups of 10 

observations, and summarized by a series of group means of conflicting flow and entering flow 

for each cluster of 10 observations. The purpose for doing this is to reduce the variability 

inherent in one-minute observations and to see if a clear pattern emerges with respect to model 

form. These models of group means should not be used for actual predictions because they mask 

the variability of the data, but they are useful in providing indicators for model form. 

Figure 32 presents the regression of group means for the entire set of single-lane data, and figure 

33 and figure 34 present plots of predicted versus measured entering flow for the exponential and 

linear regression models, respectively. Both sets of regression model parameters were selected to 

minimize RMSE for their respective forms. The exponential group mean model has a RMSE of 

55 
 

 

 

72 and an R2 of 0.95; the linear group mean model has a RMSE of 82 and a R2 of 0.93. Visual 

inspection confirms what the RMSE and R2

 values indicate: the exponential model does a better 

job of matching the group mean data throughout the range, particularly with both low and high 

conflicting flows. 

Single-Lane Sites: Regression of Group Means 

1800 

1600 

1400 

)hc/1200 p 

1000

low ( Fgn800 iretn600 E 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 

Conflicting Flow (pc/h) 

Grouped Data Exp Regr Linear Regr 

Figure 32. Scatter Plot. Regression of group means for single-lane sites. 

56 
 

 

Single-Lane Sites: Regression of Group Means 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 

Measured Entering Flow (pc/h) 

Exp Regr Match 

Predicted Entering Flow (pc/h) 

Figure 33. Scatter Plot. Exponential regression of group means, predicted vs. measured 

entering flow, for single-lane sites. 

57 
 

 

 

 

 

 

0 

200 

400 

600 

800 

1000 

1200 

1400 

0 200 400 600 800 1000 1200 1400 

Predicted Entering Flow (pc/h) 

Measured Entering Flow (pc/h) 

Single-Lane Sites: Regression of Group Means 

Linear Regr Match 

Figure 34. Scatter Plot. Linear regression of group means, predicted vs. measured entering 

flow for single-lane sites. 

A slightly different set of observations emerge when one separates the single-lane sites into two 

groups—Carmel and non-Carmel, as shown in figure 35 and figure 36, respectively. For the 

Carmel sites, the exponential group mean model has a RMSE of 78 and an R2

 of 0.88; the linear 

group mean model has a RMSE of 67 and a R2

 of 0.91. For the non-Carmel sites, the exponential 

group mean model has a RMSE of 57 and an R2

 of 0.93; the linear group mean model has a 

RMSE of 61 and a R2 of 0.92. Based on these observations, a linear regression model appears to 

fit the Carmel group mean data better than the exponential model, particularly at high conflicting 

flows. The exponential model performs slightly better for the non-Carmel group mean data. 

58 
Carmel Single-Lane Sites: Regression of Group Means 

1800 

1600 

1400 

)hc/1200 p 

1000

low ( Fgn800 iretn600 E 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 

Conflicting Flow (pc/h) 

Grouped Data Exp Regr Linear Regr 

Figure 35. Scatter Plot. Regression of group means for 

Carmel-only single-lane roundabout sites. 

59 
 

 

 

 

 

Non-Carmel Single-Lane Sites: Regression of Group Means 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 

Grouped Data Exp Regr Linear Regr 

Entering Flow (pc/h) 

Figure 36. Scatter Plot. Regression of group means for 

non-Carmel single-lane roundabout sites. 

A detailed look at two approaches of one roundabout in Carmel, IN10, (figure 37) provides an 

interesting illustration of the relationship between exponential and linear regression models. Two 

sites at the roundabout, IN10-N and IN10-W, have essentially identical geometric configurations 

but differ in flow patterns, with IN10-N experiencing low circulating flows and IN10-W 

experiencing high circulating flows, as shown in figure 37. Looked at individually, a linear 

regression model fits each site very well, with very high R2 values. However, it is clear when 

plotting the two sites together on the same graph that the two linear regression models have 

different slopes, despite having the same geometric configuration. An exponential model visibly 

provides the best overall fit (RMSE of 99) by capturing the higher slope under low circulating 

flows and the lower slope under high circulating flows. By contrast, a linear regression model 

across both sites yields an RMSE of 117. 

60 

Conflicting Flow (pc/h)
 

 

 

 

 

 

 

 

 

 

 

Single-Lane Sites: Carmel IN10-N, IN10-W Only 

2000 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 

Conflic ng Flow (pc/h) 

IN10-N,-W Exp Regr IN10-N,-W Linear Regr IN10-N 

IN10-W Linear (IN10-N) 

Entering Flow (pc/h) 

y = -1.2088x + 1715.9 

R2 = 0.9055 

y = -0.6614x + 1332.6 

R2 = 0.8604 

1600 1800 

Linear (IN10-W) 

Figure 37. Scatter Plot. Regression models for two approaches at a single roundabout in 

Carmel, IN. 

This analysis demonstrates two other important features. First, local calibration is important. The 

intercept that best fits the IN10 sites is higher than the best fitting intercept for the Carmel sites 

in general, and the intercept for the IN10 sites is much higher than experienced across the US. 

Second, both linear and exponential models appear to fit small data sets reasonably well. For 

analysis of existing roundabouts where one can calibrate to local conditions, either a linear or 

exponential model appears to work equivalently. However, when looking at larger data sets for 

prediction purposes, such as is necessary for proposed sites where local calibration is not 

possible, the exponential models appear to fit better than the linear models. 

DEVELOPMENT OF MULTILANE MODELS 

This section presents the development of models for each of the multilane cases: 2x2 sites (two 

entry lanes conflicting with two circulating lanes), 2x1 sites (two entry lanes conflicting with one 

circulating lane), and 1x2 sites (one entry lane conflicting with two circulating lanes). The 

section presents regression and calibration approaches, followed by a summary. 

61 
 

 

 

Regression 

Linear and exponential regression models were developed using the data for each of the 

multilane cases. Figure 38 through figure 41 show these models plotted on the data for four 

different roundabout lane configurations and entry lanes. 

2x2 Right Lane: Regression 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

2x2 right lane data Exp Regr Linear Regr HCM 2010 

Entering Flow (pc/h) 

Figure 38. Scatter Plot. Regression models for multilane, 2x2 roundabout sites, right entry 

lane. 

62 

Conflicting Flow (pc/h)
 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 

2x2 Left Lane Data Exp Regr Linear Regr HCM 2010 

Entering Flow (pc/h) 

Figure 39. Scatter Plot. Regression models for multilane, 2x2 roundabout sites, left entry 

lane. 

63 

2x2 Left Lane: Regression

Circulating Flow (pc/h)
 

2x1 RightLane: Regression 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 

2x1 Right Lane Data HCM 2010 Exp Regr Linear Regr 

Entering Flow (pc/h) 

Figure 40. Scatter Plot. Regression models for multilane, 2x1 roundabout sites, right entry 

lane. 

64 

Conflicting Flow (pc/h)
 

 

 

 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 

2x1 Left Lane Data HCM 2010 Exp Regr Linear Regr 

Entering Flow (pc/h) 

Figure 41. Scatter Plot. Regression models for multilane, 2x1 roundabout sites, left entry 

lane. 

For the 2x2 right lane case, the regression analysis improves the fit from an RMSE of 183 for the 

HCM 2010 to 167 and 170 for the exponential and linear regression models, respectively. For the 

2x2 left lane case, the regression analysis had little effect in improving the fit (RMSE of 218 for 

HCM 2010 versus 213 and 214 for exponential and linear regression, respectively). The 

regression for the 2x1 case had the greatest effect, reducing the RMSE by approximately 40 

percent for both the right and left lanes. Each of the models and their associated RMSE values 

are summarized in a table at the end of this section. 

Calibration 

Similar to the model development process for single-lane sites, it is desirable to determine 

whether a field-observable parameter, particularly follow-up time, can be used to anchor the 

multilane regression models and thus enable their calibration to local conditions. Follow-up time 

is especially desirable as a calibration parameter for multilane sites due to it being considerably 

easier to collect than critical headway. The collection and estimation of critical headway is 

particularly challenging at multilane roundabouts, and for consistency with most modeling 

practices for critical headway, it requires the assumption that the circulating flow is a single 

65 

2x1 Left Lane: Regression

Conflicting Flow (pc/h)
 

 

 

 

 

 

conflicting stream (i.e., without regard to lane use). Follow-up time, on the other hand, can be 

directly measured for each lane independently. 

Using the data presented previously for follow-up time, a regression model was developed that 

fixes the y-intercept and allows the slope parameter to float to achieve the minimum RMSE. 

Figure 42 and figure 43 present the regression models anchored to follow-up time for the right 

and left lanes, respectively, for the 2x2 cases. In addition, two different anchoring values for the 

intercept were tested for the 2x1 case. Figure 44 presents a regression model for the combined 

2x1 case anchored to the follow-up time for the 2x2 right lane case. Figure 45 presents a 

regression model for the combined 2x1 case anchored to a combined follow-up time for the 2x1 

sites. 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

Entering Flow (pc/h) 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

2x2 Right Lane Data Exp Regr Linear Regr HCM 2010 

Figure 42. Scatter Plot. Regression models for multilane 2x2 roundabout sites, right entry 

lane with calibration to follow-up time. 

66 

2x2 Right Lane: Calibration to tf

Conflicting Flow (pc/h)
 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 

Conflicting Flow (pc/h) 

2x2 Left Lane Data Exp Regr Linear Regr HCM 2010 

Entering Flow (pc/h) 

Figure 43. Scatter Plot. Regression models for multilane 2x2 roundabout sites, left entry 

lane with calibration to follow-up time. 

67 

2x2 Left Lane: Calibration to tf
Entering Flow (pc/h) 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 

2x1 Right+Left Lane Data Exp Regr Linear Regr HCM 2010 

Figure 44. Scatter Plot. Regression models for multilane 2x1 roundabout sites with 

calibration matching the y-intercept to the 2x2 roundabout, right entry lane.

68 

2x1 Combined Right + Left Lanes: Match intercept to 2x2 

right lane

Conflicting Flow (pc/h)
Entering Flow (pc/h) 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 

2x1 Right+Left Lane Data Exp Regr Linear Regr HCM 2010 

Figure 45. Scatter Plot. Regression models for multilane 2x1 roundabout sites, combined 

right and left entry lanes with calibration to combined follow-up time. 

The calibrated models for the 2x2 cases demonstrate a good fit to the data with a field-measured 

anchor of follow-up time. For the 2x1 cases, the observed follow-up times in the left lane were

higher than those in the right lane for reasons that the authors could not confirm, and the values 

were considerably higher than those observed for the 2x2 cases. The authors speculate a number 

of reasons for the observed follow-up times for the 2x1 cases: (1) sample sizes are smaller for the 

2x1 cases than for the 2x2 cases. This may make the results more sensitive to individual site 

variations; (2) the 2x1 sites have a strong influence from Carmel, IN, where capacities appear 

higher than the national average; and (3) there may be other unique site attributes, such as sight 

distance or the influence of exiting vehicles, that the authors were unable to explore within this 

study. The use of the 2x2 right lane follow-up time data to anchor the intercept for the 2x1 model 

demonstrates a better overall fit to the regression model and appears to give more reasonable 

results.

INFLUENCE OF EXITING VEHICLES

As noted in previous sections, the effect of exiting vehicles has been demonstrated to affect entry 

capacity. A limited investigation was conducted as part of this study to see if the fit of the above 

69 

2x1 Combined Right + Left Lanes: Calibrated to Combined tf

Conflicting Flow (pc/h)
 

 

 

 

 

 

models could be improved through the inclusion of exiting vehicles. Two approaches were 

briefly explored with the single-lane data set, in which the researchers: 

• Added a fixed percentage of exiting vehicles to the conflicting flow to create an effective

conflicting flow.

• Added a variable percentage of exiting vehicles to the conflicting flow based on splitter

island width.

A factor kex was introduced to represent the proportion of exiting vehicles that are added to the 

conflicting flow. The resulting flow, the effective conflicting flow, is calculated using the 

equation in figure 46. 

Figure 46. Equation. Equation incorporating constant exiting vehicles flow to calculate 

effective conflicting flow. 

Where vc,eff = effective conflicting flow (pcu/h), vc = conflicting flow (pcu/h), kex = proportion of 

contributing exiting flow, and vex = exiting flow (pcu/h). 

In the first case, kex is assumed to be constant, and the regression model was developed by 

holding the intercept parameter fixed to follow-up time and allowing the slope parameter to vary 

to minimize RMSE. The value of kex that produced the lowest RMSE was found to be 0.33, 

meaning that one third of the exiting flow is added to the circulating flow. The resulting models 

are shown in figure 47. For the exponential model, the RMSE is 181 and R2 is 0.56. For the 

linear model, the RMSE is 194 and R2 is 0.49. When compared to the exponential model that 

only includes calibration to follow-up time (RMSE of 190, R2

 of 0.51 for exponential; RMSE of 

223, R2

 of 0.33 for linear), little improvement can be seen due to the opposite directions of the 

two measures. 

70 
Entering Flow (pc/h) 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

Data Exp Regr - tf only Linear Regr - tf only 

Figure 47. Scatter Plot. Regression models for single-lane sites with calibration to follow-up 

time and constant effects of exiting vehicles.

In the second case, kex is assumed to be a variable associated with splitter island width. Two 

logical boundary conditions are assumed for this model. First, for splitter island widths above an 

assumed maximum value of ws,max, kex is assumed to be equal to zero. In other words, if the 

splitter island is large enough, drivers are assumed to be able to adequately distinguish exiting 

vehicles from circulating vehicles, allowing them to ignore exiting vehicles completely. Second, 

for splitter island widths below an assumed minimum value of ws,min, kex is assumed to be equal 

to one. In other words, if the splitter island is small enough, drivers are assumed to be unable to 

distinguish exiting vehicles from circulating vehicles, thus treating all exiting vehicles as 

circulating vehicles.

The model form tested for these boundary conditions is assumed to be a simple linear model, 

formulated in the equation in figure 48. 

71 

Single-Lane Sites: Calibration to tf + constant exiting effects

Effective Conflicting Flow (pc/h)
 

 

 

Figure 48. Equation. Equation incorporating variable exiting vehicle flow to calculate 

effective conflicting flow. 

Where kex = proportion of contributing exiting flow, ws = width of splitter island (ft), ws,max = 

maximum contributing width of splitter island (ft), and ws,min = minimum contributing width of 

splitter island (ft). 

Values for ws,max and ws,min were tested in increments of 1.5 m (5 ft), holding the intercept 

parameter fixed to follow-up time and allowing the slope parameter to vary to minimize RMSE. 

The values of ws,max and ws,min that were found to minimize RMSE were 25 and 0, respectively. 

Using this model for kex, the resulting models are shown in figure 49. For the exponential model, 

the RMSE is 187 and R2

 is 0.53. For the linear model, the RMSE is 203 and R2 is 0.45. These 

values are not as strong as those for the models with constant exiting effects. 

72 
Entering Flow (pc/h) 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 

Data Exp Regr - tf only Linear Regr - tf only 

Figure 49. Scatter Plot. Regression models for single-lane sites with calibration to follow-up 

time and variable effects of exiting vehicles.

A similar exercise was conducted for the left lane of the 2x2 sites. The value of constant kex that 

produced the lowest RMSE was found to be 0.10, a value considerably less than that found for 

the single-lane sites. The resulting models are shown in figure 50. For the exponential model, the 

RMSE is 213 and R2

 is 0.46. For the linear model, the RMSE is 236 and R2 is 0.34. When 

compared to the models with calibration to follow-up time (RMSE of 214, R2

 of 0.47 for 

exponential; RMSE of 243, R2

 of 0.32 for linear), neither of these models show any significant 

improvement. 

73 

Single-Lane Sites: Calibration to tf + variable exiting effects

Effective Conflicting Flow (pc/h)
 

 

 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 

2x2 Left Lane Data Exp Regr Linear Regr 

Entering Flow (pc/h) 

Figure 50. Scatter Plot. Regression models for 2x2 multilane roundabout sites and left 

entry lane with calibration to follow-up time and constant effects of exiting vehicles. 

For the variable exiting effect model, the values of ws,max and ws,min that were found to minimize 

RMSE were 35 and 5, respectively. This outcome is consistent with the expectation that 

multilane roundabouts have somewhat higher circulating speeds than single-lane roundabouts. 

Using this model for kex, the resulting models are shown in figure 51. For the exponential model, 

the RMSE is 192 and R2

 is 0.56. For the linear model, the RMSE is 210 and R2 is 0.47. When 

compared to the models with calibration to follow-up time (RMSE of 214, R2

 of 0.47 for 

exponential; RMSE of 243, R2 of 0.32 for linear), both of these models show improvement. 

74 

2x2 Left Lane: Calibration to tf + constant exiting effects

Effective Conflicting Flow (pc/h)
 

 

 

 

 

 

 

 

 

 

 

 

 

 

1800 

1600 

1400 

1200 

1000 

800 

600 

400 

200 

0 

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 

2x2 Left Lane Data Exp Regr Linear Regr 

Entering Flow (pc/h) 

Figure 51. Scatter Plot. Regression models for 2x2 multilane roundabout sites and left 

entry lane with calibration to follow-up time and variable effects of exiting vehicles. 

In summary, the investigation of the effect of exiting vehicles proved to be inconclusive. The 

modeling that includes exiting vehicles has some effect, but the modeling framework that 

appears to work best for multilane sites (variable geometric effects) does not transfer as well to 

the single-lane sites. Neither exiting vehicle model improves the fit of the model as well as the 

version that locally calibrates the model to local follow-up times. This suggests, at least within 

the confines of this limited investigation, that the inclusion of exiting vehicles adds complexity 

to the model without improving its fit as well as basic local calibration. Limitations of time and 

budget prevented further exploration in this area, and further research is recommended. 

ANALYSIS OF CAPACITY TRENDS OVER TIME 

One of the questions raised at the beginning of this study was whether the performance of 

roundabouts in the United States has changed over time, specifically whether capacities have 

increased. To examine this question, two roundabouts were selected that were used for data 

collection for this study and for NCHRP Report 572. These include a single-lane site, WA04 (SR 

166/Mile Hill Drive/Bethel Avenue in Port Orchard, WA), and a multilane site, VT03 (SR 9/US 

5 in Brattleboro, VT). The NCHRP Report 572 data was collected in the spring/summer of 2003 

and the data for this study (TOPR 34) was collected in the spring/summer of 2012, thus enabling 

75 

2x2 Left Lane: Calibration to tf + variable exiting effects

Effective Conflicting Flow (pc/h)
 

 

 

 

 

a comparison of performance over a period of nine years. This section explores whether driver 

behavior has changed over time at these locations. 

At the WA04 intersection, the north leg yielded the greatest amount of data for both this study 

and NCHRP Report 572. Figure 52 displays the 2012 data collected in this study with the data 

from 2003 for the north leg of WA04. As shown in the figure, the two data sources overlap 

considerably, with no visual evidence of change in driver behavior between 2003 and 2012. 

Significantly, the upper bounds of the two data groups are almost exactly coincident. 

0 

200 

400 

600 

800 

1,000 

1,200 

1,400 

1,600 

0 100 200 300 400 500 600 700 800 

Entering Flow (pc/h) 

Conflicting Flow (pc/h) 

SR 166/Mile Hill Drive/Bethel Avenue (WA04) - North Leg 

2012 Data 2003 Data 

Figure 52. Scatter Plot. Comparison of 2003 and 2012 flow data for single-lane roundabout 

site (WA04 North Leg). 

Figure 53, figure 54, and figure 55 display 2012 and 2003 data for the right lanes of the east, 

south, and west legs of VT03, respectively. 

76 
Entering Flow (pc/h) 

SR 9/US 5 (VT03) - East Leg - Right Lane 

700 

600 

500 

400 

300 

200 

100 

0 

0 200 400 600 800 

Conflicting Flow (pc/h) 

2012 Data 2003 Data 

1,000 1,200 1,400 

Figure 53. Scatter Plot. Comparison of 2003 and 2012 flow data for multilane roundabout 

site VT03 east leg, right lane. 

77 
 

 

Entering Flow (pc/h) 

1,200 

1,000 

800 

600 

400 

200 

0 

Circulating Flow (pc/h) 

2012 Data 2003 Data 

1,200 1,400 1,600 

SR 9/US 5 (VT03) - South Leg - Right Lane 

0 200 400 600 800 1,000 

Figure 54. Scatter Plot. Comparison of 2003 and 2012 flow data for multilane roundabout 

site VT03 south leg, right lane. 

78 
 

 

 

 

 

 

 

 

 

 

Entering Flow (pc/h) 

1,200 

1,000 

800 

600 

400 

200 

0 

Circulating Flow (pc/h) 

2012 Data 2003 Data 

1,200 1,400 1,600 

SR 9/US 5 (VT03) - West Leg - Right Lane 

0 200 400 600 800 1,000 

Figure 55. Scatter Plot. Comparison of 2003 and 2012 flow data for multilane roundabout 

site VT03 west leg, right lane. 

As shown in these figures, the scatters for the two different years of data essentially overlap one 

another, with no visible evidence of a significant difference. The examination of these plots 

provides no evidence to support the hypothesis that capacities have increased over time. Given 

that WA04 was constructed in 1998 and VT03 was constructed in 1999, it may be possible that 

increases in capacity were attained in the initial years after construction, and before 2003. 

SUMMARY OF MODEL DEVELOPMENT 

Table 19 presents a summary of the results across the various modeling methods presented 

above. Of the models, the model that is locally calibrated with individual follow-up times for 

each site performs the best based on the lowest RMSE. For the models relying on global data, the 

pure regression models perform the best based on the lowest RMSE. However, the exponential 

model that is calibrated to a global follow-up time performs nearly as well and has the benefit of 

a field-verified anchor for the y-intercept. As discussed in subsequent sections, this method is 

also consistent with the modeling approach that produced the best fit for the multilane sites. To 

this end, the recommended model is an exponential model anchored to a global follow-up time, 

with localized calibration recommended if possible. 

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The models presented in Table 19 are in one of two forms, with the values of the parameters A 

and B provided in the table. The exponential model is of the form shown in figure 56, and the 

linear model is in the form shown in figure 57. 

Figure 56. Equation. Model Summary, Exponential Model Form 

Figure 57. Equation. Model Summary, Linear Model Form 

Where ce,pce = entry capacity (pc/h) and vc,pce = conflicting flow (pc/h). 

Table 19. Comparison of single-lane roundabout models. 

Row Model Type Model 

Method 

Model 

Parameter 

A 

Model 

Parameter 

B 

RMSE 

Using 

All Data 

R2 

1 HCM 2010 Exponential 1130 0.0010 217 0.37 

2 Regression fit to all sites Exponential 1200 0.00080 182 0.55 

3 Regression fit to all sites Linear 1120 0.58 186 0.54 

4 Calibrated to global tf; 

slope set for best RMSE fit 

Exponential 1380 0.00102 190 0.51 

5 Calibrated to global tf; 

slope set for best RMSE fit 

Linear 1380 0.89 223 0.33 

6 HCM 2010 calibration 

method (calibrated to 

global tf and tc) 

Exponential 1380 0.00094 193 0.5 

7 Calibrated to local tf; slope 

set for best RMSE fit 

Exponential Variable Variable 171 0.59 

8 Best fit to Carmel sites 

only 

Exponential 1380 0.00081 212 0.4 

9 Best fit to Carmel sites 

only 

Linear 1270 0.64 219 0.36 

Table 20 presents a summary of the results across the various modeling methods presented above 

for the cases with 2x1 multilane roundabout, and the 2x2 left entry lane, and the 2x2 right entry 

lane, in that order. Of the models, the 2x2 left-lane and right-lane model with calibration to 

global follow-up time perform as well as pure regression models, and have the benefit of a fieldmeasurable anchor. 

80 
 

 

 

Table 20. Comparison of multilane roundabout models. 

Row Model Type Roundabout 

Configuration 

Model 

Method 

Model 

Parameter 

A 

Model 

Parameter 

B 

RMSE 

Using 

All 

Data 

R2 

1 HCM 2010 2x2 Right 2x2, right lane Exponential 1130 0.0007 183 0.38 

2 Regression fit to all sites 2x2, right lane Exponential 1260 0.00071 167 0.49 

3 Regression fit to all sites 2x2, right lane Linear 1110 0.48 170 0.47 

4 Calibrated to global tf; slope set for best RMSE fit 2x2, right lane Exponential 1420 0.00086 164 0.49 

5 Calibrated to global tf; slope set for best RMSE fit 2x2, right lane Linear 1420 0.82 192 0.3 

6 HCM 2010 2x2 Left 2x2, left lane Exponential 1130 0.00075 218 0.28 

7 Regression fit to all sites 2x2, left lane Exponential 1060 0.00076 213 0.31 

8 Regression fit to all sites 2x2, left lane Linear 960 0.45 214 0.31 

9 Calibrated to global tf; slope set for best RMSE fit 2x2, left lane Exponential 1350 0.00092 214 0.47 

10 Calibrated to global tf; slope set for best RMSE fit 2x2, left lane Linear 1350 0.75 243 0.32 

11 HCM 2010 2x1, fit to right-lane data only 2x1 Exponential 1130 0.0010 255 -0.13

12 Regression fit to right-lane data only 2x1 Exponential 1400 0.00085 139 0.66 

13 Regression fit to right-lane data only 2x1 Linear 1280 0.70 136 0.68 

14 HCM 2010 2x1, fit to left-lane data only 2x1 Exponential 1130 0.0010 224 -0.18

15 Regression fit to left-lane data only 2x1 Exponential 1210 0.00069 145 0.51 

16 Regression fit to left-lane data only 2x1 Linear 1190 0.63 139 0.55 

17 Calibrated to global tf combined lanes; slope set 

for best RMSE fit to all data 

2x1 Exponential 1630 0.00113 180 0.35 

18 Calibrated to global tf, combined lanes; slope set 

for best RMSE fit to all data 

2x1 Linear 1630 1.20 213 0.09 

19 Intercept set to match 2x2 right lane; slope set for 

best RMSE fit to all data 

2x1 Exponential 1420 0.00091 153 0.53 

20 Intercept set to match 2x2 right lane; slope set for 

best RMSE fit to all data 

2x1 Linear 1420 0.92 161 0.48 

81 
 

The 2x1 model reflected some inconsistencies and proved more challenging to calibrate. The 

pure regression models fit much better than the ones anchored to a global follow-up time. The 

observed follow-up times would result in an intercept that is much higher than the observed 

capacities at low circulating flows. The use of the intercept from the 2x2 right-lane model 

produces a much better fit to the data than the use of the directly measured follow-up times. 

82 
 

 

 

 

 

 

 

CHAPTER 6. CONCLUSIONS AND RECOMMENDATIONS 

This study resulted in a considerably larger set of usable data than was realized for NCHRP 

Report 572. This study included 24 single-lane sites (defined as an approach to a roundabout) 

and 37 multilane sites, versus 18 single-lane sites and 7 multilane sites in NCHRP Report 572. It 

also included 819 minutes of single-lane data and 1,230 minutes of lane-specific multilane data, 

versus 318 minutes of single-lane data and 473 minutes of lane-specific multilane data from 

NCHRP Report 572. 

The HCM 2010 models generally underestimate capacities based on the new set of data. A new 

set of models is recommended for each case in the HCM. These have been developed using a 

consistent model form: an exponential regression model (figure 56) with an intercept anchored to 

national average follow-up times. Because their form and input parameters remain the same as in 

the HCM 2010, implementation is anticipated to be straightforward. The recommended models 

are shown in table 21. 

Table 21. Recommended models for roundabout types, configuration, and entry lanes. 

Roundabout 

Type 

Roundabout 

Configuration 

Entry 

Lane 

Model Equation 

(Figure 56) 

Parameters 

From 

Single Lane n/a n/a ve = 1380 exp (-0.00102 * vc) Table 19, Row 4 

Multilane 1x2 n/a 2x2 right lane model 

Multilane 2x2 right ve = 1420 exp (-0.00085 * vc) Table 20, Row 12 

Multilane 2x2 left ve = 1350 exp (-0.00092 * vc) Table 20, Row 9 

Multilane 2x1 both ve = 1420 exp (-0.00091 * vc) Table 20, Row 19 

The exponential form fit generally the same or better than the linear form across the entire range 

of lane configurations and sites analyzed in this project. In some cases the linear form was a 

better regression fit, such as the Carmel single-lane sites. However, for generalized modeling 

purposes, the exponential model is recommended for three reasons. First, the anchor to follow-up 

time is notably stronger with the exponential form than with the linear form. Second, there is no 

evidence from this project that entering flows will reach zero under very high conflicting flows, 

as would be indicated with a linear model. No measurements of zero entering flow were found in 

the data for this project. Documentation of similar conditions for other unsignalized intersections 

appears to be limited, but anecdotal observation suggests that under heavily saturated conditions 

the two traffic streams tend to alternate rather than observe strict priority rules. This suggests that 

true zero entering flows typically are not realized in practice. Third, the exponential model form 

has an analogous analytical form, the Siegloch model, suggesting a basis for the model in 

established traffic flow theory. 

The use of critical headway to further calibrate the single-lane model did not improve the overall 

fit. Calibration using follow-up time as a primary measure is recommended for the HCM 2010 

major update. Calibration to site-specific follow-up times provides the best overall model fit, 

demonstrating that local calibration continues to be a recommended practice. This simplification 

of the calibration process should be easier for practitioners to implement in the field. 

83 
 

 

 

 

 

 

 

 

 

 

 

Effects of geometric parameters and exiting vehicles showed promise in some cases but proved 

inconclusive in a generalized model. 

The benefit of local calibration is clear from the research presented in this paper. Models 

prepared that are specific to a region, such as those demonstrated with localized follow-up times 

collected in Carmel, IN or separate regression models (exponential or linear), provide better 

predictive power for sites in that area, even though the Carmel-specific models do not fit as well 

to the full national data set. While calibration to individual sites provides even better accuracy, 

such a level of localized calibration is impractical for developing a model for predictive purposes 

for sites not yet built. Local data collection of follow-up time is anticipated to be a reasonable 

and cost-effective way to calibrate the national model to a region without the need to also collect 

critical headway as specified in the HCM 2010. 

Further research is recommended in a few areas. The effect of geometric parameters showed 

trends that are consistent with international findings but could not be developed sufficiently to 

improve the predictive power of the model. Entry angle was the most significant of the geometric 

parameters studied but did not have a strong enough correlation to pursue further. Sight distance 

was not evaluated as a geometric parameter but may be significant. The effect of exiting vehicles 

also showed some promise in specific cases but could not be generalized into a model. More 

samples are needed for the 1x2 case, as well as for sites with three-lane entries and sites with 

bypass lanes. Sites with these characteristics were included in the video data collection effort but 

were not used due to the small sample size and prioritization of study resources. 

84 
 

 

 

REFERENCES 

1. Rodegerdts, L., M. Blogg, E. Wemple, E. Myers, M. Kyte, M. P. Dixon, G. F. List, A. 

Flannery, R. Troutbeck, W. Brilon, N. Wu, B. N. Persaud, C. Lyon, D. L. Harkey, and D. 

Carter. NCHRP Report 572: Roundabouts in the United States. Transportation Research 

Board of the National Academies, Washington, D.C., 2007. 

2. Transportation Research Board. Highway Capacity Manual 2010. Transportation Research 

Board of the National Academies, Washington, D.C., 2010. 

3. Siegloch, W. (1973). Die Leistungsermittlung an Knotenpunkten Ohne 

Lichtsignalsteuerung (Capacity Calculations for Unsignalized Intersections). 

Schriftenreihe Strassenbau und Strassenverkehrstechnik, Vol. 154. 

4. Troutbeck, R. J. and W. Brilon. “Chapter 8: Unsignalized Intersection Theory.” In Revised 

Monograph on Traffic Flow Theory. Federal Highway Administration. 

http://www.fhwa.dot.gov/publications/research/operations/tft/. Accessed October 2, 2014. 

5. Kittelson & Associates, Inc. Roundabout Evaluation and Design Guidelines. City of Bend, 

Oregon, April 2010. 

6. Tian, Z. Z., F. Xu, L. A. Rodegerdts, W. E. Scarbrough, B. L. Ray, W. E. Bishop, T. C. 

Ferrara, and S. Mam. Roundabout Geometric Design Guidance. Report No. F/CA/RI2006/13. Division of Research and Innovation, California Department of Transportation, 

Sacramento, Calif., June 2007. 

7. Wei, T., J. L. Grenard, and H. R. Shah. Developing Capacity Models for Local 

Roundabouts: Streamlined Process. In Transportation Research Record: Journal of the 

Transportation Research Board, No. 2257. Transportation Research Board of the National 

Academies, Washington, D.C., 2011. 

8. Zheng, D., M. Chitturi, A. Bill, and D. A. Noyce. Comprehensive Evaluation of Wisconsin 

Roundabouts, Volume 1: Traffic Operations. Traffic Operations and Safety Laboratory, 

University of Wisconsin. Wisconsin Department of Transporation, September 2011. 

9. Mensah, S., S. Eshragh, and A. Faghri. “Critical Gap Analysis for Modern Roundabouts.” 

Presented at the 89th Annual Meeting of the Transportation Research Board, Washington, 

D.C., January 10-14, 2010. 

10. Kittelson & Associates, Inc. “Calibration of HCM Capacity Models for Kansas 

Roundabouts”, Unpublished Draft Memorandum, March 28, 2012. 

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11. Mereszczak, Y., M. Dixon, M. Kyte, L. Rodegerdts, and M. Blogg. “Incorporating Exiting

Vehicles in Capacity Estimation at Single-Lane U.S. Roundabouts.” Paper presented at the

Transportation Research Board National Roundabout Conference, Vail, Colorado, 2005.

12. Hagring, O., Derivation of Capacity Equation for Roundabout Entry with Mixed and

Circulating and Exiting Flows”, Transportation Research Record 1776, Transportation

Research Board, Washington, D.C., 2001, pp. 91-99.

13. Kimber, R. M. The Traffic Capacity of Roundabouts. TRRL Laboratory Report LR 942.

Transport and Road Research Laboratory, Crowthorne, Berkshire, England, 1980.

14. Akçelik, R. “An Assessment of the Highway Capacity Manual 2010 roundabout capacity

model.” Paper presented at the International Roundabout Conference, Transportation

Research Board, Carmel, Indiana, 2011.

15. Brilon, W., and N. Wu. “Unsignalized Intersections – A Third Method for Analysis.”

Proceedings of the 15th International Symposium on Transportation and Traffic Theory,

Pergamon-Elsevier Publications, Adelaide, Australia, pp. 157 –178, 2002.

16. Schmotz, M., and R. Maier. “Capacity of Mini-Roundabouts.” Presented at International

Roundabout Conference, Transportation Research Board, Carmel, Indiana, 2011.

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PUBLICATION NO. FHWA-SA-15-070