Roundabouts in the United States (2007)

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34 This chapter presents a variety of modeling and evaluation tasks related to the operational performance of roundabouts in the United States. First, the results of the investigation of the ability of existing capacity and delay models to represent U.S. data are presented. Next, the chapter presents an analysis of gap acceptance parameters measured for U.S. sites. This section is followed by parametric analysis of factors, both geo- metric and flow related, that may be affecting driver behavior. Finally, the chapter presents the results of efforts to develop capacity models based on the data collected for this project, as well as a recommendation for level of service (LOS). Doc- umentation for the data extraction, as well as supporting analyses and discussion for this chapter, can be found in Appendix J. Assessment of Existing Capacity and Delay Models The first step to determining an appropriate operational model for U.S. roundabouts is to determine how well existing operational models (both U.S. and international) represent U.S. conditions. Unlike safety analysis of roundabouts, which is in its relative infancy in the United States, the use of inter- national capacity models for U.S. roundabouts is common practice. To be consistent with typical practice, these models have been initially examined without providing any local calibration. The following sections discuss the assessment of single-lane and multilane models separately. Single-Lane Capacity Analysis A variety of international and U.S. models (Australian, UK, German, French, Swiss, HCM 2000, and FHWA models, as described in Appendix B) were tested against the observed entry capacity. The predictions for a single-lane site with 10 or more minutes of queuing (MD07-E, Taneytown, Maryland) are illustrated in Figure 10. The average error (the average difference between the predicted and actual entry capacity) for each model by site is illustrated in Table 29. A positive average error implies that the model overpredicts the observed entry capacity. The root mean square error (RMSE) for each model across all sites is also illustrated. In general, a lower RMSE suggests a better prediction. With the exception of two sites, all existing models predict higher capacities than observed at each site. For the WA08-S site (Kennewick, Washington), the German model most accu- rately predicts the WA08-S capacity, while the lower-bound HCM 2000 model tends to underpredict the capacity. In terms of the RMSE across all sites, the lower-bound HCM 2000, German, and FHWA models provide the best fit. The HCM 2000 and German models use default estimates of critical head- way (historically referred to as “critical gap”) and follow-up headway (“follow-up time”) that are similar to the field pre- dicted values, particularly at WA08-S, which has the lowest measured follow-up headway. Of the models tested, the uncal- ibrated French and UK models produce the largest error. Despite the large average error of the UK model, the predicted slope matches the data reasonably well. The slopes of the Australian and French predictions, dictated by the short criti- cal headways, are higher than the general slope of the data. Although the sample sizes are quite small, the international models clearly do not describe U.S. conditions well without further calibration. U.S. drivers appear to be either uncertain or less aggressive at roundabouts, and hence roundabouts currently appear to be less capacity efficient than the inter- national models would suggest. Multilane Capacity Analysis The Australian, UK, German, French, Swiss, HCM 2000, and FHWA capacity models were also tested against the observed entry capacity for multilane entries. Predictions for an example site (WA09-E, Gig Harbor, Washington) are given in Figure 11. C H A P T E R 4 Operational Findings

For each site, only those data that are considered “plausible” for both entry lanes together, the left lane individually, and the right lane individually are included. (Data are “plausible” if the lane has a known queue occurring during the entire minute, either through visual verification of the video record or through examination of the critical headway and follow-up headway.) In general, very few plausible left-lane and total-entry data exist, suggesting that little queuing was observed in the left lane or simultaneously in both lanes. The sample size, average error, and RMSE are illustrated in Tables 30 and 31, respectively, for lane-based and approach-based models. Several items are of note. First, the HCM 2000 and German models were included in the comparison, even though these were intended for use for single-lane roundabouts. Second, 35 MD07-E 0 250 500 750 1000 1250 1500 1750 2000 0 250 500 750 1000 Conflicting Flow (veh/hr) M ax E nt er in g Fl ow (v eh /hr ) Raw Data Australian British French German Swiss HCM Lower Bounds FHWA Linear (Raw Data) Figure 10. Example of uncalibrated entry capacity predictions at MD07-E. Table 29. Capacity prediction error by model (uncalibrated), single-lane sites. Site n Australian UK German French Swiss HCM 2000 Upper HCM 2000 Lower FHWA MD06-N 14 +485 +328 +172 +971 +199 +297 +80 +153 MD06-S 4 —1 +1228 +192 +1675 +382 +309 +105 +192 MD07-E 56 +535 +459 +240 +1024 +295 +362 +151 +227 ME01-E 42 +402 +507 +211 +729 +390 +328 +139 +229 ME01-N 1 —1 —1 —1 —1 —1 —1 —1 —1 MI01-E 8 +493 +933 +336 +1022 +511 +459 +282 +365 OR01-S 15 +292 +631 +122 +576 +268 +253 +85 +156 WA01-N 3 +226 +536 +246 —1 —1 +384 +223 +285 WA01-W 6 +91 +461 +117 +409 +257 +260 +101 +156 WA03-E 2 —1 —1 —1 —1 —1 —1 —1 —1 WA03-S 28 +416 +457 +260 +737 +338 +375 +185 +279 WA04-E 15 +531 +633 +134 +1091 +308 +249 +56 +149 WA04-N 85 +632 +814 +151 +1291 +352 +267 +67 +159 WA04-S 4 +411 +823 +136 +915 +317 +256 +78 +166 WA05-W 6 +450 +378 –144 +767 +209 +185 –26 +54 WA07-S 1 —1 —1 —1 —1 —1 —1 —1 —1 WA08-N 4 +609 +875 +267 +1080 +492 +389 +198 +281 WA08-S 24 +419 +460 +2 +815 +230 +119 –77 +11 RMSE across all sites 318 599 795 240 1191 376 331 183 240 Legend: n = number of observations; RMSE = root mean square error; negative errors (prediction less than observed) indicated in bold 1Insufficent observations

the MD04-E (Baltimore County, Maryland) and MD05-NW (Towson, Maryland) sites are not purely multilane for the purposes of this analysis: MD04-E has two entry lanes with only one conflicting lane, and MD05-NW has a single entry lane into two conflicting lanes. With the exception of the upper- and lower-bound HCM 2000, all models overpredict the capacity. In terms of the RMSE, the upper-bound HCM 2000 and the German model provide the best fit. The Australian lane-based model and the French approach-based model produce the largest error, likely due to the short critical headways and follow-up head- ways inherent in those models. The UK model produces the highest average error at VT03-S (Brattleboro, Vermont), in part because of the effect of the large entry width on the esti- mated capacity. 36 WA09-E Total 0 500 1000 1500 2000 2500 0 500 1000 1500 Conflicting Flow (vehs/hr) M a xi m u m E nt er in g Fl ow (v e hs /h r) Approach Data British German French Swiss HCM Upper FHWA WA09-E Left 0 500 1000 1500 Conflicting Flow (vehs/hr) Left Lane Australian Left WA09-E Right 0 500 1000 1500 2000 0 500 1000 1500 Conflicting Flow (vehs/hr) M a xi m u m E nt er in g Fl ow (v e hs /h r) Right Lane Australian Right Right Lane Left Lane Site n n Australian n Australian MD04-E 36 22 +331 32 +318 MD05-NW 31 31 +173 —1 —1 MD05-W 3 3 +264 3 —1 VT03-E 16 16 +397 13 +411 VT03-S 20 20 +448 11 +631 VT03-W 83 82 +367 35 +491 WA09-E 194 193 +536 12 +585 RMSE across all sites 383 367 1054 106 473 Legend: n = number of observations; RMSE = root mean square error 1Not calculated Figure 11. Example of uncalibrated model entry capacity predictions at WA09-E. Table 30. Capacity prediction error by lane-based models (uncalibrated), multilane sites.

HCM Delay Analysis The HCM 2000 control delay equation was tested against delay measurements obtained from the field. To maximize the use of available field data, the following assumptions were made: • During queued minutes, the determination of the arrival flow at the back of queue was not always possible because of the limited field of view of the data collection equipment. In the extracted data, the arrival flow is equal to the entry flow, and hence the volume-to-capacity ratio is capped at 1.0. Queued-minute capacity is equal to the entry volume. • For illustrative purposes, the capacity of non-queued min- utes is defined by an exponential regression of queued minutes. The right-lane capacity regression is used to define the capacity in both the left and right lanes. The arrival volume during is equivalent to the entry volume. In addition to the volume-to-capacity ratio, the HCM delay requires an analysis period, T. This parameter has a sig- nificant impact on the predicted delay at high volume-to- capacity ratios. While a value of T equals 0.25 h is typical, the volume and capacity conditions are assumed to be constant over the entire analysis period. The average delay will be higher than that predicted for an analysis period of 1 min. Because the field-delay data are presented in 1-min incre- ments, a value of T equals 1 min (0.0167 h) is assumed. As described previously, the field delay during periods of queuing likely excludes portions of the control delay. For this reason, two formulas for estimating delay have been tested: the HCM control delay equation, as documented in Appendix B, and what is termed here as the “HCM stopped delay” equation. The equation for HCM stopped delay used here is identical to that for control delay except that the “3600/c” and “5” terms in the control delay equation have been omitted.Figure 12 illus- trates the observed field delay and calculated HCM control and stopped delay for single-lane, 1-min observations. Figure 13 illustrates the HCM delay as a function of the field delay, with a 45-degree line representing an exact prediction. As can be seen in the figures, the variation in the field data is quite large, and both HCM predictions sit within the bounds of this variation. The correlations between the HCM control delay and the field delay, and the HCM stopped delay and field delay are 0.56 and 0.48, respectively. Considering the wide variation in the data, this correlation is quite good. The 5-s adjustment for acceleration and deceleration included in the control delay equation seems to overpredict the delay, especially when the volume-to-capacity ratio is small. Drivers who are not in a queue and do not have to come to a complete stop at the yield line will not experience this additional delay. The research team recommends that this constant be modified to reflect this field experience. One method may be to adjust the constant using the volume-to- capacity ratio, as higher volume-to-capacity ratios indicate a higher potential for queuing, and hence acceleration and deceleration delay to and from a queued condition. To determine whether delay prediction can be improved by reducing the overall variation in the delay data, the delay data can be aggregated into 5-min increments. This aggregation reduces the field data from 850 one-min observations to 126 five-min observations. However, this aggregation does not produce any improvement in the correlation and thus has not been carried forward. RODEL and aaSIDRA Analysis In addition to the individual capacity and delay models described previously, comparisons were made for single- lane roundabouts with two of the most common software packages used for roundabout analysis in the United States. These comparisons use the latest versions of each package available at the time of analysis: RODEL 1.0 and aaSIDRA 2.0 (note that at the time of this writing, aaSIDRA has since been updated to include additional calibration parameters). 37 Site n UK German French Swiss HCM Upper HCM Lower FHWA MD04-E 21 +1059 +313 +532 +405 –300 –462 +822 MD05-NW 31 +876 +292 +654 +255 –158 –315 —1 MD05-W 3 +234 +61 +557 +279 +160 +45 —1 VT03-E 13 —1 +308 +618 +446 +84 –25 —1 VT03-S 11 +1243 +457 +872 +636 –63 –213 +1038 VT03-W 35 +1885 +345 +1338 +425 298 –464 +829 WA09-E 12 +1165 +405 +817 +543 –172 –328 +937 RMSE across all sites 126 459 375 818 490 271 367 953 Legend: n = number of observations; RMSE = root mean square error; negative errors (prediction less than observed) indicated in bold 1Not calculated Table 31. Capacity prediction error by approach-based models (uncalibrated), multilane sites.

Approximate origin-destination matrices were developed for each roundabout during periods of continuous queuing, which have been used to estimate the turning movements and conflicting flow at each entry. In addition, flow rates were varied using a range of flow multipliers (10% to 500%) to enable capacity estimates across a broad range of con- flicting flow rates for the given geometric conditions and turning movement proportions. Parameters such as the peak-hour factor and the percentage of trucks were not used. RODEL, aaSIDRA, and the field-observed entry capacity have been plotted for each entry with more than 10 min of queued data. These plots are shown in Figure 14. As can be seen from the figure, both software models overestimate the field data. In the case of MD07-E (Taneytown, Maryland) and WA04-E (Port Orchard, Washington), the prediction is high because the entry width is unusually large. The slope of the RODEL capacity curve appears to match the field data more closely than the slope of the aaSIDRA capacity curve. Figure 15 illustrates control delay as a function of the maximum entry flow plus the conflicting flow, with control delay plotted as a logarithm. As the capacity estimates from aaSIDRA and RODEL tend to be high relative to field data, the delay estimates tend to be correspondingly low. Gap Acceptance Analysis The operational evaluation also examined how individual vehicles accept and reject gaps at a roundabout entry. The reduction of these data and the calculation of the critical headway (“critical gap”) and follow-up headway (“follow-up time”) are described in subsequent sections. Calculation of Critical Headway The critical headway, tc, is the minimum headway an enter- ing driver would find acceptable.The driver rejects any headway 38 Single-Lane Delay (1 minute intervals) 0 10 20 30 40 50 60 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Volume / Estimated Capacity D el ay (s ec /ve h) Field Delay HCM Control Delay 0 10 20 30 40 50 60 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 Volume / Estimated Capacity D el ay (s ec /ve h) Field Delay HCM Stopped Delay Figure 12. Minute-based HCM control delay, HCM stopped delay, and field delay at single-lane entries.

less than the critical headway and accepts any headway greater than the critical headway.Hence,a driver’s largest rejected head- way will typically be less than the critical headway, and the accepted headway will be typically greater than the critical head- way. Such theory assumes that the driver’s behavior remains consistent. The concept is illustrated in Figure 16. The critical headway was evaluated using the Maximum Likelihood Technique. This method is based on a driver’s critical headway being larger than the largest rejected headway and smaller than the accepted headway. The probabilistic dis- tribution for the critical headways is assumed to be log-normal. Single-Lane Critical Headway For each site, three methodologies for estimating critical headway were tested: (1) inclusion of all observations of gap acceptance, including accepted lags; (2) inclusion of only observations that contain a rejected gap; and (3) inclusion of only observations where queuing was observed during the entire minute and the driver rejected a gap. A lag is defined as the time from the arrival of the entering vehicle at the round- about entry to the arrival of the next conflicting vehicle; this time is essentially a portion of the actual gap (as illustrated in Figure 17). The lags have been converted to gaps using an approximate follow-up headway. The critical headway of each site and method is summa- rized in Table 32. The critical headway calculated using Method 1 is typically shorter than that from Method 2 because the average rejected gap is much shorter between the two methods (1 s versus 2 s), while the accepted gap is simi- lar between the two methods. Method 2 uses a subset of the same data, and the larger the subset, the closer the estimate of the critical headway. Although queued conditions were anticipated to result in more urgent acceptance of gaps, and hence a lower critical headway, such a phenomenon is not shown in the results. Some of the queued sample (Method 3) critical headways are less than and some are more than the Method 2 critical head- 39 Single-Lane Delay (1 minute intervals) 0 10 20 30 40 50 60 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Field Delay (sec/veh) H CM C on tro l D el ay (s ec /ve h) Correlation = 0.56 0 10 20 30 40 50 60 Field Delay (sec/veh) H CM S to pp ed D el ay (s ec /ve h) Correlation = 0.48 Figure 13. Comparison of control and stopped delay at single-lane entries.

40 MD06-N (Lothian, MD) MD07-E (Taneytown, MD) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 50 100 150 200 250 300 Conflicting Flow (veh/hr) M ax E nt er in g Fl ow (v eh /hr ) SIDRA Raw Data RODEL 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 0 100 200 300 400 500 600 Conflicting Flow (veh/hr) SIDRA Raw Data RODEL ME01-E (Gorham, ME) OR01-S (Bend, OR) R2 = 0.3946 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 700 800 900 Conflicting Flow (veh/hr) M ax E nt er in g Fl ow (v eh /hr ) Raw Data SIDRA RODEL 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 700 800 900 Conflicting Flow (veh/hr) SIDRA Raw Data RODEL WA03-S (Bainbridge Island, WA) WA04-E (Port Orchard, WA) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 700 Conflicting Flow (veh/hr) M ax E nt er in g Fl ow (v eh /hr ) SIDRA Raw Data RODEL 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 Conflicting Flow (veh/hr) SIDRA Raw Data RODEL WA04-N (Port Orchard, WA) 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 100 200 300 400 500 600 700 800 Conflicting Flow (veh/hr) M ax E nt er in g Fl ow (v eh /hr ) Raw Data SIDRA RODEL Figure 14. Field and software entry capacity as a function of the conflicting flow.

41 MD06-N (Lothian, MD) MD07-E (Taneytown, MD) 0 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) RODEL SIDRA 0.1 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) SIDRA RODEL ME01-E (Gorham, ME) OR01-S (Bend, OR) 0.1 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) SIDRA RODEL 0 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) SIDRA RODEL WA03-S (Bainbridge Island, WA) WA04-E (Port Orchard, WA) 0 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) SIDRA RODEL 0 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) SIDRA RODEL WA04-N (Port Orchard, WA) 0 1 10 100 0 500 1000 1500 2000 Conflicting + Entry Lo g Av er ag e De la y (s/ ve h) SIDRA RODEL Figure 15. Log of average delay as a function of the maximum entry plus conflicting flow.

ways. The difference between the average estimates is approximately 0.1 s. As Method 1 assumes rejected gaps that are equal to zero, but not observed in the field, and Method 3 is similar to the results produced by Method 2 but has insufficient data to yield a critical headway estimate at some sites, Method 2 is the recommended methodology for use in this study. The critical headway determined using Method 2 varies between 4.2 and 5.9 s, with a weighted average of 5.0 s. The average standard deviation is approximately 1.2 s, or 24%. Fewer than 1% of the drivers behaved inconsistently (accept- ing a gap smaller than previously rejected), so no additional adjustments for inconsistent drivers were required. Some sites have fewer than 50 critical headway observa- tions. 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 queu- ing was observed. Multilane Critical Headway For a multilane roundabout, the critical headway can be calculated using two techniques. One technique considers each entering lane and conflicting lane separately: the right entry lane uses the gaps in the outermost circulating lane (assuming that the entering vehicles in the right lane yield only to conflicting vehicles in the outer lane), and the left entry lane uses the combined gaps of the inner and outer 42 Conflicting Vehicles Available Gap (sec) Entering Vehicle Critical Gap, tc (sec) TIME Conflicting Vehicles Rejected Gap (sec) Critical Gap, tc (sec) TIME Conflicting Vehicles Accepted Lag (sec) Estimated Follow-up Time (sec) Entering Vehicle TIME Method 11 Method 22 Method 33 Site n tc (std. dev.) (s) n (% of Method 1) tc (std. dev.) (s) n (% of Method 1) tc (std. dev.) (s) MD06-N 733 4.2 (1.0) 32 (4%) 5.2 (1.8) 10 (1%) 5.5 (1.7) MD06-S 76 4.9 (0.9) 38 (50%) 5.0 (1.0) 0 (0%) — MD07-E 1,602 4.3 (1.0) 174 (11%) 5.4 (1.5) 66 (4%) 5.4 (1.6) ME01-E 820 4.2 (0.9) 198 (24%) 4.5 (1.0) 101 (12%) 4.6 (1.1) ME01-N 98 5.1 (1.0) 51 (52%) 5.4 (1.2) 0 (0%) — MI01-E5 —4 —4 25 (—4) 5.7 (0.9) 21 (84%)6 5.6 (0.8) OR01-S 577 4.2 (1.1) 225 (39%) 4.7 (1.2) 66 (11%) 4.9 (1.2) WA01-N 92 4.6 (0.7) 43 (47%) 4.7 (0.7) 0 (0%) — WA01-W 237 4.4 (1.8) 121 (51%) 4.4 (1.0) 0 (0%) — WA03-S 1,314 4.2 (1.1) 332 (25%) 5.0 (1.5) 66 (5%) 4.9 (0.9) WA03-E 197 4.8 (2.1) 23 (12%) 5.3 (1.1) 0 (0%) — WA04-E 481 4.9 (1.0) 240 (50%) 5.3 (1.1) 97 (20%) 5.5 (1.3) WA04-N 3,244 4.3 (0.9) 1,627 (50%) 5.2 (1.3) 152 (5%) 5.1 (1.3) WA04-S 233 3.9 (0.7) 63 (27%) 4.2 (0.8) 0 (0%) — WA05-W 528 4.1 (1.0) 36 (7%) 5.9 (1.6) 0 (0%) — WA07-S 106 —4 22 (21%) 5.0 (0.8) 0 (0%) — WA08-N 582 —4 37 (6%) 5.8 (1.1) 0 (0%) — WA08-S 661 —4 60 (9%) 5.5 (1.5) 0 (0%) — Total 11,581 3,322 (29%)7 558 (5%)7 Average 4.5 (1.0) 5.0 (1.2) 7 5.1 (1.3) 7 Legend: n = number of observations; tc = critical headway; std. dev. = standard deviation Notes: 1All observations of gap acceptance (lags and gaps) 2Observations that include a rejected gap 3Observations that include a rejected gap and occur in a minute with observed continuous queuing 4Not analyzed 5Site is single-lane entry against single circulatory stream, although roundabout is multilane 6Percentage of Method 2 7Totals exclude MI01-E Figure 16. Concept of accepted and rejected gap. Figure 17. Concept of accepted lag. Table 32. Critical headway estimates, single-lane sites.

conflicting lanes. An alternative technique estimates the crit- ical headway for the entire approach, combining the entering lanes and conflicting lanes into single entering and conflict- ing streams, respectively. For the purpose of calibrating the existing capacity mod- els, the critical headway should be calculated with the tech- nique used to develop those models. Troutbeck’s critical headway research (used within aaSIDRA) is a lane-based model that considers the combined conflicting lane gaps (see Appendix B). For the right entry lane, this approach assumes that all conflicting vehicles have an influence on the entering drivers’ behavior, which will be true in some cases and gener- ally conservative. If a vehicle in the right entry lane enters at the same time as a vehicle is circulating in the inner conflict- ing lane, the defined accepted gap may be quite small. This event is illustrated in Figure 18. The critical headways for the multilane-site data were determined using observations conforming to Methods 2 and 3 (described previously in “Single-Lane Critical Headway”) and are presented in Table 33. Some of the queued sample (Method 3) estimated critical headways are less than and some are more than the Method 2 critical headways. The difference between the average critical headways is 0.1 s in the right lane and 0.2 s in the left lane. The critical headways determined using Method 2 vary between 3.4 and 4.9 s in the right lane and 4.2 and 5.5 s in the left lane. It is interesting to note that the MD04-E (Baltimore County, Maryland) critical headways are longer than those observed at other multilane sites. Unlike the other sites with multilane entries used in this analysis, MD04-E has only one conflicting lane, which may explain the similarities of the critical headways to those observed at single-lane sites. The average standard deviation is approximately 1.6 s, or 35%. Some sites have less than 50 critical headway observa- tions for individual lanes. While the average critical headway of each site 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. Calculation of Follow-Up Headway The follow-up headway, tf, is defined as the headway main- tained by two consecutive entering vehicles using the same gap in the conflicting stream. The entering vehicles must be in a queue. The follow-up headway may also be determined from observation of two consecutive vehicles entering the same lag. An example of the time stamp vehicle data is shown in Table 34. The follow-up headway is the difference between the entry departure times of vehicles using the same gap.Vehicles using the same gap will have the same opposing vehicle time. 43 Conflicting Right Lane Combined Lane Accepted Gap (sec) Entering Vehicle from Right Lane Conflicting Left Lane Figure 18. Concept of combined lane gaps. Method 21 Method 32 n tc (std. dev.) (s) n (% of Method 2) tc (std. dev.) (s) Site Left Lane Right Lane Left Lane Right Lane Left Lane Right Lane Left Lane Right Lane MD04-E 468 307 5.5 (2.6) 4.9 (2.1) 95 (20%) 62 (20%) 5.5 (2.5) 4.5 (3.8) MD05-NW 275 —3 4.2 (2.3) —3 126 (46%) —3 4.1 (2.4) —3 MD05-W 17 35 4.3 (1.6) 3.4 (1.2) 10 (59%) 16 (46%) 3.7 (1.2) 3.2 (1.0) WA09-E 99 813 4.2 (2.2) 4.1 (1.6) 0 (0%) 629 (77%) — 4.1 (1.9) VT03-W 237 604 4.4 (1.4) 4.2 (1.3) 114 (48%) 126 (21%) 4.2 (1.4) 4.1 (1.2) VT03-E 100 115 4.3 (0.9) 4.0 (1.2) 30 (30%) 48 (42%) 5.0 (0.7) 4.5 (1.4) VT03-S 73 182 5.0 (1.4) 4.4 (1.4) 10 (14%) 68 (37%) 5.1 (1.0) 4.5 (1.4) 1,269 2,056 385 (30%) 949 (46%) Total 3,325 1,334 (40%) 4.8 (2.1) 4.3 (1.5) 4.6 (1.9) 4.2 (1.9) Average 4.5 (1.7) 4.3 (1.9) Legend: n = number of observations; tc = critical headway; std. dev. = standard deviation Notes: 1Observations that include a rejected gap 2Observations that include a rejected gap and occur in a minute with observed continuous queuing 3Short flare in right lane received little use; entry effectively functioned as single-lane entry 4Insufficient observations 4 Table 33. Critical headway estimates, multilane sites.

The opposing vehicle time is calculated based on the accepted lag or gap: • Using the accepted lag, the opposing vehicle time is the sum of the entry arrival time plus the accepted lag. • Using the accepted gap, the opposing vehicle time is the sum of the entry arrival time plus the total rejected gaps and lag. Approximately 40% of the extracted data occur within a full minute of queuing. Some of the remaining data contain valid follow-up headways observed in partial minutes of queuing. As a number of sites have limited full minutes of queuing, the time the next vehicle takes to move into entry position (move-up time) has been used to test the presence of a queue. Establishing a move-up time threshold allows valid data points within a portion of each minute of data to be used, thus expanding the overall database. Single-Lane Follow-Up Headway Figure 19 illustrates the frequency of the move-up and follow-up headway at WA04-N (Port Orchard, Washington) observed during periods of visually verified queues. Very few queues were observed beyond a move-up time of 6 s. Approxi- mately 4% of the queued data exceed a move-up time of 6 s, and 22% of the queued data exceed a move-up time of 4 s.Applying a move-up threshold of 6 s to all of the extracted WA04-N data yields a similar move-up and follow-up headway distribution. The follow-up headway for each lane has been calculated assuming that a move-up time less than 6 s indicates a queued condition. The queued and estimated follow-up headways are illustrated in Table 35. The difference between the follow-up headways of these two methodologies is approximately 0.2 s. 44 Veh# Entry Arrival Time Stamp Entry Departure Time Stamp Rejected Lag Accepted Lag Rejected Gap Accepted Gap Opposing Vehicle Time Stamp Follow up Headway Comments 1 01:11:23.2 01:11:24.5 00:12.1 01:11:35.3 2 01:11:27.5 01:11:28.7 00:07.8 01:11:35.3 00:04.2 Same lag as #1 3 01:11:30.4 01:11:30.7 00:04.9 01:11:35.3 00:02.0 Same lag as #1 4 01:11:32.7 01:11:33.0 00:02.6 01:11:35.3 00:02.3 Same lag as #1 5 01:11:49.6 01:11:58.8 00:02.0 00:04.7 00:11.2 01:12:07.5 6 01:12:00.6 01:12:00.9 00:06.9 01:12:07.5 00:02.2 Same gap as #5 7 01:12:03.0 01:12:03.6 00:04.5 01:12:07.5 00:02.7 Same gap as #5 01:12:06.0 01:12:14.2 00:03.3 01:12:18.0 8 01:12:06.0 01:12:14.2 00:01.5 00:02.4 00:07.2 01:12:20.4 Two rejected gaps before accepted gap 9 01:12:16.6 01:12:16.9 00:03.9 01:12:20.4 00:02.7 Same gap as #8 10 01:12:18.3 01:12:21.5 00:02.1 00:10.2 01:12:30.6 11 01:12:23.7 01:12:24.0 00:06.9 01:12:30.6 00:02.5 Same gap as #10 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10Move-up time (seconds) Fr eq ue nc y 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10Follow-up time (seconds) Fr eq ue nc y Queued Data Move-up threshold of 6 seconds Queued Data Move-up threshold of 6 seconds Figure 19. Move-up and follow-up time frequency (WA04-N). Table 34. Example of follow-up headway data and calculations.

Despite efforts to increase the dataset, a number of the sites have fewer than 100 follow-up headway observations. While the average follow-up headway of the entry lane may change with a larger sample size, the result is indicative of the average behavior of the entry queued minutes. The smallest follow-up headway of 2.6 s was observed at WA08-S (Kennewick, Washington), which reflects the typi- cally high maximum entry flow observations. The driver behavior at this site is likely impacted by the large student driver population. The largest follow-up headway of 4.3 s was observed at ME01-N (Gorham, Maine), which reflects the typically low maximum entry flow observations. Multilane Follow-Up Headway Table 36 summarizes the estimated follow-up headways for visually verified minutes of queuing and those for a move-up threshold of 6 s. Using a move-up threshold of 6 s, the follow- up headways in the right lane vary between 2.8 and 4.4 s. The left-lane follow-up headways are longer on average and vary between 3.1 and 4.7 s.VT03-S (Brattleboro,Vermont) has the lowest estimated follow-up headway of 2.8 s, which is reflected by a typically high maximum entering flow. Inter- estingly, the right lane behaves as two lanes (at times), which would appear as a very short follow-up headway. The weighted average single-lane and multilane follow-up headways are 3.2 s and 3.1 s, respectively. Under follow-up conditions, the driver behavior at a single-lane or multilane roundabout is similar. Summary Table 37 illustrates the weighted average field data for criti- cal headway and follow-up headway, along with various default parameters used in the international models tested. As can be seen from the table, the HCM 2000 and German mod- els have similar follow-up headways and lower estimates of the 45 Queued Move-up Time < 6 s Site n tf (std. dev.) (s) n tf (std. dev.) (s) MD06-N 219 3.3 (1.3) 637 3.2 (1.1) MD06-S —1 —1 28 3.5 (1.3) MD07-E 660 3.4 (1.1) 1,225 3.3 (1.1) ME01-E 286 3.5 (1.2) 522 3.4 (1.1) ME01-N —1 —1 39 4.3 (1.5) MI01-E2 24 3.7 (1.5) 41 3.5 (1.4) OR01-S 86 3.0 (0.8) 262 3.1 (1.0) WA01-N —1 —1 33 3.4 (1.1) WA01-W —1 —1 86 3.3 (1.1) WA03-E —1 —1 126 3.8 (1.2) WA03-S 199 3.7 (1.3) 753 3.6 (1.2) WA04-E 140 3.1 (1.1) 334 3.1 (1.4) WA04-N 952 3.3 (1.3) 2,282 3.2 (1.2) WA04-S —1 —1 120 3.1 (1.0) WA05-W 103 3.2 (1.1) 453 3.1 (1.0) WA07-S —1 —1 80 2.9 (1.1) WA08-N —1 —1 400 2.9 (1.1) WA08-S 327 2.6 (1.5) 438 2.6 (0.9) Total 2,996 7,859 Average 3.4 (1.2) 3.2 (1.1) Legend: n = number of observations; tf = follow-up headway; std. dev. = standard deviation Notes: 1Insufficient observations 2Site is single-lane entry against single circulatory stream, although roundabout is multilane Table 35. Follow-up headway estimates, single-lane sites. Queued Move-up Time < 6 s n tf (std. dev.) (s) n tf (std. dev.) (s) Site Left Lane Right Lane Left Lane Right Lane Left Lane Right Lane Left Lane Right Lane MD04-E 293 108 2.9 (1.0) 3.3 (1.7) 1,792 648 3.1 (1.1) 3.1 (1.5) MD05-NW 125 —2 3.1 (1.0) —2 315 —2 3.3 (1.2) —2 MD05-W —1 2 —1 4.4 (2.3) 6 2 4.7 (2.4) 4.4 (2.3) VT03-E 28 44 3.5 (2.8) 3.4 (1.3) 73 104 3.2 (1.1) 3.1 (1.1) VT03-S 8 159 3.4 (2.0) 2.8 (1.1) 85 478 3.4 (1.2) 2.8 (0.8) VT03-W 91 592 3.5 (1.9) 3.2 (1.5) 180 1,340 3.3 (1.1) 3.1 (1.2) WA09-E 39 1,249 5.0 (3.9) 2.9 (1.1) 28 1,773 3.5 (1.5) 3.0 (1.1) 584 2,154 2,479 4,345 Total 2,738 6,824 3.1 (1.4) 3.0 (1.2) 3.2 (1.1) 3.0 (1.2) Average 3.1 (1.3) 3.1 (1.1) Legend: n = number of observations; tf = follow-up headway; std. dev. = standard deviation Notes: 1Insufficient observations 2Short flare in right lane received little use; entry effectively functioned as single-lane entry Table 36. Follow-up headway estimates, multilane sites.

critical headway. The Australian predictions of the critical headway and follow-up headway vary based on the conflicting flow, number of lanes, diameter, and entry width.At multilane sites, the follow-up headway is also a function of the dominant and subdominant arrival flows. The dominant entry lane is defined as the lane with the largest arrival flow. The predicted gap parameters used in the various single-lane and multilane models are generally smaller than the field-observed values. In addition, the field data appear to support the concept of dom- inant and subdominant lanes with respect to follow-up head- ways. In most cases, the right lane is dominant with a shorter follow-up headway than the left lane; however, MD04-E (Baltimore County, Maryland) is dominant in the left lane with a correspondingly shorter follow-up headway in the left lane. Additional sites with dominant left-lane arrival flow should be collected to validate the concept. Parametric Analysis One of the most important elements of the analysis con- tained in this chapter is the assessment of the influence of geometric and flow parameters on the capacity of round- abouts in the United States. The primary purpose for this analysis is to develop an understanding of the factors that have the most influence on U.S. roundabout capacity. Secon- darily, it helps to assess the overall ability of various interna- tional models to represent U.S. data. Influence of Geometry on Macroscopic Capacity A number of international models use the geometry to modify capacity estimates. The Australian model suggests that the diameter influences the follow-up headway, while the entry width influences the critical headway. The French model uses the exiting path geometry and splitter width to adjust the influence of exiting vehicles on the capacity. Given that some entering vehicles tend to yield to exiting vehicles, the splitter island width may play a role in providing separation between these movements. The Swiss model accounts for a similar con- dition. The y-intercept of the UK model varies based on a combination of entry width, approach half-width, and effec- tive flare length, modified by the entry angle and entry radius. Geometry such as the entry angle and entry radius may influ- ence the speed in which the follow-up headway can be per- formed. The slope of the UK model is governed by the diameter, entry width, and flare length. Entry width has a sig- nificant influence on the capacity; the entry capacity increases by adding increments of width (the number of lanes present is implicit in the entry width and is not modeled directly). The influence of geometry on the single-lane entry capac- ity has been analyzed using multiple linear regression. Some models use linear capacity relationships, including the UK and Swiss models. The UK model, however, assumes non- linear relationships between the capacity and geometry, which are used to describe changes in the intercept and slope. For example, the shape of the relationship between the entry radius and entry capacity is logarithmic. For small values of the entry radius, less than 10 m (33 ft), the UK model sug- gests a significant and negative impact on the entry capacity. These relationships have been developed using a very large database comprising both field data and test-track data (see Appendix B). Local data provide the opportunity to examine the entry capacity as a function of the geometry on a total of 18 single-lane entries. Plots of the data have been prepared to support the identification of any non-linear relationships. The following independent flow and geometric parameters were tested based on their inclusion in the UK and Australian capacity models: qc  Circulating traffic flow (veh/h) D  Inscribed circle diameter of the roundabout (m) e  Width of the entry at the edge of the circulating roadway (m) Δe  Width of the flare of the entry  e  v (m) v  approach half-width (m) 46 1 Lane 2 Lane Model Follow-up headway, tf (s) Critical headway, tc (s) Follow-up headway, tf (s) Critical headway, tc (s) Field Measurements: Approach Right Lane Left Lane 2.6–4.3 (3.2) N/A N/A 4.2–5.9 (5.1) N/A N/A N/A 2.7–4.4 (3.1) 3.1–4.7 (3.4) N/A 3.4–4.9 (4.2) 4.2–5.5 (4.5) Model Parameters: HCM 2000 German French Australian: Dominant Lane Subdominant Lane 3.1 3.2 2.1 1.8-2.7 (2.2) N/A 4.6 4.4 N/A 1.4-4.9 (2.9) N/A N/A 3.2 2.1 1.8–2.8 (2.2) 2.2–4.0 (3.1) N/A 4.4 N/A 1.6-4.1 (2.9) Table 37. Summary of critical and follow-up headways.

l´  Effective flare length (m) r  Entry radius (m) φ  Entry angle (deg) The geometry for each site is detailed in Tables 38 and 39 for single-lane and multilane roundabouts, respectively. The geometric parameters identified above are summarized as follows: • Inscribed circle diameter: 31.7 to 58.5 m (104 to 192 ft) at single-lane sites; 27.4 to 75.6 m (90 to 248 ft) at multilane sites • Entry width: 4.0 to 12.2 m (13 to 40 ft) • Approach half-width: 3.0 to 8.5 m (10 to 28 ft) • Effective flare length: 0 to 25 m (0 to 82 ft); • Entry radius: 7.5 to 38.0 m (25 to 125 ft) at single-lane sites; 9.5 to 37.5 m (31 to 123 ft) at multilane sites 47 In sc ri be d ci rc le di a m et er , D En tr y w id th , e A pp ro a ch h a lf- w id th , v Ef fe ct iv e fla re le ng th , l ’ En tr y ra di u s, r En tr y a n gl e,  C irc u la tin g w id th A dja ce n t e xi t w id th A dja ce n t de pa rt u re w id th A dja ce n t e xi t ra di u s Tr u ck a pr o n w id th C en tr a l i sla n d ra di u s Sp lit te r isl a n d w id th Sp lit te r isl a n d le ng th Site m m m m m ° m m m m m m m m MD06-N 36.6 4.6 3.7 10.1 18.3 20.0 6.1 5.5 3.7 18.3 3.7 9.1 4.0 5.5 MD06-S 36.6 4.6 3.7 5.8 18.3 19.0 6.1 5.5 3.7 18.3 3.7 9.1 4.6 5.5 MD07-E 44.5 7.6 8.2 0.0 21.3 38.0 9.8 8.2 3.7 24.4 3.0 10.4 2.7 8.2 ME01-E 33.0 4.5 5.0 0.0 38.0 18.0 7.5 5.5 4.0 1.0 8.0 3.5 3.5 5.5 ME01-N 33.0 4.5 5.5 0.0 7.5 50.0 3.5 5.0 4.5 20.0 7.5 3.5 4.0 5.0 MI01-E 36.0 5.6 4.5 25.0 24.0 18.0 9.5 8.4 4.5 ∞ 0.0 8.9 5.0 8.4 OR01-S 58.5 5.2 5.5 0.0 19.8 32.0 6.1 5.2 5.5 12.8 6.1 11.9 5.8 5.2 WA01-N 38.1 4.3 4.3 0.0 19.4 16.5 6.1 —1 —1 —1 3.7 9.3 6.1 —1 WA01-W 38.1 4.3 4.0 0.0 22.9 2.5 6.1 5.5 4.0 30.5 3.7 9.3 4.6 5.5 WA03-E 31.7 4.9 3.4 4.6 10.7 14.0 6.1 5.3 3.5 10.7 3.0 6.7 3.8 5.3 WA03-S 31.7 4.6 3.7 6.1 10.7 14.0 6.1 5.5 3.7 10.7 3.0 6.7 3.8 5.5 WA04-E 50.0 6.1 6.1 0.0 12.2 53.0 11.3 6.1 7.3 42.7 1.5 12.2 7.9 6.1 WA04-N 50.0 6.4 6.1 0.0 26.8 48.0 11.3 6.7 5.5 14.3 1.5 12.2 8.5 6.7 WA04-S 50.0 6.1 6.1 0.0 18.8 34.0 11.3 6.7 5.2 12.2 1.5 12.2 7.6 6.7 WA05-W 34.7 4.6 3.4 0.0 21.3 3.0 4.9 4.9 4.3 7.9 5.3 7.2 2.4 4.9 WA07-S 36.0 4.0 3.0 15.0 21.0 17.0 4.9 5.5 3.6 34.4 6.0 7.1 4.0 5.5 WA08-N 45.7 5.5 5.8 0.0 28.0 13.0 6.7 5.8 5.2 42.7 3.0 13.7 8.2 5.8 WA08-S 45.7 5.5 4.3 3.0 33.5 9.0 6.7 6.1 4.3 21.3 3.0 13.7 8.8 6.1 Maximum 58.5 7.6 8.2 25.0 38.0 53.0 11.3 8.4 7.3 ∞ 8.0 13.7 8.8 8.4 Minimum 31.7 4.0 3.0 0.0 7.5 2.5 3.5 4.9 3.5 1.0 0.0 3.5 2.4 0.0 1Approach is off-ramp with no adjacent exit. In sc ri be d ci rc le di am et er , D En tr y w id th , e A pp ro ac h ha lf- w id th , v Ef fe ct iv e fla re le ng th , l ’ En tr y ra di us , r En tr y an gl e,  C ir cu la tin g w id th A dja cen t e xit w idt h A dja cen t de pa rt ur e w id th A dja cen t e xit ra di us Tr uc k ap ro n w id th C en tr al is la nd ra di us Sp lit te r i sla nd w id th Sp lit te r i sla nd le ng th Site m m m m m ° m m m m m m m m MD04-E 27.4 7.6 7.3 6.7 25.0 12.0 5.8 4.9 3.7 8.4 1.5 15.2 2.3 4.9 MD05-NW 42.7 4.6 6.4 0.0 15.2 34.0 12.2 8.5 6.4 12.5 1.5 18.3 2.7 8.5 MD05-W 42.7 7.0 7.0 0.0 9.5 16.5 11.9 7.6 7.6 6.4 1.5 18.9 1.8 7.6 VT03-E 53.0 8.5 8.5 0.0 26.3 20.0 8.5 12.5 8.5 37.5 2.0 32.0 3.5 12.5 VT03-S 53.0 12.2 8.5 25.0 37.5 19.0 8.5 10.0 8.5 30.0 2.0 32.0 3.5 10.0 VT03-W 53.0 8.5 8.5 0.0 30.0 19.0 8.5 10.0 8.5 30.0 2.0 32.0 3.5 10.0 WA09-E 75.6 9.1 7.3 16.8 10.7 27.0 9.8 10.1 7.3 15.2 3.0 50.0 4.3 10.1 Maximum 75.6 12.2 8.5 25.0 37.5 34.0 12.2 12.5 8.5 37.5 3.0 50.0 4.3 12.5 Minimum 27.4 4.6 6.4 0.0 9.5 12.0 5.8 4.9 3.7 6.4 1.5 15.2 1.8 4.9 Table 38. Geometric parameters used for analysis, single-lane sites. Table 39. Geometric parameters used for analysis, multilane sites.

• Entry angle: 2.5 to 53.0 degrees at single-lane sites; 12.0 to 34.0 degrees at multilane sites. To assess predictive quality, two attributes of each param- eter have been determined: correlation and contribution. Cor- relation illustrates the strength of the linear relationship between the capacity and each of the parameters. Contribu- tion is used to assess the usefulness of each parameter in the linear prediction of the capacity. Standardized partial correlations of the entry capacity and each of the geometric parameters are depicted in Figure 20. Because of the minute-by-minute variation in the capacity, a linear correlation between the entry capacity and each of the geometric parameters cannot be seen by inspection of the graphs. For each of the regression parameters, the slope coefficient and their significance of the contribution and correlation are shown in Table 40. The confidence level is equal to one minus 48 e [meter] a) Inscribed circle diameter b) Entry width c) Width of flare (e – v) d) Effective flare length e) Entry radius f) Entry angle 0 5 10 15 20 25 30 0 10 20 30 40 r [meter] C Linear (C) y=13,18+0,02*x (r=0,043, P=0,000) C= Qe ,m ax [v eh /m in ] 0 5 10 15 20 25 30 0 10 20 30 40 50 60 AE [degree] C Linear (C) y=12,60+0,04*x (r=0,118, P=0,000) C= Qe ,m ax [v eh /m in ] 0 5 10 15 20 25 30 0 5 10 15 20 l [meter] C Linear (C) y=13,31+0,15*x (r=0,141, P=0,000) C= Qe ,m ax [v eh /m in ] 0 5 10 15 20 25 30 0 0,5 1 1,5 2 e-v [meter] C Linear (C) y=13,14+1,59*x (r=0,180, P=0,000) C= Qe ,m ax [v eh /m in ] 0 5 10 15 20 25 30 20 30 40 50 60 D [meter] C Linear (C) y=11,99+0,04*x (r=0,077, P=0,000) C= Qe ,m ax [v eh /m in] 0 5 10 15 20 25 30 3 4 5 6 7 C Linear (C) y=7,95+1,08*x (r=0,218, P=0,000) C= Qe ,m ax [v eh /m in ] Figure 20. Partial correlations of entry capacity to geometric parameters.

the significance. For example, the inscribed diameter, D, con- tributes to the entry capacity with a confidence level, P, of 0.999 (1  0.001), and D is correlated to the entry capacity with a confidence level, Pc, of 0.925 (1  0.075). Assuming confidence-level thresholds of 0.95 and 0.99, the results have been summarized in a yes/no format in Table 41. In addition to the conflicting flow, the additional width created by any flare present, Δe  e  v, is significant for both the contribution and correlation with a confidence level, P  Pc, of 0.99. However, additional tests—including partial linear regression of the same seven parameters, mul- tiple linear regression with a reduced number of parameters, and pair-wise multiple linear regression and correlation analysis (the conflicting flow paired step-wise with each of the seven parameters)—do not yield any parameters with a confidence level of 0.95. The significant variation in the entry capacity on a minute-to-minute basis for a given entry (such that the geometry is fixed) makes drawing conclusive relationships between capacity and geometry difficult. Influence of Flow Parameters and Geometry on Driver Behavior The critical headway and follow-up headway provide an indication of the driver behavior at a given entry. The follow- up headway represents the driver behavior when there are no conflicting vehicles. Its inverse is equivalent to the y-intercept of the relationship between entry capacity and conflicting flow. The critical headway represents the driver behavior during periods of conflicting flow, which typically impacts the slope of the entry-capacity/conflicting-flow relationship. For a given conflicting flow, a short critical headway will pre- dict higher capacity estimates compared to a long critical headway. Factors influencing the average driver behavior at sites may include the proportion of heavy vehicles, exiting and con- flicting flow, and geometry. The influence of these parameters was examined using a simple correlation analysis, which measures how strong the linear relationship is between two variables. The correlation value varies between 1 and 1. A larger correlation value indicates a more linear relation- ship; a negative value implies a negative slope. A value near zero indicates the absence of a linear relationship but is not evidence of the lack of a strong non-linear relationship. Plots of the data were prepared to support the identification of any non-linear relationships. The correlation results for the percentage of heavy vehicles, conflicting flow, exiting flow, and geometry are summarized in Table 42. The average gap parameters for the right lane of a multilane entry were used. Some of the critical headway and follow-up headway estimates are based on limited data and therefore were removed from the analysis. 49 Contribution Significance to Entry Capacity Correlation Significance to Entry Capacity Total Significance to Entry Capacity Parameter P=0.95 P=0.99 Pc=0.95 Pc=0.99 P=0.95 Pc=0.95 P=0.99 Pc=0.99 Conflicting flow, Qc Yes Yes Yes Yes Yes Yes Diameter, D Yes Yes No No No No Entry width, e No No Yes Yes No No Width of flare, eΔ (= e – v) Yes Yes Yes Yes Yes Yes Effective flare length, l’ No No Yes Yes No No Entry radius, r Yes Yes No No No No Entry angle, No No Yes No No No φ Table 41. Summary of the significance of various parameters for single-lane entries. Non- Standardized Coefficient Standardized Coefficient Contribution Significance to Entry Capacity Correlation Significance to Entry Capacity Parameter B β (beta) 1–P 1–Pc Y-intercept 11.212 — 0.005 — Conflicting flow, Qc – 0.831 – 0.741 0.000 0.000 Diameter, D 0.114 0.233 0.001 0.075 Entry width, e 1.006 0.204 0.752 0.000 Width of flare, Δe (= e – v) – 0.740 – 0.208 0.002 0.000 Effective flare length, l’ 0.088 0.081 0.616 0.004 Entry radius, r 0.077 0.164 0.000 0.211 Entry angle, – 0.034 –0.099 0.896 0.013 φ Table 40. Results of the multiple linear regression analysis for single-lane entries.

The critical headway and the percentage of heavy vehicles in the entering flow have a moderate negative correlation (0.52). As illustrated in Figure 21, the critical headway decreases as the percentage of heavy vehicles increases. This finding is not intuitive (one would expect critical headway to increase with increasing heavy vehicles) but has not been explored further because of the limited amount of data with higher percentages of heavy vehicles. The critical headway and conflicting flow have a moder- ate negative correlation (0.63). Critical headway as a function of the conflicting flow is illustrated in Figure 22. The critical headway tends to decrease with increasing conflicting flow. Troutbeck notes the same observation in the Australian model (see Appendix B). In the case of the Australian model, this phenomenon was associated with the lower speed of higher conflicting traffic, enabling shorter accepted gaps. Countering this explanation, the result could simply be a function of shorter headways at high conflicting flows resulting in a lower critical headway, and longer headways at low conflicting flows resulting in a larger critical headway. However, the Maximum Likeli- hood method used to estimate the critical headway is not sensitive to changes in the traffic flow and hence the aver- age headway size. This relationship has not been investi- gated further. The average follow-up headway has a weak correlation to the percentage of heavy vehicles, conflicting flow and geometric parameters. Given that there is no conflicting flow during a follow-up event, the weak correlation (0.15) of follow-up headway to the conflicting flow is appropriate. In addition, the weak correlation (0.07) of follow-up headway to the percentage of heavy vehicles appears appropriate. Isolating the average follow-up headway for single-lane sites yields a moderate positive correlation to the exiting flow (0.56) and a negative correlation to the width of the splitter island (0.50) and the diameter (0.53). As observed in the field, some entering drivers tend to hesitate during an exiting vehicle event. This behavior results in longer follow-up headways. The width of the splitter island is plausibly correlated because it physically separates the entry and exiting movements. The diameter also can be plausibly correlated because of the strong correlation between diameter and the width of the splitter island. For multilane sites, the right-lane follow-up headway is less likely to be influenced by exiting vehicles because of the larger physical separation. The correlation of the splitter width plus the left-lane entry width is much stronger (0.62). The fol- low-up headway as a function of the splitter width plus the left-lane entry width and the diameter are illustrated in Figures 23 and 24, respectively. The follow-up headway decreases as these geometric parameters increase. 50 Parameter Correlation to t c(All Sites) Correlation to t f Correlation to t f (All Sites) (Single Lane) % Trucks (Entering) –0.52 +0.07 +0.28 Conflicting Flow –0.63 –0.15 +0.12 Exiting Flow –0.34 –0.08 +0.56 Diameter –0.37 –0.46 –0.50 Entry Lane Width +0.37 –0.08 –0.07 Approach Half-Width +0.07 –0.02 –0.10 Effective Flare Length –0.13 –0.14 +0.18 Radius –0.12 –0.41 –0.44 Entry Angle +0.18 +0.03 –0.01 Splitter Width –0.09 –0.30 –0.53 Legend: tc = critical headway; tf = follow-up headway Note: Absolute values of correlations greater than or equal to 0.50 are indicated in bold Table 42. Correlation of flow and geometric factors to driver behavior. y = -8.1343x + 5.1969 R2 = 0.273 y = 0.6039x + 3.1378 R2 = 0.0056 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0% 2% 4% 6% 8% 10% 12% % Entry Trucks G a p Pa ra m e te rs (se c) tf, all sites tc, all sites Figure 21. Critical headway and follow-up headway as a function of percentage of entering trucks.

The critical headway and follow-up headway as functions of the entry-lane width, entry angle, and radius are illustrated in Figures 25, 26, and 27, respectively. There is a slight and unin- tuitive increase in the critical headway as the entry-lane width increases. The entry-lane width does not appear to have an influence on the follow-up headway. No strong relationship is indicated between the entry angle or radius and driver behavior. In each of the correlated relationships, the prediction of the follow-up headway varies between 3.0 and 3.5 s. Based on these estimates, the y-intercept of the relationship between entry capacity and conflicting flow would vary between 17 and 20 vehicles/min. The actual data at the y-intercept vary between 14 and 25 vehicles/min, and, hence, using the aver- age follow-up headway prediction for all entries would be as effective as using description relationships for the follow-up headway. The prediction of the critical headway as a function of the conflicting flow varies between 4.0 and 5.2 s.At the single-lane sites with lower average conflicting flows (13 vehicles/min or less), the critical headway varies between 4.7 and 5.2 s. Changes in the critical gap or slope of the entering-conflicting flow relationship result in larger variation to the maximum entering flows at higher conflicting flows. At a conflicting flow rate of 13 vehicles/min, the change in the maximum entering flow is less than 1 vehicle/min. 51 y = -0.0011x + 5.5001 R2 = 0.4342 y = -0.0001x + 3.2184 R2 = 0.0148 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0 200 400 600 800 1000 1200 1400 1600 Average Conflicting Flow (veh/hr) G a p Pa ra m e te rs (se c) tc, all sites tf, all sites Figure 22. Critical headway and follow-up headway as a function of average conflicting flow. y = -0.0792x + 3.6508 R2 = 0.3873 y = -0.023x + 4.9384 R2 = 0.0075 1.0 2.0 3.0 4.0 5.0 6.0 7.0 2.0 4.0 6.0 8.0 10.0 Splitter Island Width (plus Left Lane Width if multilane) (m) G a p Pa ra m e te rs (se c) tf, all sites tc, all sites Figure 23. Critical headway and follow-up headway as a function of splitter island width (plus left-lane width if multilane).

It has also been suggested that as drivers become more familiar with roundabouts, their critical headways and follow-up headways will decrease. Similarly, as drivers are faced with more congested situations, their behavior will become more urgent and the critical headways and follow-up headways will also decrease. Correlation analysis does not suggest any strong relationship between driver behavior and these factors. Although the age of the subject roundabouts varies between 3 and 9 years and the duration of the queue varies between 1 and 30 min, no significant trend can be clearly observed. Impact of Exiting Vehicles on Driver Behavior In the critical headway and follow-up headway methodol- ogy, the conflicting headway is defined as the headway between two consecutive conflicting vehicles. Because of the presence of an exiting vehicle between conflicting vehicles, some entering vehicles are perceived to reject reasonable gaps or to follow up with hesitation. The impact is a longer estimate of the critical headway and follow-up headway, which is asso- ciated with lower field capacity. The effect of exiting vehicles 52 y = -0.0114x + 3.6703 R2 = 0.2225 y = -0.0175x + 5.5724 R2 = 0.1358 1.0 2.0 3.0 4.0 5.0 6.0 7.0 20 30 40 50 60 70 80 Inscribed Circle Diameter (m) G a p Pa ra m e te rs (se cs ) tf, all sites tc, all sites y = -0.0203x + 3.3188 R2 = 0.0044 y = 0.1307x + 4.3413 R2 = 0.087 1.0 2.0 3.0 4.0 5.0 6.0 7.0 3.0 4.0 5.0 6.0 7.0 8.0 G a p Pa ra m e te rs (se cs ) tf, all sites tc, all sites Entry lane width (m) Figure 24. Critical headway and follow-up headway as a function of inscribed circle diameter. Figure 25. Critical headway and follow-up headway as a function of entry-lane width.

at single-lane roundabouts has been explored independently by Mereszczak et al. (32). Exiting vehicles may be incorporated in the calculation of the average gap parameters by redefining the conflicting headway when there is an exiting vehicle. One preliminary assumption to simplify the methodology is to include all exit- ing vehicles in the definition of the headway. To do so, the model is adjusted to accommodate the travel time difference between the exit and the conflicting position at the entry line. A vehicle hesitates for an exiting vehicle much the same as it would if the exiting vehicle had been a conflicting vehicle at the entry line. If the first event defining the headway is an exiting vehicle at t  10 s, and the second is a conflicting vehi- cle at t  11 s, the headway is not (1110)1 s (which is unrealistic), but rather is calculated as 11(10 the travel time of the exiting vehicle to the conflicting position at the entry line). Travel speed, exit width, and splitter width enable the calculation of the travel time. The recalculated critical headways for a number of the single-lane sites are provided in Table 43. The critical headways considering all exiting vehicles vary between 3.7 and 4.3 s. These headways are much lower and more consistent than the critical headways assessed without exiting vehicle events, which vary between 4.4 and 5.9 s. In practice, the exiting flow does not 53 y = 0.0006x + 3.1536 R2 = 0.0007 y = 0.0066x + 4.6343 R2 = 0.0308 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Entry Angle (degrees) G a p Pa ra m e te rs (se c) tf, all sites tc, all sites Figure 26. Critical headway and follow-up headway as a function of entry angle. y = -0.0131x + 3.4573 R2 = 0.166 y = -0.0074x + 4.9528 R2 = 0.0154 1.0 2.0 3.0 4.0 5.0 6.0 7.0 10.0 20.0 30.0 40.0 Entry Radius (m) G a p Pa ra m e te rs (se c) tf, all sites tc, all sites Figure 27. Critical headway and follow-up headway as a function of entry radius.

impact all entering vehicles, and the exact extent of the influ- ence of exiting vehicles has not been determined. To estimate the capacity, the recalculated critical headway and follow-up headways should be used together with an estimate of the conflicting plus exiting flow. While the gap parameters are shorter, the methodology assumes that the entering vehicle is exposed to more conflicting events. Because the influence of the exiting flow is inherent in the critical head- way and follow-up headways that do specifically identify the exiting event, only the conflicting flow is considered. Capacity Model Calibration Based on the findings of the evaluation of existing interna- tional models, calibration to U.S. conditions appears neces- sary to improve the quality of capacity estimates. The calibration of the UK, Australian, German, French, Swiss, HCM 2000, and FHWA models was completed in the follow- ing step-by-step process: 1. Passenger Car Equivalents: The uncalibrated entry capacity has been converted to passenger car units (pcu) using the average percentage of heavy vehicles observed at each entry and the equivalency factors presented for each model in Table 44. For the HCM 2000 and UK models with no recommended equivalency factors, the FHWA factors were used. 2. Effective Geometry: A maximum effective entry and approach width of 16 ft (4.8 m) was assumed based on the observed physical use of the lane. The entry width impacts the UK, Australian, French, and Swiss capacity models. 3. Measured Critical Headway and Follow-Up Headways: The Australian, German, French, and HCM 2000 models were calibrated using the approach-measured values of critical headway and follow-up headway. While the use of approach-measured gap parameters demonstrates the predictive ability of the models, relationships or the aver- age gap parameters would be used in practice. 4. Revised y-Intercept: Per the calibration steps recom- mended by Kimber (19), the UK model y-intercept constant was calibrated using the field-measured capacity data. Single-Lane Roundabouts The RMSE and average error of the single-lane data for each model and calibration step is presented in Tables 45 and 46, respectively. As previously indicated, all uncali- brated models tend to predict much larger entry capacities than observed. The HCM 2000 and German models have lower RMSE than the other models, which is attributable to the long critical headway and follow-up headway. The French and UK models produce the largest error. The French model uses a very short average follow-up headway not observed in the field data. One possible explanation for the error associated with the UK model is that the UK model is based on data collected from sites where wide single-lane entries are uncommon; an entry with a width of 6 m (20 ft) would often be marked as two entry lanes with widths of 3 m (10 ft) each, for example. On the other hand, two of the sites in this database—MD07-E (Taneytown, Maryland) and WA04-N (Port Orchard, Washington)—have large curb-to-curb entry widths but are clearly marked and oper- ated with only a single entry lane. As a result, the UK model effectively treats a wide single-lane entry as having two lanes and therefore overestimates the capacity of a single-lane entry. There is a slight improvement in the RMSE when the flow inputs are adjusted for heavy vehicles. Because the conflicting flow in passenger car units per hour is larger than the con- flicting flow in vehicles per hour, the entry capacity estimates are lower. Furthermore, the measured entry capacity is larger when converted to passenger car units, and hence the differ- ence between measured and predicted entry capacity (the average error) is smaller. Larger equivalency factors could be used to reduce the error further; however, this exercise would not realistically indicate the extent of the influence of heavy vehicles on the entry capacity. Gap parameters already 54 Model Trucks Buses Motorcycles UK NA1 Australian 3 2 1 German 2 1.5 0.5 French 2 2 0.5 Swiss 2 2 0.5 HCM Upper HCM Lower NA 1 FHWA 2 1.5 0.5 1No equivalency factors specified; FHWA factors used Table 44. Passenger car equivalency factors. Site Critical Headway, 0% Exiting Flow tc, (s) Critical Headway, 1 00% Exiting Flow tc, (s) MD06-N 5.2 3.7 MD07-E 5.4 4.1 ME01-E 4.5 4.1 OR01-S 4.7 3.9 WA01-W 4.4 4.0 WA03-S 5.0 3.8 WA04-N 5.2 4.3 WA05-W 5.9 4.2 Table 43. Critical headway adjusted for exiting vehicles.

include the influence of heavy vehicles and, in examination of these against the percentage of heavy vehicles, did not show an intuitive trend. A more detailed examination of truck factors should be performed outside the model calibration. There is an improvement in the RMSE when the effective entry and approach geometry is used. As anticipated, there is a significant improvement in the UK model RMSE. The Aus- tralian, French, and Swiss models have slight improvement in the RMSE. An effective entry width threshold of 4.6 m (15 ft) was also tested, but it did not result in any additional improvement in the error. There is a large improvement in the RMSE when the field- measured critical headway and follow-up headway are used. As indicated by the average error, the French model still tends to overpredict the data. The calibrated HCM 2000 and Ger- man models yield a slight improvement and have lower RMSE than the other models. There is a large improvement in the RMSE when the y-intercept of the UK model is calibrated. The UK model has a constant, F, of 303 indicated in the y-intercept of the entry capacity equation (Equation B-6 in Appendix B). Given that the measured entry capacity and conflicting flow is known, the expression for the y-intercept can be rearranged to esti- mate the local value of this constant. The revised localized intercept for a single-lane entry is reduced by reducing F to 223. A lower constant infers a lower y-intercept and hence 55 Root Mean Square Error (RMSE) Model Uncalibrated veh/h Uncalibrated pcu/h Calibrated geometry Calibrated actual tf & tc Calibrated geometry & y-intercept factor F UK (Kimber/RODEL) 787 773 431 – 164 Australian (Akçelik/SIDRA) 589 545 473 160 German (Wu/Kreisel) 294 215 – 143 – French (Girabase) 1163 1138 1147 206 – Swiss (ETH Lausanne) 373 348 328 – – HCM Upper 326 322 – 145 – HCM Lower 180 187 – – – FHWA (Modified UK) 240 224 – – – Table 45. Calibration of single-lane capacity models. A us tr al ia n U K G er m an Fr en ch Sw iss H C M U pp er H C M Lo w er FH W A Site n pcu Cal. pcu Cal. pcu Cal. pcu Cal. pcu Cal. pcu Cal. pcu pcu WA08-N 4 +603 +120 +872 +191 +264 +133 +1089 +393 +485 +481 +388 +155 +198 +278 WA08-S 24 +360 – 79 +499 – 116 – 7 – 58 +803 +206 +212 +171 +115 –39 – 72 +2 MD06-N 14 +317 –158 +270 – 105 +112 – 20 +882 +164 +134 +133 +267 – 18 +146 +93 MD06-S 4 +529 –73 +1187 – 45 +149 – 39 +1626 +137 +331 +294 +303 – 31 +107 +151 MD07-E 56 +398 – 74 +410 – 7 +190 +39 +952 +221 +241 +238 +337 +44 +206 +178 ME01-E 42 +358 – 12 +496 +115 +198 +50 +722 +152 +376 +376 +323 +72 +135 +217 ME01-N 1 — — — — — — — — — — — — — — MI01-E 8 +496 +89 +926 +263 +329 +83 +1033 +265 +504 +491 +460 +112 +283 +358 OR01-S 15 +160 – 123 +600 +59 +84 – 16 +524 +59 +211 +204 +232 +42 +67 +119 WA01-N 3 +131 0 +510 +152 +215 +86 +580 +186 — — +365 +148 +206 +254 WA01-W 6 +41 – 67 +417 +40 +71 – 18 +360 +9 +193 +193 +250 +53 +93 +109 WA03-E 2 — — — — — — — — — — — — — — WA03-S 28 +390 – 8 +446 +86 +248 +29 +732 +119 +323 +322 +371 +46 +181 +268 WA04-E 15 +505 – 66 +602 – 120 +102 – 54 +1057 +122 +266 +231 +246 – 38 +53 +118 WA04-N 85 +572 – 100 +784 – 47 +120 – 48 +1256 +131 +314 +289 +260 – 37 +64 +128 WA04-S 4 +307 – 53 +800 +100 +110 +58 +882 +124 +278 +249 +242 +99 +65 +140 WA05-W 6 +451 – 104 +378 – 47 +64 – 80 +773 +125 +207 +206 +175 – 76 +2 +54 WA07-S 1 — — — — — — — — — — — — — — Legend: n = number of observations; pcu = passenger car units; Cal. = calibrated gap parameters and/or calibrated intercept Table 46. Average error for single-lane sites.

lower entry capacity. As illustrated by the reduction in the RMSE, the impact of this adjustment, in addition to the revised geometry, is significant. The combined average inter- cept constant of single-lane and multilane roundabouts was also tested. The intercept constant, F, decreases from 223 to 205, and the associated error increases. The capacity models with calibrated data were also tested with larger passenger car equivalency factors. The associated error does not improve. Some of the sites with high truck vol- umes have positive average errors, and an increase in the pas- senger car equivalency only serves to increase the error. Similarly, some of the sites with low truck volumes have nega- tive average errors, and an increase in the factors does not have a sufficient impact on the prediction to improve the error. Average Follow-Up and Critical Headways Where local field data for the gap parameters cannot be readily obtained, the user will likely rely on the availability of the national data collected as part of this study. Two sets of constants were tested: the measured weighted average tc and tf (5.1 s and 3.2 s, respectively), and the tc and tf required to min- imize the HCM 2000 model’s RMSE (5.4 s and 3.2 s, respec- tively). The gap parameters required to minimize the HCM 2000 model’s RMSE are similar to the average weighted field parameters. Multilane Roundabouts The RMSE and average error for the calibration of various models to the multilane data are presented in Tables 47 and 48, respectively. For the approach-based models, the entry capacity data were only used if found plausible in both the left and right lanes. When adjusted for heavy vehicles, most models show a slight improvement in ability to predict measured entry capacity. However, the RMSE for the HCM 2000 model does not improve. The uncalibrated HCM 2000 model both under- and overpredicts the data, and any increase in the con- flicting flow generally reduces the predicted entry capacity. 56 Root Mean Square Error (RMSE) Model Uncalibrated veh/h Uncalibrated pcu/h Calibrated geometry & y-intercept F Calibrated F (all sites) Calibrated actual tf & tc (move-up time < 6 s) UK (Kimber/RODEL) 1054 982 270 324 — Australian (Akçelik/SIDRA) • Right lane • Left lane 473 459 476 473 — — 161 190 German (Wu/Kreisel) 375 307 — — 252 French (Girabase) 818 692 — — 230 Swiss (ETH Lausanne) 490 392 — — — HCM 2000 • Upper • Lower 271 367 320 426 — — 372 FHWA (Modified UK) 953 857 — — — Site n A us tr al ia n ri gh t l an e A us tr al ia n le ft la ne U K G er m an Fr en ch Sw iss H C M U pp er H C M Lo w er FH W A pcu Cal. pcu Cal. pcu Cal. pcu Cal. pcu Cal. pcu/Cal. pcu Cal. pcu pcu WA09-E 194 +479 – 109 +521 +145 +905 +71 – 45 – 104 – 1 – 310 +32 – 502 – 451 – 379 +609 MD04-E 36 +437 +195 +401 +171 +884 +89 +431 +409 +648 +119 +617 – 343 – 256 –181 — MD05-NW 31 +173 +28 — — +205 +229 +37 +100 +519 +223 +237 +24 +185 +137 — MD05-W 3 +264 +24 — — — — +264 +214 +545 +199 +357 – 53 – 9 +53 — VT03-E 16 +397 – 180 +411 – 70 +1131 +263 +331 – 94 +687 – 181 +478 – 309 – 453 – 163 +930 VT03-S 20 +448 –209 +631 +186 +1748 +193 +182 +103 +1034 – 62 +250 –562 – 506 – 404 +716 VT03-W 83 +367 – 66 +491 +133 +1054 +179 +283 +263 +631 +222 +386 – 429 –341 – 275 +829 Legend: n = number of observations; pcu = passenger car units; Cal. = calibrated gap parameters and/or calibrated intercept Table 47. Calibration of multilane capacity models. Table 48. Average error for multilane sites.

It should be noted that the HCM 2000 model is not intended to predict capacity of a multilane entry. There is a moderate to large improvement in the RMSE when the field-measured critical headway and follow-up headway are used. The Australian model uses an approach- based critical headway and a lane-based follow-up headway. The German, French, and HCM 2000 models use an approach-based critical headway and follow-up headway. As the field-measured critical headway and follow-up headway were determined by lane, the right-lane parameters were assumed to apply to the approach. There is a large improve- ment in the Australian capacity estimates, as the field gap parameters are longer than published parameters (as noted previously). There is very little change in the calibrated German model, mostly because the estimate of the critical headway does not differ significantly from the published parameters. The French model assumes a very short follow- up headway that was not observed in the U.S. data; an increase in the follow-up headway greatly improved the esti- mates. The calibrated HCM 2000 model capacity estimates lie between the HCM 2000 upper-bound and lower-bound models (with a little more variation than captured by the HCM 2000 model limits). It should be noted that the lower- bound model results represent MD05-NW (Towson, Mary- land), which has a single-lane entry and as such has approximately half the capacity of the multilane entries. The y-intercept constant, F, in the UK model was recali- brated to local conditions and reduced from 303 to 220. While the approach error typically improves, the capacity estimate for MD05-NW is low. The recalibration of the y-intercept overcompensates the required adjustment needed at this site. Incorporating the Effects of Exiting Flow Because of the presence of an exiting vehicle, some enter- ing vehicles were perceived to reject reasonable gaps or to follow-up with hesitation. The impact is a longer estimate of the critical headway and follow-up headway, which is associ- ated with lower field capacity. Assuming that an exiting vehi- cle always impacts the entering driver behavior, the gap parameters were recalculated for single-lane sites. In practice, the exiting flow does not impact all entering vehicles; how- ever, the exact extent of the influence of exiting vehicles was not determined in this exercise. To estimate the capacity, the recalculated critical headway and follow-up headways were used with an estimate of the “conflicting plus exiting flow,” rather than just the conflicting flow. While the gap parameters are shorter, the methodology assumes that the entering vehicle is exposed to more conflict- ing events. The HCM 2000 model using the revised critical headway and follow-up headways is illustrated in Figure 28. For any given conflicting flow, the variation in the capacity estimate is due to the inclusion of exiting flow. The estimated variation in the capacity appears to be similar to the spread in the field data. However, there are two issues: (1) the RMSE is much higher with the inclusion of the exiting flow, and (2) the prediction of high conflicting flow is poor. The increase in the RMSE also occurs in the Australian and German capacity estimates. 57 0 250 500 750 1000 1250 1500 1750 0 100 200 300 400 500 600 700 800 900 1000 Conflicting Flow (pcus/hr) M ax im um E nt er in g Fl ow (p cu s/h r) Raw Data HCM - with Exiting HCM - without Exiting with exiting - RMSE = 214 without exiting - RMSE = 139 Figure 28. Effect of exiting vehicles on estimated capacity.

In summary, the inclusion of exiting vehicles in the analy- sis methodology did not improve the estimate of the capac- ity. However, because such behavior was observed in the field, refinements to the assumptions may suggest otherwise. Where the exiting event was not incorporated in the method- ology, the derived gap parameters inherently include the influence of the exiting vehicles. That is, any hesitation due to an exiting vehicle is indicated as a long follow-up headway or rejected critical headway. While this approach does not pre- dict as much variation as seen in the field data, it does more accurately reflect the average condition. Capacity Model Development Based on the analysis, this study determined that several models—ranging in complexity from simple regression models to more complex analytical (e.g., SIDRA) and regression (e.g., UK) models—can be recalibrated to achieve essentially the same goodness of fit. This section compares the goodness of fit of a simple regression model against other model forms pre- sented previously, followed by the recommended model form. Single-Lane Capacity Model Development Regression curves (both linear and exponential) are illus- trated in Figure 29, along with the class mean of the data (the mean observed capacity value for each conflicting flow value). Both regressions constitute a good representation of the class means of the entry capacity. The coefficient of determination (R2) of the linear and exponential relation- ships is approximately 0.5. Figure 30 illustrates a plot of two capacity estimates: the capacity estimate using the HCM 2000 model and average field values for the gap parameters, and the capacity estimate using exponential regression of the data. The exponential regression model yields a RMSE of 155, which is slightly bet- ter than the RMSE of 160 from the HCM 2000 model. The error also compares favorably to the error predicted by the calibrated models presented previously, with the lowest RMSE of 145, obtained using the approach gap parameters within the HCM model form. Both models tend to overesti- mate capacities at higher circulating flows. Upon closer inspection, the form of the HCM 2000 model can be transformed to be similar to that of the regression model. The HCM 2000 model form is as follows: where qe,max  entry capacity (veh/h) qc  conflicting circulating traffic (veh/h) tc  critical headway (s) tf  follow-up headway (s) The HCM 2000 expression can be simplified to yield the following: which is of the same form as where A  3600/tf B  (tc  tf /2)/3600 tc  critical headway (s) tf  follow-up headway (s) q A B qe c,max exp( ) ( )= ⋅ − ⋅ 4-3 q t t t qe f c f c,max exp / ( )= − −⎛ ⎝⎜ ⎞ ⎠⎟ 3600 2 3600 4-2 q q q t q t e c c c c f ,max exp( / ) exp( / ) (= − − − 3600 1 3600 4-1) 58 y = -0.7799x + 17.464 R2 = 0.5074 y = 18.286e -0.0677x R2 = 0.5388 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Conflicting Flow (veh/min) M ax E nt er in g Fl ow (v eh /m in) Single-Lane Data Class Mean Linear (Single-Lane Data) Expon. (Single-Lane Data) Figure 29. Linear and exponential regression and class means prediction for the single-lane entry capacity.

The predicted exponential regression intercept and slope of 1129 and 0.0010 compares favorably with the HCM intercept of (3600/tf 3600/3.2)1125 and slope of [(tctf /2)/3600 (5.13.2/2)/3600]0.0010. Such findings expand the practi- cal application of the exponential regression and allow users in the future to calibrate the constants against local data. Based on the above findings, the following form (using variables consistent with current HCM practice) is recom- mended for the entry capacity at single-lane roundabouts: where c  qe,max  entry capacity (veh/h) vc  qc  conflicting circulating traffic (pcu/h). The model parameters can be calibrated using local values of the gap parameters, per Equation 4-3. Multilane Capacity Model Development The multilane data were extracted during periods of queu- ing in the left or the right lane. Because some data for a given lane do not represent a queued condition, a plausibility check of the data was performed. The plausibility of the right- and left-lane entry capacity is given by the following equation: where qe,max  entry capacity (veh/h) qc  circulating flow (veh/h). 20 50 4− ≤ ≤ −q q qc e c,max ( )-5 c vc= ⋅ − ⋅1130 0 0010 4exp( . ) ( )-4 Using these thresholds, the right- and left-lane entry capac- ity data are reduced from 400 to 385 and 121 observations, respectively. The right-lane data also include observations at MD05-NW (Towson, Maryland), which is a single-lane entry. The multilane linear regression, exponential regression, and class mean of the entry capacity data for the right and left lanes are illustrated in Figures 31 and 32, respectively. At high conflicting flows, the right-lane linear regression tends toward zero entry capacity. The exponential model is a better fit and a good representation of the class means of the entry capacity. The coefficient of determination, R2, of the linear and exponential relationships for the right lane is 0.49 and 0.57, respectively. The regression constants are very similar to those predicted for the single-lane data. Despite the plausibility check, the left-lane data are lower than the right-lane data. The data from MD04-E (Baltimore County, Maryland), which has a dominant left-entry flow, more reasonably reflects the observed entry capacity in the right lane. Beyond a conflicting flow of 20 vehicles/min, data are limited, as reflected by the variation in the class mean. The coefficients of determination for the linear and exponential relationships for the left lane are 0.31 and 0.33, respectively. The true measurement of entry capacity requires the pres- ence of a queue in both lanes. Therefore, to predict entry capacities, plausible data must be available in both the left and right lanes, which reduces the available data from 400 to 110 observations. The multilane linear and exponential regres- sion and the class mean for the entry are illustrated in Figure 33. There are limited data at high conflicting flows, as 59 0 250 500 750 1000 1250 1500 0 200 400 600 800 1000 Conflicting Flow (pcus/hr) M ax E nt er in g Fl ow (p cu /hr ) All Data HCM Field Average tc/tf Exponential Regression y=1130e-0.001x Figure 30. Capacity using HCM and exponential regression models.

reflected by the variation in the class mean. The coefficients of determination of the linear and exponential relationships for the left lane are 0.50 and 0.53, respectively. The regression predictions are a reasonable representation of the class mean at lower conflicting flows. One of the challenges in developing a regression model for a multilane entry is incorporating the flexibility to accom- modate different lane configurations and the variety of factors that may influence the utilization of those lanes such as lane designation (e.g., left turn only versus left through), turning movement patterns, downstream influences on lane choice, and driver discomfort with the inside lane. Currently, too few sites in the United States are operating at capacity to allow the development of a separate regression model for each entry and circulating configuration; however, a lane- based model can be developed that allows the consideration of many of these factors. To maximize the available plausible data, a regression model based on the maximum entry volume in the left or right lane has been developed. In short, this model represents the capacity 60 y = -0.4188x + 15.56 R2 = 0.4899 y = 19.343e-0.0564x R2= 0.567 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 Total Conflicting Flow (veh/min) M ax im um E nt er in g Fl ow (v eh /m in) Right-Lane Data Class Mean Linear (Right-Lane Data) Expon. (Right-Lane Data) y = -0.405x + 12.066 R2 = 0.3053 y = 14.457e -0.0657x R2 = 0.3288 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 Total Conflicting Flow (veh/min) M ax im um E nt er in g Fl ow (v eh /m in) Left Lane Data Class Mean MD04-E Linear (Left Lane Data ) Expon. (Left Lane Data ) Figure 31. Regression and class mean prediction for capacity of right lane. Figure 32. Regression and class means prediction for capacity of left lane.

of the most heavily utilized lane, or critical lane, thus removing the number of entering lanes from the capacity model. Effec- tively, a capacity condition is reached when the critical lane has a constant queue. This method is akin to the concepts related to signalized intersections, where one of the lanes is assumed to have a higher flow rate than the others. The critical-lane data are illustrated in Figure 34. The RMSE of the regression is 145, which is better than the mul- tilane model’s RMSE (170 to 250) demonstrated previously. The linear regression tends toward zero at a conflicting flow of 2,300 pcu/h. The exponential regression provides a better fit and has a higher coefficient of determination. The expo- nential regression is given by the following equation: where qe,max,crit  capacity of the critical lane (pcu/h) qc  conflicting flow (pcu/h) q qe crit c,max, exp( . ) ( )= ⋅ − ⋅1230 0 0008 4-6 61 y = -0.7947x + 26.316 R2 = 0.4964 y = 33.578e-0.061x R2 = 0.527 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Total Conflicting Flow (veh/min) M a xi m u m E nt er in g Fl ow (v e h/ m in ) Left + Right Lane Data Series1 Linear (Left + Right Lane Data) Expon. (Left + Right Lane Data) Figure 33. Regression and class means prediction for entry capacity. y = -0.42x + 980 R2 = 0.4876 y = 1227e-0.0008x R2 = 0.5747 0 200 400 600 800 1000 1200 0 500 1000 1500 2000 2500 Conflicting Flow (pcu/hr) Cr itic al E nt ry F lo w (pc u/h r) Max Right or Left Lane Entry Linear (Max Right or Left Lane Entry) Expon. (Max Right or Left Lane Entry) Figure 34. Critical-lane entry data.

The following influences in the multilane data should be noted: • The critical-lane data mostly comprise right-entry-lane observations. The critical right- and left-lane observations are illustrated in Figure 35. Regression suggests that the crit- ical left-lane capacity is lower; however, there are limited left-lane observations, most of which occurred at MD04-E (Baltimore County, Maryland). Because of limited critical left-lane observations, it is difficult to establish if there is any difference in the capacity between the right lane and left lane and therefore there is insufficient evidence to suggest the need for factors that correct the regression. • The critical-lane data mostly comprise behavior of enter- ing vehicles against two conflicting lanes. MD04-E has only one conflicting lane, but too few observations to draw any conclusions. The single-lane and multilane critical-lane exponential regressions are illustrated together in Figure 36. The single-lane regression has a lower intercept than the multilane critical-lane regression. This finding is not intuitive because the average follow-up headways for the single-lane and multilane sites were found to be approximately the same; consequently, the inter- cepts should be the same. The disparity in the intercept may be caused by a number of reasons, including the lack of multilane critical-lane data observations at the intercept. The slopes of the single-lane and multilane regressions are also different. Again, the lack of multilane critical-lane data at the intercept and observations at higher conflicting flows may explain this result. Furthermore, if right-lane entering vehi- cles can accept a gap alongside a left-lane conflicting vehicle, then the actual conflicting flow may be slightly lower than the “total” conflicting flow. This event may be more likely for low conflicting flow conditions, which would influence the regression slope. Fixing the critical-lane intercept to the single-lane inter- cept of 1130, and adjusting the slope to minimize the error, yields a RMSE of 145. The single-lane and adjusted multilane critical-lane model is shown in Figure 37. Based on these findings, the recommended capacity model for the critical lane of a multilane (two-lane) roundabout is as follows: where ccrit  qe,max,crit  capacity of the critical lane (pcu/h) vc  qc  conflicting flow (pcu/h) The multilane critical-lane regression model also can be cal- ibrated using the parameters presented previously in Equation 4-3. This finding allows for the development of localized con- stants for the critical-lane regression model, thereby extending its use to accommodate changes in driver behavior. c vcrit c= ⋅ − ⋅1130 0 0007 4exp( . ) ( )-7 62 0 250 500 750 1000 1250 1500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Conflicting Flow (pcu/h) M a xi m u m E nt er in g Fl ow (p cu /h ) Critical Right-Lane Data Critical Left-Lane Data Left-Lane Extrapolation Right-Lane Extrapolation Expon. (Critical Right-Lane Data) Expon. (Critical Left-Lane Data) RL = 353 Observations; LL = 43 Observations Figure 35. Critical right-lane and left-lane entry data.

63 0 250 500 750 1000 1250 1500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Conflicting Flow (pcu/hr) M ax E nt ry F lo w (pc u/h r) y=1130e-0.001x y=1227e-0.008x All Rdbts Critical Lane Single Lane Critical Lane Regression Single Lane Regression 0 250 500 750 1000 1250 1500 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Conflicting Flow (pcu/hr) M a x En try F lo w (p cu /h r) y=1130e-0.001x y=1130e-0.0007x All Rdbts Critical Lane Single Lane Critical Lane Regression Single Lane Regression Extrapolated Regression Extrapolated Regression Figure 36. Single-lane and multilane critical-lane regression. Figure 37. Single-lane and adjusted multilane critical-lane regression.

64 Level of Service In the HCM 2000 (2), the criteria for levels of service for stop-controlled intersections and signalized intersections differ because the intersection types create different user per- ceptions. A signalized intersection is expected to carry higher traffic volumes and have longer delays. Also, with the excep- tion of permissive left turns, drivers are protected from other movements during their go phase and are not expected to find their own gap. To determine the intersection LOS at a sig- nalized intersection, the average control delay for the entire intersection is commonly used. On the other hand, the delay and the LOS for two-way-stop–controlled intersections are calculated for only the minor streets because through traffic on the major street is generally not impeded. The difference in how critical or average delay is calculated, coupled with dif- ferent LOS thresholds, makes comparing the different inter- section types difficult. Using a procedure similar to that used by drivers at two- way-stop–controlled intersections, drivers at roundabouts are required to find their own gap. The fundamental difference is that all drivers entering the roundabout are required to yield to conflicting traffic. In addition, drivers performing left-turn movements are required to find a gap in only the one direc- tion of travel. While these differences may warrant new delay thresholds for roundabouts, the magnitude of the round- about delay data generally supports using the unsignalized intersection thresholds in HCM 2000. The proposed LOS criteria for roundabouts are given in Table 49 and are the same as the LOS criteria for stop- controlled intersections in HCM 2000. The LOS for a round- about is determined by the computed or measured control delay for each lane. Defining the LOS for the intersection as a whole is not recommended because doing so may mask an entry that is operating with much higher delay than the others. Conclusion The operational analysis described in this chapter results in a new set of proposed capacity models for single-lane roundabouts and for the critical lane of two-lane round- abouts; these models fit better than any existing models, even with calibration. The effect of geometry appears to be most pronounced in terms of number of lanes (a first-order effect); the effect of fine-tuned geometric adjustments (e.g., lane width, diameter) does not appear to have as significant an effect. The current equations used for calculating control delay appear to be reasonable for use at roundabouts, with a possible adjustment at low volume-to-capacity ratios. Levels of service have been defined to correspond with other unsignalized intersections. Further discussion of the signifi- cance and applicability of these findings can be found in Chapter 6. Level of Service Average Control Delay (s/veh) A 0 – 10 B > 10 – 15 C > 15 – 25 D > 25 – 35 E > 35 – 50 F > 50 Table 49. Proposed LOS thresholds for roundabouts.