Appendixes to NCHRP Report 572: Roundabouts in the United States (2007)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

APPENDIX J OPERATIONS APPENDIX This appendix supports the operational analysis presented in Chapter 4 and provides detail on the specific operational data used for this project. Operational Data Characteristics Time Periods of Interest Extraction of data from video recordings is a time-consuming and costly process. The limited project budget required that a strategy be developed to focus only on those time periods that would provide data to meet requirements established by the project team. One of the major requirements was to identify periods during which queues were present, so that measurements of capacity could be made. To identify these periods, each of the 166 DVDs recorded for individual approaches was reviewed, and the beginning and ending periods of each queue were noted. This review identified that queues were present during 61 hours and 24 minutes, or 13 percent of the total of 474 hours of video recording. The maximum continuous queue recorded was 31 minutes and 39 seconds. However, most queues were much shorter, often one or two minutes in duration. The selection of the time periods for which data would be extracted was based on the following criteria: • The maximum queue duration, the mean queue duration, and the total queue duration were computed for each of the approaches. The approaches were then ranked according to each of these three factors. • Time plots of the queues were reviewed to visually identify periods of queuing. For example, Figure J-1 shows periods for which vehicles are continuously present at the yield line for MD07-E (Taneytown, Maryland) during a thirty-minute period (the upper lines in the figure). The figure and its associated data show one queue that was present for a period of nine minutes and 37 seconds, from 1:50:29 through 2:00:06. By contrast, there was no queue present from 2:01:14 through 2:09:10, a period of nearly eight minutes. For the three hours of video available on the MD07-E1 DVD, the maximum queue duration was nearly eleven and a half minutes while the mean queue duration was one minute and 43 seconds. A queue was present 55 percent of the time, or one hour and 40 minutes. Using these data and criteria, a total of 34 hours and 24 minutes of operations (at 13 sites) was identified for data extraction. This includes four two-lane sites (nine individual approaches) with a total of 18 hours and 30 minutes of continuous queuing and nine one-lane sites (15 individual approaches) with a total of 15 hours and 53 minutes of continuous queuing. This represents only seven percent of the total field video recording time, and demonstrates the extent of field recording that must be made to secure a useful amount of data. NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-1

0.5 1 1.5 2 2.5 1:45:00 1:50:00 1:55:00 2:00:00 2:05:00 2:10:00 2:15:00 Time V eh ic le a t s to p lin e Yes No Queue No queue Figure J-1. Presence of Vehicle at Stop Line, MD07-E1. Data Extraction Process The data extraction process consisted of five steps, including (1) an initial review of the DVD to identify periods of queuing, (2) the extraction of the raw or event data using event recording software, (3) error checking, (4) data set merging, and (5) preparation of final data sets that included one-minute summaries and computation of selected parameters such as flow rates, delays, and critical gaps. Table J-1 summarizes the steps included in the data extraction process. The parameters and events listed in this table (entry time, for example) are defined in the following sections. Primary Event Data. Five events were extracted from the DVDs using software that records keystrokes. When any of these five events occurred, the proper key was pressed and a time stamp was generated in a computer file. These events are listed in Table J-2 and illustrated in Figure J-2 for ME01-E (Gorham, Maine). For example, when a vehicle arrived at the yield line, the “1” event was recorded; when a vehicle entered the circulating roadway, the “2” event was recorded. NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-2

TABLE J-1. Data Extraction Process Activity Purpose Description Step 1. Initial DVD review To identify periods of continuous queuing and pedestrian/bicycle activity • Each DVD is reviewed for quality of field of view (can all points of interest be clearly observed?). • Each Sony camera DVD is reviewed for periods of continuous queuing. The begin and end times for queuing activity are noted. • Each time period is reviewed for pedestrian and bicycle activity. Flow rate data. The following events are extracted for selected DVDs recorded with the omni-directional camera: • Entry time • Entry approach • Exit time • Exit approach • Vehicle type (passenger car or other) Gap data. The following events are extracted for selected DVDs recorded with the Sony camera: • First-in-queue time • Entry time • Conflict time • Exit time Delay data. The following events are extracted for selected DVDs recorded with the Sony camera: • Upstream time • First-in-queue time • Entry time Step 2. Raw data (event) extraction To record the time stamps for all events of interest during periods of continuous queuing Pedestrian/bicycle data. The following events are extracted for selected DVDs recorded with the Sony camera: • Pedestrian first-in-queue time • Pedestrian entry time • Vehicle yield • Pedestrian exit time • Pedestrian type • Pedestrian conflict time Step 3. Error checking and time corrections To identify keystroke (event recording) errors and to account for differences in DVD starting times • Common events (Entry time, first in queue time, exit time) from the three data sets (flow rate data, gap data, delay data) are compared for consistency. Problems are reviewed and corrected. • Common vehicle events are identified for each DVD covering the same time periods. Time correction factors are computed based on the observation of these common vehicle events. Time stamps are adjusted based on this time correction factor. • One minute summaries are prepared for the common events to further verify the accuracy of the event data sets. NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-3

TABLE J-1 (cont.). Data Extraction Process Activity Purpose Description Step 4. Merge event data sets To merge data sets for each roundabout approach Data from the three data sets (flow rate data, gap data, delay data) for each approach and time period are merged. The following time/events are included for each vehicle: • Upstream time • First-in-queue time • Entry time • Exit time • Exit approach • Vehicle type The following data (time/events) are also recorded for the circulating vehicles affecting the subject approach: • Conflict time • Exit time Step 5. Prepare data summaries and compute parameters of interest To prepare one- minute summaries for each data set and to compute selected parameters The following data are computed based on the merged data sets prepared in step 4. • Turning movement flow rates, 1-minute summaries • Delays, 1-minute summaries • Follow up times • Critical gaps • Entry and circulating flows during periods of continuous queuing, 1-minute summaries TABLE J-2. Operational Events of Interest Event Keystroke Description Entry time 2 The entry of a vehicle into the roundabout from the approach. The time was recorded when the vehicle crossed the yield line; the lane placement of the vehicle (either left lane or right lane) was recorded for two lane roundabouts. The vehicle type was also recorded. First-in-queue time 1 The arrival of a vehicle into the server or first-in-line position on the approach. The time was recorded when the vehicle was about to enter the roundabout (if it did not stop) or the time that it stopped at or near the yield line waiting to enter the roundabout. Upstream time z The passage of a vehicle past a point upstream of where a queue will form on the approach. Conflict time s The passage of a vehicle through the conflict point on the roundabout, a point that is adjacent to the point of entry for a minor street vehicle. Exit time a The exiting of a vehicle from the roundabout. NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-4

z1 2 a s Note: Numbers and letters in figure are defined in Table J-2. Figure J-2. Location of Events of Interest on Roundabout Approach (ME01-E). Secondary Derived Data. The event data were used to compute a set of secondary, or derived, data. For example, the number of events that occur during a specified time interval is the flow rate past the point at which the event was recorded. Similarly, the time difference between the passing of two vehicles at a given point is the headway between these two vehicles. A complete list of the secondary data is given below: • The flow rate is the number of vehicles passing by a given point during a specified time interval. Flow rates were computed for entry flows, circulating flows, and exit flows. Events “2”, “s”, and “a” described previously were used to compute these flow rates. • Delay is the time spent traveling from the “z” line to the yield line (the “2” event) on a given approach that is in excess of the free flow time for this same path. The free flow time was measured for each approach, considering a sample of vehicles moving unobstructed from the “z” line to the “2” (yield) line. The actual travel time for each vehicle was computed for this same pair of events. The difference between these two travel times is the delay for a given vehicle. • The turning movement proportion is the proportion of vehicles entering from one approach and traveling to each of the possible exit points on the roundabout. The “2” and “a” events were used to compute the turning movement data. • The gaps between vehicles on the circulating roadway that were accepted or rejected by vehicles on the minor approach were recorded. A gap sequence is the sequence of events that includes the first circulating vehicle (events “s” or “a”), any intervening entry vehicles (event “2”), and the second circulating vehicle (events “s” or “a”). NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-5

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-6 For multi-lane roundabouts, the lane position of vehicles on the circulating roadway must be considered in this gap sequence. • The service time is the time difference for a minor approach vehicle between the “1” event and the “2” event. This is the time that a vehicle spends in the server. • The move up time is the time difference between the entry of one vehicle into the roundabout (the “2” event) and the arrival of the following vehicle at the yield line (the “1” event). • The travel time on the roundabout is the elapsed time from the entry of a vehicle into the roundabout (the “2” event) and the exit of the vehicle from the roundabout (the “a” event). • The proportion of time that a queue exists on an approach for each minute (referred to later in this paper as proportion time queued) is the sum of the service times plus the move-up times for all vehicles that entered the roundabout during that minute, divided by sixty seconds. One-minute summaries were prepared for the following secondary data: • Entry flow • Conflicting flow • Exit flow • Average delay • Proportion time queued The following gap data were computed for each vehicle entering the roundabout: • The duration of the accepted or rejected lag, defined as the time from the arrival of the minor vehicle at the server (the “1” event) to the arrival of the next conflicting vehicle (the “s” event). • The durations of all gaps that are rejected by the minor vehicle, defined as the times between subsequent vehicles on the circulating roadway (“s” events). • The duration of the gap that is accepted by the minor vehicle, defined as the time between the two consecutive conflicting vehicles on the circulating roadway (“s” events). The following terms are used in the subsequent analysis of the gap data. • The lag is defined as the time between the arrival of the vehicle in the first in queue position (the “1” event) and the passage of the next conflicting vehicle (the “s” event). • The gap is defined as the time between consecutive passages of two conflicting vehicles (the “s” event). Turning Movement Data Turning movement flow rates were determined using the entry flow rate and the turning movement proportions. The entry flow rate was based on the “2” event data, described earlier. Turning movement proportions were estimated by tracking randomly selected vehicles through the roundabout, where the turning movement proportion of the sample was assumed to be similar to that of the population. Vehicle samples were chosen randomly, by following the steps below, while viewing the omni-directional video: • Step 1. Select a vehicle to sample

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-7 • Step 2. Track the selected vehicle to its exit leg • Step 3. Record the turning movement and times for entry and exit for each vehicle • Step 4. Repeat steps 1 through 3. The turning movement proportions were then calculated from the sampled data. Finally, the turning movement flow rate was determined by multiplying the entry flow rate by the turning movement proportion. Summary of the Operational Database The operational database assembled for this project represents a rich resource for roundabout operations, not only for this project but also for future research efforts. The database for one-lane sites includes fifteen unique approaches and a total video time of 15:53:16. The database for two-lane sites includes nine unique approaches and a total video time of 18:30:18. In addition, additional video provided by others was used to supplement the video collected and extracted using the methods described above. Table J-3 shows some of the highlights of the data sets that were produced based on the 34 hours and 24 minutes of traffic operations. The database for the one-lane sites includes 884 one-minute time intervals. The maximum entry flow rate is 24 vehicles per minute, while the maximum conflicting flow rate is 18 vehicles per minute. The maximum one-minute average delay is 47.1 seconds per vehicle. The mean one-minute proportion time queued for all one- minute data points is 0.78. The database for the two-lane sites includes 923 one-minute time intervals. The maximum entry flow rate per lane is 19 vehicles per minute, while the maximum conflicting flow rate per lane is 48 vehicles per minute. The maximum one-minute average delay is 121.7 seconds per vehicle. The mean one-minute proportion time queued data is 0.55 for the left lane data and 0.65 for the right lane data. A gap sequence consists of all gaps that must be considered by an entering vehicle. For the one-lane sites, 10,751 gap sequences were measured. Of these: • The entry vehicle accepted the lag 77 percent of the time (8,282 gap sequences), • The entry vehicle rejected the lag but then accepted the first gap 12 percent of the time (1,318 gap sequences), and • The entry vehicle rejected the lag, rejected the first gap, but then accepted a subsequent gap 11 percent of the time (1,151 gap sequences). For the two-lane sites, 13,530 gap sequences were measured. Of these: • The entry vehicle accepted the lag 39 percent of the time (5,295 gap sequences), • The entry vehicle rejected the lag but then accepted the first gap 8 percent of the time (1,067 gap sequences), and • The entry vehicle rejected the lag, rejected the first gap, but then accepted a subsequent gap 53 percent of the time (7,168 gap sequences). The mean travel time (from the entry to the exit of the roundabout) for one lane sites ranged from 3.1 seconds for right turning vehicles to 10.8 seconds for left turning vehicles. For two lane sites, the range was 2.7 seconds for right turning vehicles to 11.9 seconds for left turning vehicles.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-8 TABLE J-3. Operational Data Set Highlights Parameter One-lane sites Two-lane sites Summary • Number of sites • Number of unique approaches • Total video time for extracted data 9 15 15:53:16 4 9 18:30:18 Number of one-minute data points • Total • Number in which proportion time queued exceeded 0.90 884 344 923 135 (left lane) 218 (right lane) Ranges, one minute measurements • Entry flow per lane, veh/min • Conflicting flow per lane, veh/min • Delay, sec/veh 2 – 24 0 – 18 0.0 – 47.1 0 – 19 0 – 48 0 – 121.7 Mean proportion time queued for all one-minute data points 0.78 0.55 (left lane) 0.65 (right lane) Gap sequences • Total • Number involving an accepted lag • Number involving a rejected lag followed by an accepted gap • Number involving a rejected lag, followed by one or more rejected gaps, followed by an accepted gap 10,751 8,282 1,318 1,151 13,530 5,295 1,067 7,168 Turning movement proportions, means for sites • Left turns • Through movements • Right turns 0.29 0.46 0.31 0.35* 0.35 0.29 Travel time through roundabout (sec) • Left turns • Through movements • Right turns • U-turns 10.8 6.6 3.1 16.2 11.8 7.4 2.7 18.8 * Turning movement proportion data were not available for all multi-lane roundabouts. The data shown here are averaged over all four approaches for two different roundabouts (MD04 and VT03), a total of eight approaches. Capacity and Delay Data For capacity analysis, the data described above were extracted in one-minute intervals during periods of persistent queuing. Persistent queuing was identified at eighteen one-lane approaches (from a total of eleven one-lane sites) and seven two-lane approaches (from a total of four multilane sites). A total of 320 and 400 minutes of data during visually verified queuing was extracted at the single-lane and multilane sites respectively. The delay observations are not dependant on periods of persistent queuing, and hence a much larger data based is available for the analysis. Respectively, 849 and 1,012 minutes of delay data were extracted at the single- and multilane sites. The strength and duration of queuing, the entry capacity flow relationships, and the approach delay and variation are described in subsequent sections.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-9 Single-Lane Approach Summary A summary of the general operational characteristics of the eighteen single-lane approach data is illustrated in Table J-4. A maximum of 85 queued minutes were observed at WA04-N (Port Orchard, Washington). As noted, the total minutes of queuing are not sequential, and in the case of WA04-N the data were collected over two days. Ten of the eighteen approaches have less than 10 minutes of full minutes of queuing. The maximum observed entry flow is 24 vehicles per minute, or 1440 vehicles per hour, observed at MD06-N (Lothian, Maryland). The maximum conflicting flow is 18 vehicles per minute, or 1080 vehicles per hour, observed at WA01-W (Gig Harbor, Washington). The maximum delay is 47 seconds per vehicle. The duration of the queue (sequential minutes of queuing), and queue characteristics, are illustrated in Table J-5. While the maximum number of minutes of queuing is observed at WA04-S (Port Orchard, Washington), ME01-E (Gorham, Maine) had a sustained queue for 32 minutes, followed by MD07-E (Taneytown, Maryland), which had a sustained queue for 12 minutes. Five of the eighteen approaches only have a sustained queue of one minute. The maximum queue length was in excess of 20 vehicles. Table J-5 also illustrates the total time that the approach queue exceeds the distance z upstream of the entry line. This distance varies based on the approach, and is between five and eight vehicles in length. Approximately 10 of the full minutes of queuing observations have a queue length less than z. Most queued minute observations have queues that extend beyond z for some portion of the minute. TABLE J-4. Parameter Summary for One-Lane Sites, One-Minute Data Entry flow (veh/min) Conflicting flow (veh/min) Delay (sec/veh) Site Location Full minutes of queuing (# mins) Min Max Min Max Min Max MD06-N Lothian, MD 14 2 24 0 5 0.3 16.0 MD06-S Lothian, MD 4 3 10 5 15 5.4 35.7 MD07-E Taneytown, MD 56 2 20 0 11 0.0 44.7 ME01-E Gorham, ME 42 5 18 1 13 0.2 42.3 ME01-N Gorham, ME 1 2 9 5 15 3.0 38.0 MI01-E Okemos, MI 8 4 12 3 13 1.5 47.0 OR01-S Bend, OR 15 2 15 0 15 0.4 44.1 WA01-N Gig Harbor, WA 3 2 10 3 16 1.1 47.1 WA01-W Gig Harbor, WA 6 3 11 3 18 2.9 43.5 WA03-E Bainbridge Island, WA 2 5 16 1 7 1.7 14.3 WA03-S Bainbridge Island, WA 28 2 16 0 12 0.3 25.8 WA04-E Port Orchard, WA 15 6 22 0 14 2.3 18.9 WA04-N Port Orchard, WA 85 3 23 0 13 0.2 28.6 WA04-S Port Orchard, WA 4 5 16 3 13 0.6 32.4 WA05-W Sammamish, WA 6 8 21 0 6 1.3 15.1 WA07-S Lacey, WA 1 11 18 3 7 4.8 13.2 WA08-N Kennewick, WA 4 7 17 3 13 0.5 19.9 WA08-S Kennewick, WA 24 8 23 0 10 0.5 19.7 Note: Bold indicated maximum value observed.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-10 TABLE J-5. Intervals and Length of Queuing for One-Lane Sites Approach Full minutes of queuing (# mins) Maximum duration of queuing (mins) Maximum queue length (vehs) Total time where queue > z MD06–N 14 2 20+ 0:26:34 MD06–S 4 1 7 NA MD07-E 56 12 22+ 0:54:08 ME01-E 42 32 20+ 0:43:29 ME01-N 1 1 7 0:01:33 MI01-E 8 1 NA NA OR01-S 15 4 8 0:15:35 WA01–N 3 4 8 0:03:26 WA01-W 3 2 5 0:02:15 WA03-E 2 1 4 0:02:16 WA03-S 28 5 8 0:34:08 WA04-E 15 5 10+ 0:18:18 WA04-N 85 8 11+ 1:59:53 WA04-S 4 3 8 0:03:41 WA05-W 6 6 12+ 0:15:31 WA07-S 1 1 5 0:04:23 WA08-N 4 3 NA NA WA08-S 24 15 NA NA As shown in Table J-6, a large number of entering vehicles hesitate unnecessarily at the entry line. No conflicting vehicles were observed during these periods; however, the impact of the exiting vehicles on the entering vehicles is significant enough to warrant further investigation. Single-Lane Entry Flow and Conflicting Flow Data Figure J-3 illustrates the entry flow as a function of the conflicting flow for queuing and non-queuing minutes. The density of the data is shown for each entry flow-conflicting flow combination. A large number of observations fall between an entry-plus-conflicting flow of 18 vehicles per minute, or 1080 vehicles per hour. The maximum observed entry-plus-conflicting flow was 25 vehicles per minute, or 1500 vehicles per hour. A potential caution regarding the data is that other roundabout sites may be serving higher volumes (and thus operating at higher capacities) but were not included in the data due to a lack of observed queuing. However, as can be seen in Figure J-4 for the sites for which data were reduced, entry volumes are much lower for the non-queued minutes than for queued minutes. There are very few non-queued data points that fall within the queue data, and there are no non-queued data points that exceed the queued data. This cannot discount the possibility that sites outside of those for which data were collected and reduced may experience higher capacities, but a more extensive data collection and reduction effort was not possible within the scope and budget of this effort.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-11 TABLE J-6. Percent of Vehicles that Hesitate Unnecessarily at One-Lane Sites The maximum entry flow as a function of the conflicting flow for data measured during period of continuous queuing is illustrated in Figure J-5. When there is no conflicting flow (data along the y-axis) the maximum entry flow varies between 15 and 25 vehicles per minute, or 900 and 1500 vehicles per hour. A maximum conflicting flow of approximately 15 vehicles per minute or 900 vehicles per hour was observed. Under this condition the entry capacity varies between 5 and 10 vehicles per minute, or 300 and 600 vehicles per hour. The maximum entry and conflicting flow for site approaches with 15 or more minutes of queued data are illustrated by site in Figure J-6. For a given conflicting flow, WA04-N (Port Orchard, Washington) and MD07-E (Taneytown, Maryland) have significant variation in the maximum entry flow. Given that the geometry at the approach is fixed, the minute-by-minute variation in the maximum entry flow is dictated by driver behavior, vehicle type, and in some cases the apparent influence of exiting vehicles. The OR01-S site (Bend, Oregon) has high conflicting flows with maximum entering flows that are typical when compared with observations at other sites. The WA08-S site (Kennewick, Washington) has typically high maximum entry flows; these are likely the result of a large proportion of high school drivers due to the site’s proximity to a high school. Site # % Entry Vehicles (that yield to non- conflicting vehicles) MD06-N 26 MD06-S 0 MD07-E 6 ME01-E 5 ME01-S 33 MI01-E NA OR01-S 5 WA01-N 8 WA01-W 0 WA03-E 40 WA03-S 13 WA04-E 14 WA04-N 11 WA04-S 4 WA05-W 11 WA07-S 7 WA08-N NA WA08-S NA

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-12 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 24 1 23 1 22 1 1 21 1 1 20 2 1 2 19 3 3 2 4 18 5 4 9 4 3 2 1 17 2 3 7 7 7 1 2 16 2 5 6 10 5 4 1 1 15 2 6 9 15 6 7 4 4 2 1 1 14 4 8 6 20 17 9 8 5 2 13 1 3 9 10 7 16 13 2 3 1 1 12 3 3 5 9 16 12 16 8 7 3 11 4 5 6 7 6 11 12 5 7 9 3 2 2 10 1 3 5 8 8 8 7 9 11 6 7 3 9 1 4 5 5 9 5 6 7 6 4 6 2 4 8 2 1 4 4 7 5 9 8 5 3 4 1 2 2 4 2 7 1 1 2 4 7 2 8 2 3 5 1 4 2 1 2 6 1 5 1 2 2 6 8 2 4 1 3 1 3 3 1 5 2 2 1 1 2 1 1 2 5 2 2 2 2 2 1 4 1 1 2 1 5 2 2 1 5 1 2 3 3 3 2 1 1 1 1 1 2 2 2 1 2 2 1 1 1 1 2 1 1 En tr y flo w (v eh /m in ) Conflicting flow (veh/min) Figure J-3. Entry Flow vs. Conflicting Flow, Number of Observations for Each Entry Flow/Conflicting Flow Cell, One-Lane Sites 0 5 10 15 20 25 30 0 5 10 15 20 Conflicting Flow (veh/min) En te rin g Fl ow (v eh /m in ) Queued No Queue Figure J-4. Entry and Conflicting Flow for Queued and Non-Queued Minutes

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-13 0 5 10 15 20 25 0 5 10 15 20 Conflicting Flow (veh/min) M ax E nt er in g Fl ow (v eh /m in ) Figure J-5. Maximum Entry Flow as a Function of Conflicting Flow, One-Minute Data WA04 (Port Orchard) North 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) M ax E nt er in g Fl ow (v eh /m in ) Taneytown (MD07) East 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) Figure J-6. Maximum Entry Flow as a Function of Conflicting Flow – Sites with Greater Than 15 or More Full Minutes of Queuing

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-14 ME01 (Gorham) East 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) M ax E nt er in g Fl ow (v eh /m in ) OR01 (Bend) East 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) WA03 (Bainbridge) South 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) M ax E nt er in g Fl ow (v eh /m in ) WA04 (Port Orchard) East 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) WA08 (Kennewick) South 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) M ax E nt er in g Fl ow (v eh /m in ) MD06 (Lothian) North 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 Conflicting Flow (veh/min) Figure J-6 (cont). Maximum Entry Flow as a Function of Conflicting Flow – Sites with Greater Than 15 or More Full Minutes of Queuing

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-15 Single-Lane Delay Data The measured delay is based on the difference between the free flow and measured travel time of a travel trip between z (an arbitrary distance upstream of the entry line) and the entry line. By definition, control delay at a roundabout includes the initial deceleration delay, queue move-up time and stopped delay caused by the traffic control device and the right-of-way rules it establishes. If the queue is greater than z, the deceleration delay and some of the queue move-up time is excluded. As noted in Table J-5, most of the data collected during a full minute of queuing are also observations where the queue exceeds z. Furthermore, the deceleration delay is also excluded for observation where the queue is just less than z. Because this behavior has not been identified on a minute-by-minute basis, only preliminary delay comparisons can be made. Figure J-7 illustrates the frequency of delay observations for the one-lane approaches, using five-second bins from zero seconds to 50 seconds. The mean delay is 9.9 seconds. Most of the delay measurements are less than 15 seconds per vehicle. Figure J-8 illustrates a plot of the mean delay for each entry flow/conflicting flow pair. As expected, delays increase as the combination of entry and conflicting flows increase. Multilane Approach Summary Table J-7 summarizes the multilane approach characteristics. Of the eight approaches, four different lane configurations: • Two entry and two conflicting lanes (5 approaches), • Two entry and one conflicting lane (1 approach), • One entry and two conflicting lanes (1 approach), and • Two entry lanes (one short lane) and two conflicting lanes (1 approach). 0 50 100 150 200 250 300 350 0 5 10 15 20 25 30 35 40 45 50 Average delay (sec/veh) N um be r o f o bs er va tio ns Figure J-7. Number of One-Minute Observations, Average Delay, One-Lane Sites

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 25 24 2.8 23 2.6 22 3.9 6.9 21 5.0 5.0 20 4.1 11.7 5.1 19 4.1 4.4 2.6 7.7 18 6.5 5.3 6.0 5.7 6.0 6.3 11.9 17 4.1 4.3 13.1 9.1 9.1 5.1 8.6 16 4.3 6.4 9.2 9.0 7.4 9.5 10.0 7.3 15 9.9 8.5 6.5 8.7 8.8 9.2 8.3 11.9 15.4 12.5 10.2 14 5.4 7.5 14.7 8.0 9.9 8.5 10.6 8.7 9.9 13 1.0 10.4 15.1 8.3 10.6 12.3 11.0 7.5 12.9 9.5 6.5 12 5.6 11.5 7.2 6.8 9.3 10.7 10.9 12.5 11.1 17.4 11 5.2 4.7 8.7 6.6 7.4 16.6 14.1 9.9 10.6 13.0 16.7 18.2 25.2 10 4.9 6.3 9.2 6.1 10.9 9.2 10.9 12.9 14.9 13.8 14.7 19.0 9 1.7 4.0 4.5 4.4 7.3 9.6 7.9 8.3 13.2 12.0 18.6 7.8 21.5 8 2.6 3.6 6.2 10.6 7.5 3.8 4.2 8.4 14.6 11.6 16.1 31.8 12.6 30.2 19.2 18.4 7 18.7 3.0 10.3 5.3 10.4 8.7 9.2 5.7 12.5 10.2 7.8 21.0 10.3 44.1 20.9 6 0.6 6.1 0.8 6.7 3.2 5.5 5.6 5.3 8.6 21.0 6.1 43.5 21.5 18.3 25.9 5 6.9 5.7 2.1 2.2 9.3 4.9 3.8 4.9 11.7 20.2 15.6 19.1 25.2 29.2 20.6 4 3.6 4.1 5.8 3.8 5.9 14.5 5.2 6.6 11.2 38.0 26.3 3 1.2 2.3 11.6 2.8 1.2 15.0 6.8 4.6 21.5 14.0 2 1.9 0.9 1.6 5.8 1.4 0.3 3.0 5.6 3.5 1 En tr y flo w (v eh /m in ) Conflicting flow (veh/min) Figure J-8. Entry Flow vs. Conflicting Flow, One-Minute Data, Delay for One-Lane Sites TABLE J-7. Multilane Site Characteristics Turning Proportion Site Location Lane description Year Open Entry Lane Utilization (R/L) Left Thru Right U-Turn Notes CO51-E Vail, CO 2L entry 2L circulating 1995 60/40 N/A N/A N/A N/A FL11-E Clearwater, FL 2L entry 2L circulating 1999 55/45 N/A N/A N/A N/A FL11-W Clearwater, FL 2L entry 2L circulating 1999 55/45 N/A N/A N/A N/A MD04-E Baltimore, MD 2L entry, 1L circulating 1999 35/65 72% 28% 1% 0% 20% of lefts in right lane MD05-NW Towson, MD 1L entry, 2L circulating - unstriped 1996 N/A (1L) N/A N/A N/A N/A MD05-W Towson, MD 2L entry 2L circulating- unstriped 1996 65/35 N/A N/A N/A N/A Short right lane VT03-W Brattleboro, VT 2L entry, 2L circulating 2000 75/25 30% 49% 21% 0% VT03-E Brattleboro, VT 2L entry, 2L circulating- unstriped 1999 60/40 28% 39% 31% 3% VT03-S Brattleboro, VT 2L entry (at times 3L), 2L circulating- unstriped 1999 75/25 19% 32% 46% 4% 50% of lefts in right lane; 15% of throughs in left lane WA09-E Gig Harbor, WA 2L entry, 2L circulating 2001 90/10 9% 86% 5% 1% 10% of throughs in left lane

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-17 The two-lane southern approach at VT03-S (Brattleboro, Vermont) behaves as three lanes at times (it was previously a three-lane entry before being re-striped as a two-lane entry with no changes to the curb locations). A utilization of 90 percent in the right lane and 10 percent in the left lane was observed on the east approach of WA09-E (Gig Harbor, Washington). The heavy demand for the right lane is due to the two single-lane downstream exits. MD04-E (Baltimore County, Maryland) is the only site with heavy use of the left lane. Despite markings that allow left turns in both lanes, only 20 percent of left turn vehicles queue in the right lane. The VT03 (Brattleboro, Vermont) site has heavy use of the right lane; however, 50 percent of the left turn movements are performed from the right lane, and only 15 percent of the through movements are performed from the left lane. In this case, drivers do not appear to find the left lane desirable. A summary of the general operational characteristics of the multilane approach data is illustrated in Table J-8. A maximum of 194 queued minutes were observed at WA09-E (Gig Harbor, Washington). The total minutes of queuing are not sequential, and in the case of WA09- E the data were collected over two days. The maximum observed entry flow in the right lane is 21 vehicles per minute, or 1260 vehicles per hour, observed at WA09-E. The maximum observed entry flow in the left lane is 15 vehicles per minute, or 900 vehicles per hour, observed at MD04-E (Baltimore County, Maryland). The maximum conflicting flow is 42 vehicles per minute, or 2520 vehicles per hour, observed at MD05-NW (Towson, Maryland). The maximum delay in the left and right lanes, respectively, is 55 seconds per vehicle (MD04-E) and 121 seconds per vehicle (MD05-NW). The duration of the queue (sequential minutes of queuing), and queue characteristics, are illustrated in Table J-9. While the maximum number of minutes of queuing is observed at WA09-E (Gig Harbor, Washington), the MD04-E (Baltimore County, Maryland) has the longest sustained queue of 21 minutes. Two of the eight approaches only have a sustained queue for two minutes. TABLE J-8. Summary of Multilane Sites, One-Minute Data Left entry flow (veh/min) Right entry flow (veh/min) Total conflicting flow (veh/min) Left entry delay (sec/veh) Right entry delay (sec/veh) Site Location Min Max Min Max Min Max Min Max Min Max CO51-E Vail, CO 3 10 5 14 N/A N/A 13 25 N/A N/A FL11-E Clearwater, FL N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A FL11-W Clearwater, FL N/A N/A N/A N/A N/A N/A N/A N/A N/A N/A MD04-E Baltimore, MD 4 15 1 14 2 16 10 55 1 33 MD05-NW Towson, MD N/A N/A 1 16 8 42 N/A N/A 16 121 MD05-W Towson, MD 0 4 2 5 20 28 19 36 25 40 VT03-W Brattleboro, VT 0 9 4 16 3 23 4 33 0 26 VT03-E Brattleboro, VT 0 10 1 11 11 20 6 40 9 40 VT03-S Brattleboro, VT 1 10 8 15 7 14 5 22 1 22 WA09-E Gig Harbor, WA 0 16 3 21 3 18 0 36 4 76

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-18 TABLE J-9. Summary of Multilane Site Operational Characteristics Site # Location Full queued minutes (Left or Right) Duration of queue (mins) CO51-E Vail, CO 16 14 FL11-E Clearwater, FL N/A N/A FL11-W Clearwater, FL N/A N/A MD04-E Baltimore, MD 36 21 MD05-NW Towson, MD 33 14 MD05-W Towson, MD 16 2 VT03-W Brattleboro, VT 16 5 VT03-E Brattleboro, VT 20 5 VT03-S Brattleboro, VT 83 2 WA09-E Gig Harbor, WA 194 17 Multilane Entry Flow and Conflicting Flow Data Figure J-9 illustrates the right-lane and left-lane entry flow as a function of the conflicting flow for queuing and non-queuing minutes. The density of the data is shown for each entry- conflicting flow combination. In the right-lane, a large number of entry plus conflicting flow observations are around 20 to 22 vehicles per minute. In contrast, the left-lane observations are much lower, around 13 to 15 vehicles per minute. The maximum entry plus conflicting flow is 29 vehicles per minute or 1740 vehicles per hour. Figure J-10 illustrates the data for visually observed minutes of queuing identified in either the left or right-lane. The data are broken into observations for the different lane configurations. The two-entry/two-conflicting lane data are dominated by observations at WA09-E (Gig Harbor, Washington). As noted, WA09-E has high right-lane utilization, and there are a number of zero entry flow observations in the left lane. The MD04-E (Baltimore County, Maryland) has two entry lanes, one conflicting lane, and high utilization of the left lane. As a result, the right-lane data is typically low. MD05-NW (Towson, Maryland) has one entry lane and, as shown, some of the highest conflicting flows observed at the multilane sites. Capacity of the approach is defined as the sum of the maximum entry flow in each lane. Problematic to the investigation of capacity of the approach is the lack of queuing in each lane within the same minute. The two-entry/two-conflicting right-lane data is illustrated in Figure J-11. For a given conflicting flow, the WA09-E (Gig Harbor, Washington) and VT03-W (Brattleboro, Vermont) sites have significant variation in the maximum entering flow. Given that the geometry at the approach is fixed, the minute-by-minute variation in the maximum entry flow is dictated by driver behavior, vehicle type, and in cases the influence of exiting vehicles.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 0 1 1 1 1 1 1 2 1 1 3 3 1 2 2 2 2 1 1 1 1 2 3 1 1 2 2 1 1 2 1 2 4 1 1 3 2 2 1 1 2 2 2 3 3 1 1 2 1 1 3 1 1 2 3 3 4 8 4 7 7 1 2 5 2 2 5 1 2 3 3 1 1 1 1 2 4 3 2 4 1 1 1 1 9 1 5 7 5 4 8 7 5 5 5 2 3 5 1 1 1 2 1 1 1 2 1 5 3 1 2 1 6 2 3 8 7 8 2 7 6 8 5 2 1 2 1 3 3 1 1 1 2 1 2 2 6 1 3 3 3 7 6 8 6 6 2 3 7 1 6 3 2 3 1 1 1 1 1 1 7 5 3 4 3 6 3 7 8 7 9 9 6 3 2 3 1 2 1 1 1 8 1 1 3 3 5 2 2 7 5 2 4 12 10 6 7 2 5 2 3 1 1 1 9 1 4 2 4 4 10 7 7 5 4 3 8 2 1 1 1 10 2 3 2 2 1 9 4 4 5 8 4 3 2 3 1 11 1 1 1 1 3 3 7 6 4 6 5 4 2 4 3 1 12 1 1 1 5 1 3 3 12 8 3 1 5 2 1 13 1 1 1 4 5 6 4 8 4 1 4 1 14 1 1 1 4 3 2 2 3 1 3 2 2 15 1 2 1 1 2 1 1 16 2 1 3 1 1 1 17 1 1 18 1 19 1 20 21 22 23 24 25 En tr y Fl ow , R L (v eh /m in ) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 0 2 1 3 4 3 4 2 2 1 4 2 1 1 1 1 1 1 2 1 1 1 2 3 2 4 7 9 8 4 7 9 1 7 4 4 2 1 1 1 1 2 2 1 1 1 6 6 6 8 7 12 13 4 6 3 1 2 2 3 1 2 1 1 1 3 1 2 3 3 7 5 9 3 7 5 13 8 7 6 3 1 3 1 1 1 4 2 1 1 4 3 5 5 8 9 3 3 8 5 1 3 3 2 3 1 1 5 1 1 1 3 4 2 5 4 5 7 7 5 2 6 4 3 3 1 1 1 1 1 6 1 1 5 1 1 5 5 5 6 7 3 2 4 2 2 2 1 1 1 7 2 3 3 2 4 4 13 4 5 7 2 4 2 2 1 8 3 3 7 1 5 5 2 1 2 3 5 5 1 1 1 1 9 2 2 1 1 1 4 2 5 3 3 5 7 5 1 1 2 10 2 1 6 3 4 3 7 6 6 1 4 1 2 1 11 3 1 6 5 2 1 2 12 1 2 4 2 3 1 3 1 3 1 13 2 1 2 1 5 2 2 1 1 14 1 1 2 2 2 1 15 1 1 1 16 2 1 17 1 1 18 1 19 1 20 21 22 23 24 25 En tr y flo w , L L (v eh /m in ) Figure J-9. Right and Left Entry Flow vs. Conflicting Flow

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-20 Right Lane Multilane Data - Visually Verif ied Queues 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 ) 2L Entry / 2L Conflicting 1L Entry / 2L Conflicting 2L Entry / 1L Conflicting Left Lane Multilane Data - Visually Verif ied Queues 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 ) 2L Entry / 2L Conflicting 2L Entry / 1L Conflicting Figure J-10. Right and Left Entry Flow vs. Conflicting Flow

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-21 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 ) All 2L Entry/ 2L Conflicting Data WA09-E 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 Total Conflicting Flow (veh/min) All 2L Entry/ 2L Conflicting Data VT03-E 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 ) All 2L Entry/ 2L Conflicting Data VT03-S 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 Total Conflicting Flow (veh/min) All 2L Entry/ 2L Conflicting Data VT03-W Figure J-11. Right Maximum Entry Flow vs. Conflicting Flow for Two Conflicting Lane Approaches Comparison of Single-and Multilane Entry and Conflicting Flow Data The single-lane data have a conflicting flow range of approximately 0 to 15 vehicles per minute, while the multilane data vary between 5 and 40 vehicles per minute. For a conflicting flow of 5 vehicles per minute, the maximum entry flow for the single and multilane sites is approximately 19 vehicles per minute. For a conflicting flow of 15 vehicles per minute the maximum entry flow for the single and multilane sites is approximately 8 and 15 vehicles per minute respectively. Two factors are at play. Firstly, there are fewer observations for the single- lane sites at higher conflicting flows. Secondly, the maximum flow at the multilane sites are typically observed in the right lane and the total conflicting flow does not necessarily represent the actual conflicting flow negotiated by vehicles in the right entry lane.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-22 Multilane Delay Data Figure J-12 illustrates the frequency of the delay observations for all multilane sites, using five-second bins from zero seconds to 95 seconds. The mean delay is 10.7 seconds per vehicle. Most of the delay measurements are less than 20 seconds per vehicle. Figure J-13 shows plots of the mean delay for each entry flow/conflicting flow pair. As expected, delays increase as the combination of entry and conflicting flows increase. 0 50 100 150 200 250 300 350 400 450 5 15 25 35 45 55 65 75 85 95 Average delay (sec/veh) N um be r o f o bs er va tio ns LL RL Figure J-12. Number of One-Minute Observations, Average Delay, Two-Lane Sites 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 0 3.3 19.2 6.1 1 0.5 2.4 6.3 2.8 24.4 3.6 6.8 1.5 22.1 5.8 14.5 3.2 14.4 71.3 4.5 52.2 5.0 17.0 22.2 84.2 2 8.2 0.0 4.9 3.9 17.0 7.1 2.0 12.6 3.4 1.1 9.8 2.4 13.7 23.2 17.5 1.3 17.4 10.7 5.5 34.7 20.1 35.5 61.6 43.4 12.1 3 2.0 13.8 0.0 0.3 2.0 1.6 3.0 4.5 7.3 8.3 3.2 6.9 8.9 10.6 6.2 5.4 11.5 16.1 21.4 4.0 45.1 43.7 37.5 27.4 29.2 25.3 62.4 56.6 30.0 4 3.6 0.7 1.2 4.4 10.4 24.4 6.0 4.8 4.3 4.3 7.9 15.8 12.0 13.6 11.9 22.0 19.8 3.2 10.0 27.7 16.9 27.9 36.6 22.2 41.7 46.7 1.9 1.8 3.1 5 0.6 0.4 0.8 3.8 3.4 1.6 2.1 11.0 7.6 10.4 5.5 9.0 11.1 6.6 16.3 11.6 12.3 8.0 21.0 20.0 59.6 81.2 4.2 12.2 39.5 10.1 37.9 44.6 52.2 12.2 6 0.6 1.8 3.0 1.2 3.9 6.7 9.9 5.6 5.5 5.8 4.4 16.0 14.0 11.1 31.1 2.4 17.0 63.1 32.4 12.8 73.5 17.0 12.8 7 1.7 3.2 6.0 6.1 5.7 6.5 22.8 11.1 11.5 12.3 9.7 12.7 15.4 14.9 3.6 12.7 72.6 15.6 19.4 112.4 17.9 8 14.9 2.2 8.7 5.7 3.5 3.5 2.8 4.0 6.0 10.4 7.3 10.9 9.7 11.1 20.6 5.3 14.9 22.5 24.6 92.3 24.2 54.4 9 7.4 3.7 16.5 8.0 3.3 11.2 7.5 4.9 12.0 12.4 7.1 17.4 5.3 8.1 22.3 6.7 8.1 10 1.6 11.0 4.4 5.8 9.2 4.3 9.4 9.7 16.9 7.8 36.0 13.6 4.4 8.4 3.0 11 0.8 37.9 10.5 1.2 7.4 5.4 10.5 9.7 6.0 9.3 4.8 14.6 8.5 4.7 6.7 7.2 12 6.6 4.3 16.5 4.5 2.0 5.2 5.3 4.1 11.2 5.3 7.5 22.2 13 1.3 4.3 1.4 2.4 4.7 12.4 2.2 6.2 4.9 19.3 1.8 3.8 14 11.6 1.2 0.5 5.9 2.8 0.6 6.2 2.5 3.8 3.8 5.0 3.7 15 11.2 1.9 2.6 7.8 10.4 4.1 10.9 16 1.4 12.7 7.0 4.8 4.6 7.7 17 1.2 0.2 18 0.0 19 2.2 20 21 22 23 24 25 En tr y flo w , R L, v eh /m in Conflicting flow, veh/min Figure J-13. Right-Lane Entry Flow vs. Conflicting Flow, One-Minute Data, Right-Lane Delay for Two-Lane Sites

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-23 Required Sample Size for Capacity Regression The required sample size for each predefined increment of conflicting flow (otherwise known as a class width) is given by the following expression: 2 2 σα ⋅⎟⎠ ⎞⎜⎝ ⎛= d znx (J-1) where: nx = Required sample size for a confidence level P zα = standard normal variable = 1.96 for P = 0.95 (2.58 for P = 0.99) d = allowed deviation of the class mean σ2 = variance of date in the class (≈ s2) Figure J-14 illustrates the one-minute capacity data, class mean and standard deviation for single-lane sites. The standard deviation varies between 2 and 3 vehicles per minute. The standard deviation of the sample has been used to approximate the standard deviation of the population, σ. In Figure J-15, the actual sample size, n, the confidence level for a deviation Pd = 0.5 veh/min, and the required sample size, nx, for a confidence level of P = 0.95 is illustrated. The observed sample size n is much smaller than the required size nx. An average sample size of 100 per class width is needed to ensure an accuracy of 0.5 veh/min (30 veh/hr) and a confidence level of 0.95. 0 5 10 15 20 25 30 0 5 10 15 20 Conflicting flow qc (veh/min) E nt ry c ap ac ity q e, m ax =q e/ x (v eh /m in ) 0 1 2 3 4 5 6 st an da rd d ev ia tio n (v eh /m in ) qe/x Cmean s Figure J-14. Class Mean (Cmean) and Standard Deviation (s) of the Single-Lane Entry Data

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-24 0 20 40 60 80 100 120 140 160 0 5 10 15 20 Conflicting flow [veh/min] n , n x [-] 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 C on fid en ce le ve l [ -] n nx P,d=0,5 veh Figure J-15. Sample Size n of the Data Classes (Class Width = veh/min), Confidence Level P with d=0.5 veh/min, and the Required Sample Size nx for P=0.95 and d=0.5 veh/min (1-Lane Entry Data) In Figure J-16, the actual sample size, n, the confidence level for a deviation of 1.0 vehicles per minute, and the required sample size, nx, for a confidence level of P = 0.95 is illustrated. The confidence level for the actual sample size is between P = 0.7 to 1.0. An average sample size of 25 per class width is needed to ensure an accuracy of 1 vehicle per minute for a confidence level of 0.95. For the whole data range (class width = 1 veh/min) a sample size of 320 is required. This compares well with the actual available sample. These reliability considerations treat each integer value on the horizontal axis (conflicting flow) as independent from its neighbors. There is, however, correlation between the conflicting and maximum entering flow. A more useful reliability analysis would also take the correlations between all points into account to come to a higher degree of estimated statistical precision. The confidence interval of the linear regression function can be used for this determination. A simple linear regression model has been defined. The confidence interval of the regression function can be calculated as follows: αα dyy ±= (J-2) where: y = entry capacity qe.max x = conflicting flow qc yα = α-percentile of y

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-25 dα = deviation = )1( )(1 2 2 2, − −+− n xx n t x xyn σσα σx2 = variance of x (≈sx2) σxy2 = covariance between y and x (≈sxy2) n = sample size tα,n-2 = t-variable for a confidence level P = α with freedom (n-2) x = mean of x For the single-lane sites, the confidence interval with P = 0.95 is presented in Figure J-17. The required sample size for a predefined confidence level P is obtained by inversing Equation J-2. In Table J-10, the required sample size for a deviation of 0.5 and 1.0 veh/min and a P = 0.95 and 0.99 is presented for changing values of conflicting flow. The empty cells of the table could not be obtained (nx → ∞). For a confidence level P = 0.95 and a deviation of 1.0 vehicles per minutes for the y-intercept yields a required sample size nx = 288. The total sample required is greater than the actual sample size. Because the actual sample size is small, it may be unreasonable to interpret the individual approach data. 0 10 20 30 40 50 60 0 5 10 15 20 Conflicting flow [veh/min] n , n x [-] 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 C on fid en ce le ve l [ -] n nx P,d=1 veh Figure J-16. Sample Size n of the Data Classes (class width = veh/min), Confidence Level P with d=1 veh/min and the Required Sample Size nx for P=0.95 and d=1 veh/min (1-Lane Entry Data)

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-26 0 5 10 15 20 25 30 0 5 10 15 20 25 Conflicting flow qc (veh/min) E nt ry c ap ac ity q e, m ax (v eh /m in ) qe/x qe,max,re,linear y*+(0,95) y*-(0,95) Figure J-17. Confidence Interval of the Regression Function for the Single-Lane Entries with P=0.95. TABLE J-10. Required Sample Size nx According to the Confidence Interval of the Regression Function P=0.95 P=0.99 Conflicting Flow Deviation=1 veh/min Deviation=0.5 veh/min Deviation=1 veh/min Deviation=0.5 veh/min veh/min Sample Size Sample Size Sample Size Sample Size 0 288 — — — 2 137 — 327 — 4 106 512 191 — 6 100 405 174 707 8 113 743 217 3461 10 165 — 542 — 12 603 — — — 14 — — — — 16 — — — — 18 — — — — 20 — — — —

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-27 Validity of Regression Models Using a customized simulation program, the validity of regression has been demonstrated. A number of assumptions have been made within the simulation program including the following: 1. The observed conflicting and maximum entering flows can be regarded as random variables. To simulate these observations, a Monte-Carlo method can be employed. 2. The inter-arrival times both between the circulating vehicles as well as between the entering vehicles can be generated according to a Borel-Tanner distribution (i.e. an exponential distribution). Because the theoretical distribution can generate very small values of the inter-arrival headway, all times are capped at the minimum acceptable headway, ∆. 3. All other parameters, such as critical headway tc and the follow-up headway tf, are generated according to a shifted Erlang distribution. 4. The driver’s behavior is assumed to be homogeneous and consistent. One-minute entry and conflicting flows were generated using an average tc = 6.0 s and tf = 3.0 s, and a minimum headway, ∆ = 2.0 s. The results are shown in Figure J-18 and include: • simulated data points (500 1-min-intervals); • class means (the mean entry for each 1 min/veh of conflicting data); • regression function (German exponential) representing the simulated data; • regression function (German exponential) representing the class mean data; and • standard deviation of the simulated data. The standard deviation has a tendency towards zero as the conflicting flow approaches zero (capacity approaching its maximum possible value), and as the conflicting flow approaches its maximum value. The standard deviation for this artificial system is always below 2 vehicles per minute. For real systems the deviation is between 2 and 3 vehicles. The German regression (both of the simulated and the class mean estimates) is very similar to the class means of the simulated data. The class means are regarded as the most reliable estimation since the form of the regression function does not manipulate the results. While the parameters within the German regression do not precisely correspond with the parameters used to define the simulation data, the differences between the class mean average of the simulated data and the regression estimates are small (0.1 s). To ensure that the class mean is a reasonable, a certain sample size of the simulation of one-minute capacity data for a given confidence level is needed. Using Equation J-1 presented previously, the required sample size for deviations of 0.3, 0.5 and 1.0 veh/min, and a confidence level P = 0.95, is presented in Figure J-19. As shown the smaller the allowed deviation, the larger the required sample size. If a predefined deviation of 0.5 veh/min is used, a sample of 40 simulated entry data per class width is needed. This results in a total sample size of 40 * 30 = 1200 simulated entry data per minute for the range of conflicting flow. For a deviation of 0.3 and 1.0 veh/min, the required sample size is approximately 450 and 3000 simulated entry data, respectively. For practical applications, a deviation of 1 veh/min (i.e., 60 veh/h) and a confidence level P = 0.95 is sufficient. Hence, each class width should have an observed sample size of about 15 one-minute data points—a total of 450. The simulated sample of 500 data points is therefore acceptable.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-28 0 5 10 15 20 25 0 5 10 15 20 25 30 35 Conflicting flow (veh/min) M ax im um E nt ry fl ow (v eh /m in ) 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 St an da rd d ev ia tio n (v eh /m in ) Simulation mean Reg Reg.Cl.M s Legend: • Simulation = results of the simulation (500 data points in 1-min-intervals with given tc = 6.0s, tf = 3.0s, and ∆ = 2.0s) • Mean = class mean. • Reg = regression (with tc = 5.9s, tf = 3.1s, and ∆ = 2.0s) • Reg.Cl.M = regression for the class mean (yields tc = 6.2s, tf = 3.0s, and ∆ = 2.0s) • s = standard deviation Figure J-18. Simulation Results for Demonstrating the Stochastic Nature of Capacities.

NCHRP Web-Only Document 94: Appendixes to NCHRP Report 572: Roundabouts in the United States J-29 0 20 40 60 80 100 120 140 160 180 200 220 0 5 10 15 20 25 Conflicting flow qc [veh/min] re qu ire d sa m pl e si ze n x nx,d=0,3 veh nx,d=0,5 veh nx,d=1 veh Figure J-19. Required Sample Size for a Confidence Level P=0.95 and the Allowed Deviation d=0.3, 0.5, and 1 veh/min