Roundabout Performance Analysis Using Connected Vehicle Data

There are over 8000 roundabouts in the United States. The current techniques for assessing their performance require field counts to provide inputs to analysis or simulation models. These techniques are labor-intensive and do not scale well. This paper presents a methodology to use connected vehicle (CV) trajectory data to estimate delay and level of service for roundabout approaches by adapting the Purdue Probe Diagram used for traffic signal analytics. By linear referencing vehicle trajectories with a particular movement based on the location and time they exit a roundabout, delay can be calculated. The scalability is demonstrated by applying these techniques to assess over 100 roundabouts in Carmel, IN during the weekday afternoon peak period in July 2021. Over 264,000 trajectories and 3,600,000 GPS points were analyzed to rank over 300 roundabout approaches by delay and summarize in Pareto-sorted graphics and maps. The paper concludes by discussing how these techniques can also be used to analyze queue lengths and origin-destination characteristics at roundabouts. The methodology presented in this study can be used by any agency that wants to assess the performance of all roundabouts in their system.


Literature Review
Roundabout performance measures can be primarily classified into two groupssafety and operational [3]. The operational performance measures can be further divided into two sections-capacity estimations and operational characteristics including delay, level of service (LOS), and queue length.
Kyte et al. [16] performed some of the foundational research using video recording with omni-directional video cameras at 16 roundabouts in the United States to study the safety and operational impacts of roundabouts. Although this was a time-consuming and costly process, the study was able to identify queue lengths, queue duration, turning movement counts and gap sequences. The control delay at the studied roundabouts ranged from 0.0 -47.1 sec/veh. Kyte's study became part of a larger effort that analyzed over 300 roundabouts in the United States [3]. In another study, Flannery et al. [15] compared five two-way stop-controlled intersections that were later replaced by roundabouts and found that the sites experienced a reduction in accident frequencies, rates, and control delay. The researchers used video detection to quantify control delay as the time spent in the queue, move-up time, and service time at the head of the queue.
Giuffrè et al. [34] utilized microsimulation to conclude that safety of any road unit may be measured from surrogate safety assessments.
Some studies have also used simulation to characterize the impact of connected and autonomous vehicles on the operational performance of roundabouts. Mohebifard et al. [35] evaluated the effect of various market penetration rates of connected autonomous vehicles (CAVs) on traffic operations at roundabouts using a simulation-and an optimization-based approach. The results showed that CAVs improved traffic operations in under-and semi-saturated flow conditions at 100% market penetration. Another study suggested that CAVs could provide higher throughput with lower average control delay compared to conventional vehicles' operation at roundabouts [36]. A few studies have generated vehicle trajectories or paths from aerial footage to estimate performance measures at roundabouts [37] [38].

Objective
The objective of this paper is to develop a methodology based on the Purdue Probe Diagram (PPD) for computing delay and LOS [42]. The PPD was originally developed for estimating control delay and LOS for signalized intersections, but those techniques can apply to roundabouts with some minor changes in locating the reference points and delay thresholds. Eliminating the need to collect turning movement counts dramatically improves the scalability of the analysis. This paper describes these techniques and demonstrates their application in Carmel, Indiana for over 100 roundabouts.

CV Data
CV data is used to calculate delay, LOS, queue lengths, and origin-destination characteristics. The data consists of individual vehicle waypoints with latitude, longitude, the vehicle speed and heading, a timestamp, and an anonymized unique journey identifier. The data reports with a temporal frequency of three seconds and a spatial accuracy of 1.5 meters. For this study, over 264,000 unique journeys and 3.6 million waypoints are used from July 2021 weekdays from 3:00 PM to 6:00 PM.

Methodology
This section presents the methodology in four steps: 1) Estimating delay from connected vehicle trajectories; 2) Data aggregation and visualization graphics; 3) Estimating queue lengths; 4) Tabulating roundabout origin-destination characteristics.

Trajectory-Based Roundabout Control Delay Estimation
The HCM proposes LOS as the main performance indicator for both, interrupted and uninterrupted flows. LOS provides 6 categories (A-F) to describe traffic operations at a particular location, "A" being ideal free-flow conditions and "F" being inefficient congested conditions. For the interrupted flow scenario at roundabouts, LOS is based on control delay, and its definition is shown in Control delay is the delay caused by traffic control. For a roundabout, the traffic control is performed by the roundabout itself, its markings, and its signage. Therefore, control delay at a roundabout can be estimated by calculating the difference in travel time through the studied location between a vehicle trajectory and a free-flow trajectory (FFT), which is the hypothetical trajectory of a vehicle traveling at the posted speed limit [2] [42] [43].
Recently, several papers have been published that describe how the Purdue Probe Data Diagram [39] [41] [42] [44] can be used to estimate control delay for signalized intersections using CV trajectory data. Those techniques can be readily adapted to roundabouts. From Table 1 and the estimated control delay, individual vehicle trajectories can be assigned a LOS. Figure 1(a) shows a Purdue Probe Diagram (PPD) [42] for a roundabout, which is the time-space diagram of a vehicle trajectory that follows a particular movement [45] referenced to the distance and time in which the vehicle exited the roundabout. Callouts i-vi are vehicle trajectories approaching the roundabout from the west, traveling eastbound, at Ditch Rd. and W 96 th St. color-coded by their estimated LOS. Callout vii is a FFT. Control delay can be estimated by comparing how far away a particular trajectory is from the FFT. The farther to the left a trajectory is, the greater its control delay. Callout viii is a segregation line that helps to visually separate trajectories by their LOS (in this case separating E and F trajectories). Figure 1(a) is a subset of Figure 1(b) to illustrate the LOS concept. Figure  1(b) shows 38 trajectories sampled between 17:00 and 17:15 hours during July 12-16, 2021 at the same roundabout approach. Figure 1(b) also has a pie chart that shows the percentage of trajectories categorized with the estimated LOS. For this approach and time period, over 30% of trajectories had a LOS F, and only 8% had a LOS A. Using geographic information system (GIS) linear referencing, roundabout PPDs such as Figure 1(b) can be systematically generated for all the approaches at a roundabout to quantify approach delay. Approach delay is defined in this study as the delay experienced by vehicles entering from the same approach regardless of exit choice. Figure 2 shows PPDs for all four approaches at Ditch Rd. and W 96 th St. during the same peak 15-min period over five days. The southbound direction of travel, callout i, is the most efficient approach with most of the vehicles experiencing a LOS B. On the other hand, vehicles traveling westbound, callout ii, present the highest proportion of vehicles having a LOS F. Journal of Transportation Technologies analyzed in Figure 1 and Figure 2(d). This visualization provides an efficient performance summary for a single location that helps identify direction of travel and time-of-day (TOD) where the roundabouts underperform.

Data Aggregation and Visualization Graphics
Until now, only LOS that describes the performance at individual roundabouts E. Saldivar-Carranza et al.
have been discussed. However, agencies are typically interested in system-wide assessment of all their approaches, as well as the weighted average of all approaches of each roundabout.   can provide practitioners with insight on the effects that certain roundabouts may have on adjacent locations. Figure 7(a) shows the analyzed roundabouts color-coded by their highest-delay approach's LOS. Callouts reference the roundabouts' ID and direction of travel (SB, EB, NB, or WB) as presented in Figure   6(b).
Roundabout 3 has two approaches that are within the 10 highest approach delays in the system during the study period. Vehicles coming from the west, traveling EB, have the highest delay between all approaches at roundabouts 6 and 7. Therefore, vehicles traversing EB through these roundabouts are likely to experience significant delay at each location. Given roundabouts' 6 and 7 proximity to each other, it is possible that the poor performance at roundabout 7 is propagating to roundabout 6. Thus, improving operational performance at 7 can potentially benefit 6 as well. Additionally, studied locations can be color-coded by the LOS based on the weighted average control delay from all the approaches (Figure 7(b)), instead of only focusing on the highest-delay approach. With weighted average control delay, the total level of performance at a roundabout is shown, and it is calculated by dividing the total control delay of all vehicles by the number of samples. If a location has a poor LOS when based on the highest-delay approach, but a good LOS when taking into consideration all the approaches, it is an indication that few approaches in that roundabout are under-performing. In contrast, if a location shows poor LOS in both maps (Figure 7(a) and Figure 7(b)), that indicates that most of the entering vehicles have high control delay. Table 2 shows the 10 highest estimated control delays by approach ( Figure  6(b) and Figure 7(a)). Further, the weighted average, by entering volume, for the entire roundabout is also provided.

Queue Length Estimation
The Purdue Probe Diagram can also estimate queue length at signalized intersections based on vehicle stops and their distance from the stop bar ( Figure 1). The same methodology can be also extended to estimate queue lengths for roundabout approaches [1] [8].
The HCM provides a technique to compute 95 th percentile queue lengths at roundabouts based on volume-to-capacity ratios, lane capacities, and study time periods [8]. In this study, queue length is estimated as the distance to the center of the roundabout when a vehicle first stops during its approach. The queue lengths from several days can be aggregated over various TOD periods to estimate the 95 th percentile queue length. Figure 8 shows the estimated 95 th percentile queue length, as used by the HCM [8], at Ditch Rd. and W 96 th St. from data sampled during all the weekdays in July 2021. As expected, the delay presented in Figure 4 relates to the queue length in Figure 8, since the highest delays occur during the time with the longest queues (from the 16:00 to the 18:00 hrs. for approaches WB, NB, and EB).

Origin-Destination Characteristics
The technique used to automatically identify vehicle turning movements from trajectory data can provide valuable information on the origin-destination characteristics at roundabouts and the variation over time [45].

Conclusions
This study presented a methodology to use CV data with a three-second reporting interval to estimate delay, level of service, queue length, and origindestination characteristics for roundabouts. The benefit to consultants and agencies is that these techniques can be performed without any extensive and costly field data collection efforts currently required to evaluate the performance of a roundabout. The delay and level of service techniques were based on the Purdue Probe Diagram, commonly used in traffic signal analytics (Figure 2 and Figure 3). A heatmap was used to illustrate how the control delay varies by approach and TOD ( Figure 4). The scalability of this methodology was demonstrated by applying it to analyze over 100 roundabouts in Carmel, Indiana during the afternoon peak period in July 2021. Over 264,000 trajectories and 3,600,000 GPS points were analyzed during weekdays to rank over 300 roundabout approaches by delay and summarize in Pareto sorted graphics ( Figure 5 and Figure 6) and maps ( Figure 7). The paper concluded by illustrating how additional performance characteristics such as queue length ( Figure 8) and variation in origin-destination patterns (Table 3) can be analyzed with CV data.
The techniques presented in this paper can be used to assess system-wide performance of roundabouts. Longer term, as agencies and consultants develop libraries of roundabout performance analyzed using CV data, that data can be used to improve the calibration of roundabout models and simulation models used in planning applications.