CV trajectory data consists of location, speed, heading, and unique trip identifier information of anonymized private passenger vehicles sourced from third-party traffic service providers [37]. The data is provided at a 3-second frequency with a spatial accuracy of 3 meters. In the state of Indiana, the penetration of this data is between 3% - 4% evaluated from a 2021 study [38]. Figure 3 shows the traces of GTCVs over a day of collected samples in the Indianapolis metro area. During the study period, there were nearly 30 million GTCV records on the Red line with an average of roughly 318,000 records per day and approximately 7000 trips per day.

Bus trajectory data consisted of attributes including timestamped speed, location, heading, and direction with a reporting frequency ranging from 5 to 30 seconds. Additional attributes such as occupancy status, headway and schedule adherence (number of seconds ahead of or behind schedule at each sample) are also available. Figure 4 shows a snippet of the bus data on College Ave. During the three months between March and May 2022, trajectory data from the buses on the Red line generated a total of approximately 3 million records, with an average of roughly 40,000 records per day and 150 unique bus trips per day. Roughly 64% of the trips had an average reporting frequency of 5 seconds or less.

To perform spatial analysis and to visualize the trajectories on a distance-time plot, it is necessary to snap the bus and CV data points to their nearest roadway route in the direction of their heading. Linear referencing is carried out using spatial polygons generated every 50 feet from the origin for both northbound and southbound route [39]. The polygons are extended over the width of the roadway to include datapoints with low GPS accuracy. The datapoints are then spatially joined to these polygons to obtain their linear reference with respect to the route origin. Finally, a heading filter of ±10˚ with respect to the route heading is applied to remove directional outliers.

There are several well-documented methodologies in the literature that discuss the estimation of total delay from vehicle trajectories [36] [37] [40] [41]. Control delay for buses can also be computed in a similar way, however there are additional factors that need to be considered:

1) Dedicated bus lanes—With dedicated lanes, buses do not experience any queuing compared to other vehicles in the traffic stream.

2) Near-side intersections—At some intersections, the bus stations are present on the near-side, mostly within 50 - 100 ft of the stop bar (Figure 5). In these cases, the bus dwell times also need to be accounted for while estimating the control delay. For example, in Figure 5, the bus is experiencing delay in the form of dwelling even though the traffic signal indication is green (callout i).

3) Reporting frequency—For accurate estimates, it is preferable to have higher sampling intervals, ideally within 1 to 3 seconds.

To address the above factors, the following methodology is adopted:

1) Discard bus trips with an average reporting frequency greater than 5 seconds (highest frequency available).

2) Develop custom dimensional polygons (wide enough to cover all lanes but with different lengths) for every intersection in their direction of travel. All polygons begin from the center of the intersection.

a) For intersections with dedicated bus lanes, ~100 ft long (Figure 6(a)).

b) For intersections with near-side bus stations, ~50 ft long polygons that excludes the bus station (Figure 6(b)).

c) For intersections having mixed traffic lane, ~200 ft long polygons to account for the queue upstream of the stop bar (Figure 6(c)).

3) Perform spatial join of bus trajectory points with the intersection polygons.

4) For each trip i at intersection j, estimate delay as:

D i , j = t l , i , j − t f , i , j (1)

where D_i,j = delay for trip i at intersection j;

t_l,i,j = timestamp of last point of trip i exiting the intersection polygonj;

t_f,i,j = timestamp of first point of trip i entering the intersection polygonj.

5) Due to the 5 seconds reporting frequency, it is likely that some trips passing through the intersections without any delay may not report a point inside the polygon. In such cases, D_i,j is set to zero and the timestamp of the nearest point (t_n,i,j) is approximated as the time of entering the intersection t_f,i,j.

6) For each trip i having delay D_i,j at timestamp t_f,i,j, the timestamps are then floored to the nearest 15 minutes. Then, all dates in the study period are aggregated to the time bin.

7) Average delay D j , b ¯ , for intersection i at bin b is then estimated as

D j , b ¯ = ∑ i = 1 n D i , j , b n (2)

where D_i,j,b is the delay estimated for trip i at intersectionj in bin b;

n is the total number of sample trips in bin b.

8) The average delay for the bin is discarded if n is less than 5 samples.

For every bus data record, the schedule adherence is reported as an attribute. The methodology to estimate average schedule adherence at intersections is the same as the above methodology to estimate average intersection delay, except that the schedule adherence of the first point entering the intersection polygon is extracted as the schedule adherence of the trip at that intersection at that instant of time. For trips without a datapoint inside the polygon, the schedule adherence of the nearest data point and timestamp are extracted.

Control delay from connected passenger vehicle trajectory data is estimated by comparing the travel time of a vehicle traversing an intersection to the travel time of a hypothetical trajectory of an unimpeded vehicle traversing the same intersection under free-flow conditions. This technique takes into consideration deceleration, stopped, and acceleration delays [40]. Further, since passenger CV data has a 3-second reporting interval, no additional filtering is required. Detailed methodology behind the estimation of delay can be found in [37].

As passenger vehicles are affected by queues, each vehicle is analyzed up to 1320 ft. (1/4 mi.) upstream of the intersection or until another control flow device is encountered. Moreover, turning movements are identified from the trajectory data itself without any geofencing by using a center point of an intersection and estimating the approach ingress and egress directions of the trajectories [42].

Figure 7(a) and Figure 7(b) show boxplots comparing weekday travel times between buses and GTCV by every hour in the northbound direction on College Ave and Shelby St, respectively. Travel times computed for every weekday trip during the analysis period is aggregated by the start time of the trip when the buses or GTCVs enter the corridor. On College Ave (callout v on Figure 1), northbound and southbound buses share a dedicated bus lane, whereas on Shelby St (callout i on Figure 1), the buses run mixed with general traffic. Both these corridors of College Ave and Shelby St are approximately 3 miles in length.

On College Ave (Figure 7(a)), the median travel times for buses and GTCVs are comparable (around 7.5 minutes), with GTCVs taking slightly less time than buses. However, during the 17:00 hour peak period buses are found to be quicker than GTCVs, with a median travel time savings of roughly 1 minute. On Shelby St (Figure 7(b)), buses take slightly more time than GTCVs, with an overall median travel time of 8.5 minutes for buses compared to 8 minutes for GTCVs. Buses are also less reliable on Shelby St (interquartile range of 1.9 minutes) compared to College Ave (interquartile range of 1.6 minutes).

The maximum difference in median travel times between buses and GTCVs on College Ave is around 0.9 minutes (buses quicker at 17:00 hours) whereas on Shelby St is 1.4 minutes (vehicles quicker at 19:00 hours). Moreover, the buses are also more reliable with the dedicated bi-directional lanes with a travel time range of about 4 minutes compared to 6 minutes with mixed traffic. This highlights the impact of dedicated bus lanes in saving travel time and improving reliability. It should also be noted that the bus travel time estimated in this analysis are inclusive of the dwell time lost at bus stations.

Figure 8(a) and Figure 8(b) compare heatmaps color coded by the average delay experienced by GTCV and buses, respectively on intersections in the northbound direction of College Avenue. Each cell represents a 15-min period, and the intersections are shown on the y-axis with the time of day on the x-axis. Near-side intersections with possible capture of dwell times are highlighted in blue. In addition to the delay, the corresponding HCM level of service (LOS) [43] is also shown in the legend. Blank cells represent periods where there are insufficient samples (less than 5 samples). Broad Ripple intersection did not

have enough CVs as this section was only open to limited traffic due to construction activities during the analysis period.

Figure 8(a) and Figure 8(b) show similar patterns of delay for buses and GTCVs, with GTCVs experiencing more severe delays. For example, at E 54th St, where CVs experience more than 55s of delay during the PM peak between 16:00 and 19:00 hours, buses are found to have delays of 35s or less. At E 46th St and E 42nd St, buses are mostly travelling at free flow speed when GTCVs face a delay of 20s or more. During peak periods and saturated conditions, buses take

advantage of the dedicated lanes and TSP to flow through traffic without any significant impedance. However, general traffic experiences congestion and control delays at signalized intersections.

Figure 9(a) shows a distance-time plot of buses (red) and GTCVs (black) on College Ave traveling northbound between the period 17:30 and 18:30 hours on Wednesday May 25, 2022. The bus stations are shown on the left as solid blue lines and intersections are shown on the right as dotted blue lines. While GTCVs encounter split failures [44] over a number of times, the buses ever only experience arrivals on red. Figure 9(b) shows a zoomed in view of callout i between

18:12 and 18:15 hours at the E 54th St intersection. The GTCV experiences a split failure [37] denoted by the two stops upstream of the intersection (callout ii and iii) but the bus arrives on red (callout iv) and proceeds through the intersection instantly at the onset of green before stopping at the bus station (callout v). The general traffic vehicle, however, again undergoes additional delay waiting for the queue to clear (callout vi) before passing the intersection. In this instance, the bus only faces a delay of roughly 10s at the intersection, compared to the GTCV’s overall delay of about 90s.

Figure 10(a) and Figure 10(b) show boxplots comparing the directional bus route travel time by hour of the day for weekdays and weekends, respectively.

Travel times computed for every trip during the three-month analysis period is aggregated by the start time of the trip. In general, it takes less than an hour to complete a trip, with northbound trips found to be quicker than southbound trips during both weekdays and weekends. The southbound trip travels an extra 1000 ft and two additional signalized intersections than the northbound trip, thus resulting in additional travel time.

Overall, on weekdays (Figure 10(a)), the median travel times for northbound and southbound trips are around 46 and 49 minutes, respectively. Median travel time patterns are also similar between the directions, with a slight increase during morning peak (45 - 50 minutes) and continuing throughout the day before hitting the maximum during the evening peak (50 - 55 minutes). After 8PM, median travel times are between 40 - 45 minutes and just above 50 minutes for northbound and southbound respectively. During weekends (Figure 10(b)), the peaking in travel time occurs around 11AM, with median travel time around 45 minutes on northbound and 50 - 55 minutes on southbound. This continues until 5PM before reducing to around 45 minutes for both directions.

There are several factors that contribute towards the fluctuations in bus travel time; two primary factors are control delay and bus station dwellings. Figure 11

show a heatmap (similar to Figure 9(b)) color-coded by the LOS experienced by buses across all signalized intersections in the northbound route. Each color on the left of the Y-axis represents a corridor as shown in Figure 1.

In general, buses are progressing at free flow conditions or LOS B during most of the time, highlighting the impact of the dedicated bus lane and TSP. The route south of E Washington St (callout iv) runs mixed with general traffic. E 38th St, E 22nd St, E Washington St and Campus Dr are few intersections (callout i) with some of the longest delays, however since these are near-side intersections, it is possible that some of the delay could be influenced by the dwell time. Apart from the near-side intersections, Raymond St (callout ii), E South St (callout iii) and E 54th St (callout v) are some intersections that warrant retiming operations.

On-time arrival of buses or schedule adherence is also an important performance measure for assessing system performance and reliability. Figure 12(a) contrasts the actual bus trajectories (solid red line) along the entire 13-mile northbound route with the ones that would have been expected had they arrived on time (dashed red lines). Figure 12(b) shows a zoomed-in version of Figure 12(a) on College Ave between the intersections E 42nd St and E 57th St on 25 May 2022 between 15:30 and 19:00 hours. Callout i shows a trip that is perfectly on schedule whereas callout ii shows two trips that are off schedule. On average, in both directions, more than 3% of buses arrive within 1 minute during 05:00-06:00 hours. The worst adherence is during the 17:00-18:00 hours with approximately 5% of buses arriving within 9 minutes (northbound) and 6 minutes (southbound). Although agencies strive towards maintaining a regular on-schedule performance, sometimes non-recurring factors such as interim construction, operator unfamiliarity due to route scheduling, and consistent feedback loops between operators and route managers could lead to trips being off-schedule.

For the on-schedule trip in Figure 12(b) (callout i), the schedule adherence at E 54^th St or any intersection is zero. However, for the off-schedule trip (callout ii), the schedule adherence at E 54^th St is approximately +19.5 minutes (19.5 minutes late, callout iii).

Figure 13 illustrates a heatmap color coded by the average schedule adherence experienced by buses across all signalized intersections in the northbound direction during the three-month study period. Each cell represents a 15-min period, and the intersections are shown on the y-axis (in route order) with the time of day on the x-axis.

Buses operate mostly within schedule from origin (Campus Dr, callout i), but start going off-schedule as they enter E Washington St (callout ii). This intersection is near the transit center where the operators take a short break. Heading further on Washington St (light gray highlight on left of y-axis) and Capitol Ave (dark gray highlight), the buses deviate further from schedule as they navigate

through downtown Indianapolis. On Meridian St (brown highlight), the buses seem to catch up on schedule. The highest deviation from schedule is seen during the evening peak between 16:00 and 19:00 hours, where the buses are late on average by 15 - 20 minutes.

The average intersection delay (Figure 11) and average schedule adherence (Figure 13) are two key performance measures that can help identify which intersections may have opportunities for signal timing adjustments. Figure 14(a) shows a scatter plot for every 15-min of average schedule adherence (x-axis) against the average intersection delay (y-axis) in the northbound direction. Figure 14(b) illustrates a cumulative frequency diagram of the above delays and schedule adherence. In general, across all signalized intersections in the northbound direction and their 15-min periods, the median schedule adherence in approximately +4 minutes (callout i) and the median delay is roughly 4s (callout ii). Buses experience an intersection delay of 20s or less (LOS B or better) during 90% of all the displayed 15-min periods (callout iii). This indicates that a small fraction of the signalized intersections would benefit from signal timing adjustments.

Figure 14(c) shows the same scatter plot as Figure 14(a) but excludes the near-side intersections. The LOS values and their thresholds are also color-coded in this plot. Intersections and periods to the left bottom of the plot (callout iv) are doing exceptionally well in terms of delay and schedule adherence. Points to

top right with high delay and extreme schedule adherence values (callout v) are candidates for schedule adjustments and signal retiming. Points to the bottom right show cases where the buses are off schedule but do not face any significant delays at the intersections (callout vi).

Figure 15 overlays a dot on the average schedule adherence heatmap from Figure 13 when the buses experience an average delay of 20s or more (LOS C or worse). Excluding the near-side intersections, three intersections that stand out are E South St (callout i), New York St (callout ii) and Raymond St (callout iii). Figure 16 illustrates the same visualization for the southbound route. In the southbound direction, E South St (callout i), New York St (callout ii) and E 38th St (callout iii) stand out. These comprehensive visualizations of the delay and schedule adherence by time of day helps practitioners prioritize intersections and time periods for evaluation, and potential adjustments to schedules and signal timing if they are found to be warranted.

Considering delay, the top two intersections (callouts i and ii on Figure 15 and

Figure 16) that stand out in both the northbound and southbound directions throughout the day are E South St (at Virginia Ave with mixed traffic), and New York St (at Capitol Ave with dedicated running way). Further examination of the intersection geometry reveals that these two intersections have more than four legs (Figure 17(a) and Figure 17(b)) which explain the high delay faced by buses at these intersections since within one cycle length the signal has to serve more movements than a typical four-legged intersection. Signal timing changes that reduce bus control delay include running the intersection on free or allowing the signal controller to extend phase length past max green or exceed cycle length. In the southbound direction, E 38th St (at College Ave) and Shelby St (at Virginia Ave) also experiences high delay throughout the day (callouts iii and iv on Figure 16, respectively). Shelby St is also an intersection with more than four legs (Figure 17(c)). E 38th St is one of the intersections where the southbound bus needs to make a right turn from the dedicated bus lane on the center of College Ave across three through and right general traffic lanes (Figure 17(d)). Possible adjustments including decoupling the bus phase overlap from the eastbound and westbound left or westbound through could make the bus phase come up sooner.

Looking at schedule adherence in northbound direction, the buses deviate from schedule after E Washington St (callout ii on Figure 13), accruing up to seven additional minutes of delay after the intersection. Similarly in the southbound direction, the buses seem to deviate from schedule after Alabama St (callout v on Figure 16), accruing additional delay of about seven minutes past the intersection. Evidently, these intersections are near the transit station in downtown where the operators take a short break. Operationally, this may present an opportunity for route managers and bus operators to communicate how schedules are calibrated during the dwell time and when the buses depart the transit station. Adjusting the schedules to accommodate anticipated short breaks could be one possible way to align on-time performance expectations for riders.