Indiana and Texas CV data for August 2020 weekdays, with an estimated penetration rate of 4.5% and 4.2% respectively [27], was used in this study. Two different CV datasets are utilized: trajectory data and event data.

Three-phase control is commonly used at diamonds where the intersections are located more than 400 ft. (121 m.) apart [5]. Such is the case of the study location in Indiana (Figure 1), where the intersections are 500 ft. away from each other. Figure 3 illustrates the 3-phase control implemented at this location. Figure 3(a) shows a common representation of the phases on a simplified geometry diagram of the CDI. Figure 3(b) shows the ring structure for the left intersection (X) and Figure 3(c) shows the ring structure for the right intersection (Y).

The three phases are the entering arterial, the internal left turn, and the ramp movement at each signal. The distance between X and Y provides storage for ramp traffic. If no queue spillback occurs, three-phase operation usually generates less delay than four-phase control and facilitates two-way progression on the arterial when the offsets between the two signals are close to zero [5] [28].

Four-phase control is typically used where interior left-turn volumes are high and the spacing between intersections is less than 400 ft. (122 m.) [5] [28]. Such is the case of the study location in Texas (Figure 2), where the intersections are 240 ft. apart. Although there are a variety of techniques that signal equipment vendors and state agencies use to implement four-phase control, we use the general ring diagram in Figure 4. Figure 4(a) shows a typical phase numbering scheme. Figure 4(b) shows the ring structure for the left intersections W (top ring) and Z

(bottom ring).

Both intersections of the interchange are tightly coordinated and are operated as if they were one big intersection. The four phases are the two arterial movements and the two ramp movements. If proper splits and offsets are set, this type of control provides progression through the interchange to all major movements which allows for an efficient queue management that is critical for CDIs with limited internal storage space [5] [28].

As the critical objective for CDI operation is to keep the internal storage free of long queues to avoid spillback which blocks adjacent arterial and ramp movements, the progression of vehicles needs to be evaluated. The Purdue Probe Diagram [21] provides a systematic visualization of linear-referenced vehicles trajectories that pivot at the far side (FS) of the intersection. This provides a framework that allows for quantitative and qualitative approach-level analysis.

A PPD is a time-space diagram that color-codes vehicle trajectories based on the number of experienced stops, identified as horizontal lines, before crossing the FS of the intersection. The following performance measures can be estimated from PPDs:

· AOG: assessment of progression calculated as the proportion of non-stopping vehicles (color green).

· SF: indication of an approach operating on congested conditions calculated as the ratio of vehicles stopping more than once (color red or purple).

· DSB: measurement of the level of obstruction by adjacent intersections calculated as the ratio of vehicles slowing down or stopping after crossing the intersection.

· Control delay: summation of deceleration, stop, and acceleration delay. A free-flow trajectory (FFT) is also included in the PPD (black line) to facilitate qualitatively estimations of approach delay by comparing CV and FFT arrivals [21].

Figure 5 shows the PPDs of August 2020 weekdays vehicle trajectories that traversed the 3-phase CDI in Indiana from 16:00-18:00 hrs. Figure 5(a) shows the movements that conform the ring structure of intersection X (Figure 3(b)) ordered in the same manner. Only one movement is shown per phase, where exterior through movements have precedence followed by exterior left. Similarly, Figure 5(b) shows the movements that conform the ring structure of intersection Y (Figure 3(c)).

Figure 6 shows the PPDs of August 2020 weekdays vehicle trajectories that traversed the 4-phase CDI in Texas from 16:00-18:00 hrs. Figure 6(a) illustrates the movements that conform barrier 1 of the implemented ring structure (Figure 4(b)) and Figure 6(b) shows the movements that conform barrier 2.

The visualizations presented in this sub-section allow for a qualitative assessment of progression, congestion, queue-length, and delay at the movement level focused on the implemented signal control. For example, at the 3-phase CDI in Indiana, the southbound interior movements show a number of vehicles stopping once (Figure 5(b), orange lines) at both the through (phase 2) and left turn (phase 5), while the northbound interior movements also show substantial arrivals on red. In contrast, the 4-phase CDI in Texas has internal through movements relatively well-progressed with all sampled vehicles having arrived on green southbound (OL-B) and a low density of one-stop trajectories in the northbound (OL-A). A limitation of the PPD is that each internal movement is shown in isolation and does not discern the origin of vehicles from the adjacent signal. This detail is important for assessing the quality of progression on the arterial.

The Extended Purdue Probe Diagram (EPPD) is a visualization tool developed to show the queue and progression quality relative to a number of signals in a system to help assess performance based on the origin of vehicles.

EPPDs are based on the standard PPD (Figure 5 and Figure 6) [21], but instead

of only characterizing the performance of a single signal approach, they show the complete movement of vehicles through a system of signals. This is accomplished by linear-referencing the distinct trips and pivoting at the last intersection’s far side of a complete origin-destination path. Each vehicle approach to the different intersections is independently color-coded based on the number of stops. The trajectory’s transition segment from one intersection to the next is shown in black. Additionally, the location of every signal’s far side is indicated by horizontal lines for spatial referencing. Finally, a FFT is included to allow for delay estimations.

In the case of diamond interchanges only two intersections need to be included in the EPPD. The sampled volume distributions for the eight main origin-destination paths of the three- and four-phase controlled interchanges are provided on Table 1 and Table 2, respectively. This information is relevant as it helps identify which paths have the highest demands and are more likely to congest the storage area.

Figure 7 shows the EPPDs of August 2020 weekdays vehicle trajectories that traversed the 3-phase CDI in Indiana from 16:00-18:00 hrs. The air photo in the lower left corner of all the figures have a movement arrow that graphically illustrates the path of vehicles analyzed in each EPPD. All EPPDs reveal significant number of vehicles stopping before entering the interchange and most of them show internal stops (callout i), except for Figure 7(d). From this subfigure, it is apparent that the CDI is timed with the objective of serving and progressing vehicles coming off the westbound ramp to southbound as efficiently as possible, with essentially none of those vehicles having to stop internally at all. By looking at and connecting the trajectories across the two signals, the EPPD is able to shed light on decisions and safety trade-offs made in the signal timing plan.

Figure 8 shows EPPDs for six paths of August 2020 weekdays vehicle trajectories

that traversed the four-phase CDI in Texas from 16:00-18:00 hrs. Similar to the interchange in Indiana, the CDI in Texas shows significant number of vehicles stopping before entering the system. However, once vehicles enter the interchange, they continue their progression unimpeded (callout ii), which is the main benefit of properly implemented four-phase control. This is an important characteristic as closely spaced intersections have higher risk of getting blocked by internal queues. The four-phase CDI operates similarly as a split-phased signal, which contributes to increased congestion on the movements entering the CDI (callout iii) shown by vehicles stopping more than once (color-coded red and purple).

The following subsection discusses performance evaluation by TOD.

The EPPDs provide a detailed characterization of progression, stops, split failures, downstream blockage, and delay for a specific time period. However, it is important to have a comprehensive summarized overview of how all the movements perform across different time-of-day (TOD) periods to effectively evaluate a CDI. To address this need, graphical heat maps summarizing performance by movement and by TOD are proposed.

Figure 9 and Figure 10 show heatmaps with 15-minute resolution indicating the percentage of vehicles arriving on green for the four external movements and four internal movements. For the three-phase controlled interchange (Figure 9), it is shown how the internal movements have AOG around 50% (callout iv),

with northbound-left (NBL, Figure 9(a)) having poor progression (~0% AOG) and southbound-through (SBT, Figure 9(b)) having good progression (~100% AOG). For the four-phase controlled interchange (Figure 10), all internal movements have efficient progression as vehicles do not have to stop before exiting the CDI (callout v).

Figure 11 and Figure 12 show the percentage of sampled vehicles that

experienced split failures at the three- and four-phase CDI intersections, by time of day. The three-phase control (Figure 11) has very few split failures throughout the day. The CDI shown in Figure 12 has significant split failures at most of the external movements during different TOD (callout vi) but no split failures on the internal movements.

Figure 13 and Figure 14 show heatmaps indicating the percentage of sampled vehicles that experienced DSB. For the CDI in Indiana (3-phase control, Figure 13),

the northbound-through (NBT) movements are being significantly obstructed soon after they cross each intersection during the PM peak period between 15:00 and 18:00 hrs. (callout vii). This is of particular interest as DSB is a consequence of long downstream queues. In the case of the external NBT movement (Figure 13(b)), this means that the internal CDI queue is long enough to affect progression. In contrast, four-phase control (Figure 14) has minimal number of vehicles experiencing DSB internally.

Finally, Figure 15 and Figure 16 show the LOS based on control delay (Table 3) for the relevant movements at the three- and four-phase CDI intersections, respectively. The effects that poor progression and congestion have on delay are illustrated.

The following subsection discusses the CV-event-based safety evaluation of CDIs.

Connected vehicle hard-acceleration and hard-braking events have proven to be effective datasets for the evaluation of safety at intersections without the need of long wait periods for statistically significant crash data [16] [17] [23] [26]. In this subsection, the HA and HB events patterns at the studied CDIs are evaluated.

Figure 17 and Figure 18 show linear-referenced event histograms, pivoting at the stop bar of the entry intersection, color-coded based on the speed of the vehicle at the time of the event, for the three- and four-phase controlled interchanges, respectively. The event counts are normalized as a percentage of the number of unique CV trajectory identifiers sampled at the same location and

time of the analysis.

Figure 17 shows results for vehicles traveling northbound-through at the Indiana interchange (three-phase signal control). Only a small percentage of sampled vehicles perform HB. In contrast, there are two significantly higher concentrations of HA (~1%) near the intersections’ stop bars (callout viii for Y and ix for X) made up mainly from slow-speed traveling vehicles (0 - 20 mph). This may be an indication of drivers rushing through the intersection as soon as they

are given green or vehicles traveling with a moving queue attempting to clear the intersection before the onset of amber.

Figure 18 shows results for vehicles traveling southbound-through at the Texas CDI (four-phase signal control). Similar to the Indiana interchange, just a small percentage of sampled vehicles have HB. However, the Texas CDI only presents one concentration of HA events near the entry intersection’s stop bar (callout x for W). As progression at the exit intersection (Z) is highly efficient (~100% AOG, Figure 10(b)), drivers do not have to rush to cross; hence, the

proportion of vehicles hard-accelerating is smaller (callout xi).