Currently, most performance analyses of DDIs have been done by means of simulation to provide information on travel times, v/c ratios, throughputs, queue lengths, delays, level of service, and number of stops [2] [4] - [12]. Safety performance has been evaluated from historical crash data to assess improvements compared to other types of interchange and to calibrate crash modification factors [13] [14] [15]. Hainen et al. made use of high-resolution event data to assess the internal queuing dynamics and the inflow/outflow demand balance within a DDI [16]. An Automated Traffic Signal Performance Measure (ATSPM) [17] was developed by using traffic signal phase data and point sensors to estimate travel time and arrivals on green (AOG) of vehicle trajectories through the intersection. The results of the analysis recommended a change from a two-phase to a three-phase configuration that led to an AOG increase of 39% for the heaviest internal movement.

With the emergence and improvement of commercially available connected vehicle (CV) data, new techniques have been developed to assess operational and safety performance at intersections without the need for costly infrastructure investments. CV hard-braking events have been proven to be a surrogate of crashes [18]. Vehicle trajectories have been used to estimate queue lengths [19] [20]. Traditional travel times [21] [22], Highway Capacity Manual (HCM) Level of Service (LOS) [23] [24] [25] [26] [27], and arrivals on green [24] [25] [26] [28] have also been calculated. In addition, critical analysis on the percentage of vehicles experiencing split failures and downstream blockage can also be derived from CV trajectory data [24] [25]. However, there are no studies that have used this recently available dataset to generate performance measures for DDIs. The advantage of using CV trajectory data to assess DDIs’ is stated in the following sub-section.

Estimating performance measures from simulation requires traffic signal timing plans, peak factors, volumes, and model configuration. Usually, this information is not easily accessible and time-consuming data collection is required. Further, the analyst needs to calibrate and validate each simulation based on the personal understanding of the DDI, which can potentially yield different results between different analysts [2]. With regards to data from point sensors to derive ATSPMs, capital and maintenance costs remain a barrier for widespread implementation. Depending on the sensors deployed, some types also cannot distinguish the presence of individual vehicles, queue length, and inflow origins, especially during near- or over-capacity periods.

This study uses commercially available CV trajectory data to generate DDI performance measures. This is particularly important for two reasons:

1) Even with investment in significant traffic sensing infrastructure, there is no robust way for evaluating progression through the two adjacent signals.

2) DDIs are relatively new. The scalability of CV data allows evaluation of a broad cross section of DDIs scattered across the United States to identify best practices for operating these new intersections as well as uniform performance measures.

An extension of the Purdue Probe Diagram (PPD) is proposed that provides insights on the DDI’s levels of delay, progression, and saturation. Further, an additional PPD variation to evaluate critical queue dynamics within the crossover (i.e., internal) storage is presented. Finally, traditional AOG and level of service (LOS), as well as the percentage of vehicles experiencing split failures and downstream blockage, are calculated for different segments of the DDI. By utilizing the presented techniques, agencies can evaluate the performance of any DDI in their jurisdiction to identify movements and time-of-day (TOD) periods that require field adjustments.

The main contribution of the study is the development of DDI-specific CV trajectory-based performance measures that can provide near-real-time assessments without the need for investing in new traffic signal infrastructure.

Since the signals’ dynamics between crossover areas 1 and 2 (Figure 2) are crucial for the correct operation of DDIs, it is important to provide analytical performance measures (and graphics) that provide insight on the operation status at both locations simultaneously. To accomplish this goal, a variation of the PPD [24] [25] is proposed. A PPD shows the linear-referenced progression of vehicles relative to the far side of an intersection, color-coded by the number of stops. Usually, a PPD provides quantitative information on the experienced delay, progression, split failure, and downstream obstruction of trajectories crossing through a singular traffic signal.

By linear-referencing trajectories of vehicles traveling through both crossover areas in a DDI relative to the far side of the downstream intersection, and by color-coding each upstream trajectory segment based on the number of stops by traffic signal, the Diverging Diamond Interchange Purdue Probe Diagram (DDI PPD) can be plotted. DDI PPDs provide valuable information on the performance state at both crossover signal systems simultaneously.

Figure 3 shows DDI PPDs for the four different traffic sources shown on Figure 2. The location of the traffic signals’ is shown with blue lines and labelled 1 and 2. For example, for Figure 3(a), callout i shows the far side of signal 1 and callout ii the far side of signal 2. Each trajectory’s upstream segments are connected by a black line, which corresponds to vehicles moving through the traffic signal in the DDI. Additionally, a free-flow trajectory (FFT), which is the theoretical trajectory of a vehicle traveling at the speed limit, is shown with a thick black line for comparison.

In a DDI PPD, as with a traditional PPD, vehicle delay can be assessed by analyzing how far away from the FFT a trajectory approaches the first signalized intersection. The farther away from the FFT a trajectory starts, the longer the experienced delay at the DDI. AOG, a measurement of progression, can be evaluated by comparing the amount of green-colored (no-stops, arrived on green) and non-green-colored (one or more stops) trajectories. The larger the proportion of green trajectories is, the better the progression. Saturation can be assessed

by identifying the number of trajectories with two or more stops at a traffic signal since those events are indicative of split failures. Finally, downstream blockage, as defined in [24], can be identified by looking at the vehicle’s progression immediately after crossing the far side of an intersection (blue lines). The more delay after a vehicle crosses the far side of an intersection, the more likely downstream blockage is experienced. The following qualitative statements can be said from Figure 3:

• Trajectories going EB from the external street (Figure 3(a)) and NB from the ramp (Figure 3(b)) experience the most delay since they approach the intersections the farthest away from the FFT;

• Figure 3(c) and Figure 3(d) have the highest AOG, and therefore, the best progression;

• Vehicles traveling EB from the external street (Figure 3(a)) are experiencing split failures when approaching both, intersections 1 and 2;

• Trajectories traveling NB from the ramp (Figure 3(b)) are experiencing split failures when approaching intersection 2;

• Trajectories traveling WB from the external street (Figure 3(c)) experience split failures when approaching intersection 2.

Figure 4 shows on the studied DDI two of the trajectories exiting from the interstate’s ramp, traveling SB, and turning left, that were plotted on the DDI PPD in Figure 3(b).

• For trajectory A, it can be seen how the vehicle approaches the traffic signal at the crossover area 1, but before it can make it through the intersection, it has to stop (Figure 4(a), callout i). Then it moves to stop one more time in the middle of the crossover storage (Figure 4(a), callout ii). Finally, it advances again to clear the interchange.

• Similarly, trajectory B stops once before clearing the signal on area 1 (Figure 4(b), callout iii). However, once in the crossover storage, the vehicle had to stop on two different occasions (Figure 4(b), callout iv and v). This is a clear case of a vehicle experiencing a split failure, which is a sign of an oversaturated approach since one cycle length of the traffic signal on area 2 did not provide enough green time to clear the queue. As previously discussed, saturation in the crossover storage needs to be avoided, because if there is queue spillback, both the external and ramp approaches would be affected (of which long queues on the ramp would be of major concern due to the possibility of rear-end crashes on the interstate).

The most critical segment of a DDI is crossover storage. To facilitate the qualitative assessment of progression patterns, and to evaluate queue length for spillback in the critical interior crossover storage, a DDI PPD variation that provides information on progression by traffic source is presented.

In this variation of the DDI PPD, trajectories coming from the external street and the interstate ramp, that share lanes on the crossover storage, are superimposed. When doing this, the progression dynamics between signals at the crossover areas 1 and 2 become apparent. Figure 5 shows a progression DDI PPD for the different movements at the study location.

For the EB through and SB left movements (Figure 5(a)), it can be seen that there is a significant number of vehicles coming from both sources stopping when approaching signal 1, as well as stopping when approaching signal 2 (callout i). Most of the traffic in this figure is from the EB through approach, and

approximately 50% must stop at signal 2. In this case, the EB through and SB ramp have unbalanced. In addition, for the analyzed period, 89% of the trajectories traveled EB through, and only 11% traveled SB left.

For the WB through and NB left movements (Figure 5(b)), it can be observed that there are vehicles from both sources stopping when approaching area 1 (callout ii). However, it is shown how most vehicles coming NB from the ramp can progress without stopping through the signal at 2 (callout iii). This is an indication that the NB left movement has an effective clearance when entering the crossover storage area. Further, for the analyzed period, 66% of the trajectories traveled WB through, and 34% traveled NB left.