Detector-Free Optimization of Traffic Signal Offsets with Connected Vehicle Data

Transcription

1 Detector-Free Optimization of Traffic Signal Offsets with Connected Vehicle Data Christopher M. Day, Howell Li, Lucy M. Richardson, James Howard, Tom Platte, James R. Sturdevant, and Darcy M. Bullock Signal offset optimization recently has been shown to be feasible with vehicle trajectory data at low levels of market penetration. Offset optimization was performed on two corridors with that type of data. A proposed procedure called virtual detection was used to process 6 weeks of trajectory splines and create vehicle arrival profiles for two corridors, comprising 25 signalized intersections. After data were processed and filtered, penetration rates between.9% and.8% were observed, with variations by approach. Then those arrival profiles were compared statistically with those measured with physical detectors, and most approaches showed statistically significant goodness of fit at a 9% confidence level. Finally, the arrival profiles created with virtual detection were used to optimize offsets and compared with a solution derived from arrival profiles obtained with physical detectors. Results demonstrate that virtual detection can produce good-quality offsets with current market penetration rates of probe data. In addition, a sensitivity analysis of the sampling period indicated that 2 weeks may be sufficient for data collection at current penetration rates. Data from connected vehicles (CVs) (e.g., vehicle position, speed, and heading) are expected to transform traffic operations by enabling numerous applications, such as enhanced methods of traffic control (1, 2). Applications at intersections might include warning of an impending red light violation to avoid collision, suggesting speeds to drivers to improve signal operation, or using the enhanced information to improve signal timing. One key factor that determines the degree of impact of potential CV applications is the level of market penetration (p), that is, the proportion of the vehicle fleet that is connected. Another important factor is the time scale of the application. Real-time control applications generally require a high level of penetration to achieve benefits. However, other applications that sample traffic patterns over longer periods potentially can work at lower levels of penetration. One example is the sampling of vehicle arrivals for the evaluation and optimization of offsets in coordinated traffic signal control. In this application, if the arrival patterns are cyclic and remain consistent over a time period, they can be sampled with a low p over a sufficiently long sample. A previous proof-of-concept study that investigated the impact of market penetration and sampling period on the feasibility of offset optimization found that 1% p was adequate for a 3-hour sampling period and that lower values of p potentially were feasible if multiple days of data could be layered (3). The ability to aggregate data from multiple days depends on the consistency of traffic across time periods. One near-term application for the sampling of arrival profiles would be to optimize offsets on corridors where no detection is available to measure arriving flow profiles. This application would be relevant to fixed-time corridors that operate without detection (e.g., in central business districts), corridors on which no detection was installed on the mainline approaches as a cost-saving measure, or corridors on which detectors have failed on some approaches. In such scenarios, offset optimization typically would require modeling (which may not accurately reproduce field conditions) or manual adjustment in the field. CV data might fill the role of detection in enhancing or automating offset optimization. If detection can be done at low levels of market penetration, as in the proof-of-concept study (3), then offset optimization could be an early application of CV data that could improve signal operations now, while markets increase to levels needed for more advanced applications. This study uses vehicle trajectories obtained from private-sector data providers as a proxy for CV data obtained via dedicated shortrange communications or other means to investigate whether detectorfree offset optimization is possible. A concept called virtual detection is proposed for determining individual arrival times from the privatesector trajectory data. The sampled arrival profiles are statistically compared with those measured with detectors. Finally, the sampled arrival profile data were used to drive an offset optimization process, and the arterial travel times were compared for one solution based on detector data and one based on CV data. C. M. Day and H. Li, HAMP 415, and L. M. Richardson and D. M. Bullock, HAMP 417, Lyles School of Civil Engineering, Purdue University, 55 Stadium Mall Drive, West Lafayette, IN J. Howard, Indiana Department of Transportation, 185 Agrico Lane, Seymour, IN T. Platte, Indiana Department of Transportation, 315 Boyd Boulevard, Laporte, IN J. R. Sturdevant, Indiana Department of Transportation, 862 East 21st Street, Indianapolis, IN Corresponding author: C. M. Day, cmday@purdue.edu. Transportation Research Record: Journal of the Transportation Research Board, No. 262, 217, pp Virtual Detection with CV Data Overview of Concept Advance or setback detectors are located several seconds travel time upstream from the stop bar on approaches to signalized intersections. They are used primarily to add initial timing and protect dilemma zones by phase extension. They also can be used to measure arrival profiles, which can be used to adjust signal offsets (4). 54

2 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock 55 Distance Connected Vehicle Nonconnected Vehicles Stop Bar Reporting Interval Detection Zone Vehicle Detection Times Timestamped Positions from Connected Vehicle Time Arrival Profile Time Connected Vehicle Nonconnected Vehicles FIGURE 1 Comparison of vehicle arrival profile sampling with a physical detector and with CV trajectory data (3). The availability of such detectors varies considerably by agency and location. Figure 1 is a time space diagram that shows several vehicle trajectories on the approach to a signalized intersection. The chart shows the location of an advance detector relative to the stop bar, from which an arrival profile can be determined. Each record in the arrival profile corresponds to a vehicle detection time. In this example, trajectories are illustrated for a vehicle stream that contains one CV and six non-cvs. The detector enables direct measurement of arrival time each time an individual vehicle physically passes over the detection zone. Usually, such a measurement would not be possible in the absence of a detector. However, the single CV reported its position periodically, with a fairly short reporting interval. Even though the reported CV locations do not necessarily align with the detection zone, interpolation between those time-stamped positions is possible to estimate when the CV was likely to have crossed the detector. The arrival profile determined from CVs does not provide a lot of information about the vehicle fleet during one cycle, but aggregated data from many cycles would enable the development of a profile to estimate the overall profile shape. Implementation To implement the concept, a suitable data source was needed. Many mobile devices, including most smartphones, have the ability to determine their location from GPS signals. Several vendors have developed applications that analyze GPS data to calculate values such as minute-by-minute segment speeds. The 215 Urban Mobility Scorecard, for example, is created by analyzing such speed data (5). Some researchers have begun to use this type of data for more detailed analysis of signal performance. Researchers at the Bavarian Road Administration used a combination of geofencing and map matching to measure delays on movements through 2,3 traffic signals (6). Argote-Cabañero et al. measured delay and several other measures of effectiveness by sampling trajectories from the Next Generation Simulation data set (7). For this study, data were obtained from a private-sector vendor. The data consisted of probe vehicle trajectories observed in the state of Indiana between May 1 and June 11, 216. The data were organized into individual trips for which a single identifier was maintained from the beginning and end of travel from an origin point to a destination point. Reporting intervals varied from 1 second to every few minutes. Approximately 2,, time-stamped vehicle positions per day were available in the statewide data set. Figure 2 illustrates how virtual detections were extracted from the trajectory data (8). First, a detection line was identified by denoting two points that represented the left and right sides of a line perpendicular to the roadway and stretched from the centerline to the edge of the right-of-way (D L and D R, respectively). Virtual detections were identified when the splines between two consecutive time-stamped positions (P i and P i+1, respectively) intersected the detection line at the point of intersection (P X ), as in Figure 2a. Because of variations in the spatial resolution of the individual time-stamped locations, some intersecting splines could represent travel in the opposite direction. To establish the direction of travel

3 56 Transportation Research Record 262 Roadway Spline of Trajectory P i+1 Virtual Detection D L P X Detection of Travel P i D R Detection Line P i+1 D L P X Detection of Travel P i D R P i D L P X Detection of Travel P i+1 D R (c) FIGURE 2 Extracting virtual detections from vehicle trajectory data: with trajectory splines, with enclosed area for spline traveling in same direction as roadway, and (c) with enclosed area for spline traveling in opposite direction from roadway.

4 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock 57 of a spline, a polygon was made by joining points P i, D R, P i+1, and P i. If these points defined a relatively small triangular region (as in Figure 2b), then the direction of travel for the spline was the same as for the roadway. However, if these points defined a very large region (approximately the entire surface of the Earth, as in Figure 2c), then the direction of travel was opposite to that of the roadway. The time of intersection (T X ), or the virtual detection time, was determined by interpolating between P i and P i+1 as T X dx = Ti+ v where T i is the time when the vehicle was reported at position P i and v is vehicle speed, expressed as d v = T T i+ 1 i where d is the Euclidean distance between P i and P i+1. The intersecting lines were subjected to additional filtering to eliminate the inclusion of erroneous splines caused by CVs with long reporting intervals. A 3-second filter was applied, the purpose of which is illustrated more clearly by example in the next section. To construct a cyclic arrival profile, each individual T X was transformed as T = ( T ) mod C (3) C X where T C is the time in cycle of the arrival and C is the cycle length. The arrival profiles were created by counting the number of vehicles per 1-second bin, from to C 1 (9). In this study, all controllers used a common Network Time Protocol time server to synchronize clock times, and no additional corrections were applied to accommodate differences between phase times and trajectory data times. Application to Field Data Two corridors in greater Indianapolis, Indiana, were chosen to test the virtual detection concept. On both corridors, advance detection (inductive loops) was located approximately 5 seconds upstream of the stop bar on the coordinated movements and could be used to evaluate the CV arrival profiles for accuracy. SR-37 is a high-speed arterial that passes through rural and suburban areas (Figure 3a). It is a four-lane divided highway between Intersections L and F and a six-lane highway between Intersections F and A. US-36 (Pendleton Pike) passes through urban and suburban areas (Figure 3b). It has six lanes between Intersections M and S, and four lanes between Intersections T and Y. These two corridors serve mainly commuter traffic into and out of Indianapolis and tend to have consistent patterns from one day to the next during a typical week. No disruptive events occurred during the study period. Detectors generally are well maintained on the corridors, but detectors were not working on a few individual approaches during this study. Figure 4 illustrates the use of the virtual detection technique and the 3-second reporting interval filter for Intersections M through Q (1) (2) on Pendleton Pike. Figure 4a shows all of the trajectory splines from a 48-hour period about 36 million splines distributed across the state of Indiana, comprising about 46, individual trips. The map is almost entirely covered by this collection of lines. However, the locations of major roadways are visible, as though they had been roughly scribbled over the map. The heaviest saturation of lines coincides with the location of the Interstate highway. Figure 4b shows only the splines that intersect the virtual detection lines along the desired direction of travel; many but not all of the trajectories that clearly are from travel on other roadways have been eliminated. Still, many splines appear to originate from travel along the Interstate and a few from crossing streets. Also, many splines are so long that they extend across the entire map. Figure 4c shows the effect of the 3-second filter. The splines are limited almost entirely to travel along the roadway of interest, and long splines have been removed; the number of intersecting splines has been reduced by about two-thirds, from 3,75 to 1,141. Determination of Arrival Profiles Profile Construction from Trajectory Data The proof-of-concept study speculated that 1% market penetration would be sufficient to conduct a measurement for a 3-hour sampling period (3). The unfiltered trajectory data likely approach this rate overall, but the penetration rates fall to less than 1% for many approaches when the data are filtered to include only those trajectories from which useful arrival times can be extracted. However, layering multiple days to extend the sampling period has been demonstrated to reduce the penetration needed to capture an arrival profile even more (3). Purdue Coordination Diagrams (PCDs) are used to compare real and virtual detections in Figure 5 (4). The arrival time for every cycle in a 24-hour period is shown as well as its relationship to the signal phase. The green shaded region represents the green interval; arrivals aligned with this region show vehicles arriving on red, and arrivals below the green line occur during the red interval. Vertical blue lines indicate time-of-day pattern changes. Data from a physical detector show very good progression during the morning peak, with most of the arrivals aligned with the green interval; midday and afternoon plans show many vehicles arriving in red (Figure 5a). Virtual detection data from one 24-hour period show a very sparse distribution of points over the day that is insufficient to get a sense of overall arrival patterns (Figure 5b). When data from 6 weeks of virtual detection (May 1 through June 11, 216) are overlaid onto a representative 24-hour period of phase times, point density increases and platoons become distinguishable (Figure 5c). The patterns are quite similar to those made with physical detector data (Figure 5a). A cyclic arrival profile illustrates the layering concept in Figure 6, in which the sampling period expands from 1 day to 6 weeks. As in the PCD, 1 day does not yield enough data points to begin to confidently characterize an arrival profile (Figure 6a). However, with 1 week of data, the overall shape begins to take form (Figure 6b). As each additional week is added, the number of observations increases linearly and the profile grows steadily.

5 58 Transportation Research Record 262 Location of corridor Location of corridor FIGURE 3 Maps of corridor locations and intersections: SR-37 and US-36 (Pendleton Pike).

6 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock 59 Virtual Detectors (c) FIGURE 4 Process of extracting virtual detections from vehicle trajectories (data for westernmost five intersections on Pendleton Pike for May 1 and May 2, 216): all trajectory splines from a 48-hour period (35,884,46 lines across the state), splines that intersect virtual detectors (3,75 lines at 1 detectors), and (c) intersecting splines after application of a 3-second filter (1,141 splines at 1 detectors).

7 6 Transportation Research Record 262 Beginning of green End of green Green interval Vehicle arrival Free a.m. Peak Midday p.m. Peak Evening Free : 2: 4: 6: 8: 1: 12: 14: 16: 18: 2: 22: : Time of Day Beginning of green End of green Green interval Vehicle arrival Free a.m. Peak Midday p.m. Peak Evening Free : 2: 4: 6: 8: 1: 12: 14: 16: 18: 2: 22: : Time of Day Beginning of green End of green Green interval Vehicle arrival Free a.m. Peak Midday p.m. Peak Evening Free : 2: 4: 6: 8: 1: 12: 14: 16: 18: 2: 22: : Time of Day (c) FIGURE 5 Purdue coordination diagrams showing real and virtual detections (data for inbound approach at Intersection Q): physical detector data, 1 day of virtual detections, and (c) 6 weeks of virtual detections.

8 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock Number of Trip Data Virtual Detections (c) (d) FIGURE 6 Building an arrival profile by increasing sampling period duration (data for inbound approach at Intersection Q): 1 day, N = 11; 1 week, N = 67; (c) 2 weeks, N = 116; (d) 3 weeks, N = 158; and (e) 4 weeks, N = 22. (continued on next page) (e)

9 62 Transportation Research Record Number of Trip Data Virtual Detections (f) (g) FIGURE 6 (continued) Building an arrival profile by increasing sampling period duration (data for inbound approach at Intersection Q): (f ) 5 weeks, N = 26 and (g) 6 weeks, N = 333. A worthy consideration is that the identity of each vehicle is not known from one day to the next. The data give only a general category of each vehicle type. Whether the same vehicles are being sampled multiple times across different days of the week is impossible to determine. This methodology assumes that the data represent a random sample of overall traffic. Additional investigation of the data for potential bias would be helpful to validate whether such an assumption is true and whether the sampled profiles are sensitive to such bias. Statistical Comparison To make it more useful for optimization, the profile is smoothed with a 5-second moving average and normalized so that its magnitude matches the expected volume on the approach. The 5-second value was selected from a qualitative comparison of the resulting profiles. The raw data and the 3-second and 5-second moving averages were substantially different, but increasing the moving average beyond 5 seconds did not produce much more change in profile shapes. A normalized physical detector profile is compared with the normalized, smoothed virtual detector profile for the same approach in Figure 7. The physical detector data (Figure 7a) were extracted from 1 representative week, and the virtual detector data (Figure 7b) were developed from a 6-week period. The profiles also are visually similar, with the platoon indicated by the bulk of the distribution ranging from about 8 seconds in cycle through 2 seconds in cycle (wrapping around the cycle boundary). The two cumulative cyclic distributions of the two profiles were compared, and the maximum absolute difference between the two cumulative distributions is highlighted in Figure 7c. This value, called the D-statistic, can be used to evaluate the statistical goodness of fit between the two cyclic distributions with a Kolmogorov Smirnov (KS) test. For the example shown here, the D-statistic is.46. For 1 bins (representing 1-second bins and a cycle length of 1 second), this value represents a significant result at a confidence level of 9%. The D-statistics for all approaches at the 25 intersections where a comparison could be made are listed in Table 1; boldface denotes the values for which the statistical test yielded a significant result at the 9% confidence level (i.e., most of the approaches on the two corridors). Intersections A, B, and O had relatively poor fits for both directions, perhaps due to their proximity to the Interstate highway, which would seem to increase the likelihood that erroneous detections could be picked up by the detection lines, even after filtering. More comprehensive map matching of the trajectory points to roadway segments likely would improve agreement between the field loop detectors and virtual detectors at intersections A, B, and O. The market penetration p of each approach also is shown in Table 1. Penetration rates were determined by comparing the number of filtered intersecting splines with volumes measured by vehicle detectors at each location. Market penetration rates were less than 1% on all system approaches and less than.1% on a few. Offset Optimization A comparison of virtual detector profiles and physical detector profiles indicated that not every approach yielded a statistically significant goodness of fit; however, the goodness of fit result does not necessarily reflect the utility of the data for optimization. The proof-of-concept study showed that good optimization results could be achieved even though the estimated profiles did not fit the actual ones with high statistical confidence (3). As long as the part of the cycle where the bulk of the vehicles arrived was identified well by the distribution, small differences in overall profile shape that may accumulate into large D-statistics might not affect the optimization results. The Link Pivot algorithm (9), a formulation of the combination method for arterial highways (1), was used to prepare two sets of optimized offsets: Physical detector offsets were determined by running the optimizer with arrival profiles from physical detectors and green times

10 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock 63 Frequency Frequency Virtual detector profile Physical detector profile 1. Cumulative Frequency Maximum absolute difference at 5 s. (c) FIGURE 7 Comparison of arrival profiles from real and virtual detectors (data for inbound approach at Intersection Q): physical detector profile, tabulated over a 1-week period; virtual detector profile, tabulated over a 6-week period; and (c) comparison of cumulative frequency distributions.

11 64 Transportation Research Record 262 TABLE 1 Market Penetration Rate (p) and Kolmorogov Smirnov D-Statistics from Comparing Physical and Virtual Detector Arrival Profiles Inbound Outbound System Intersection p (%) D-Statistic p (%) D-Statistic SR-37 A. Pilot B. I-465 WB ramp C. I-465 EB ramp D. Thompson E. Harding.27.4 NA a NA a F. Epler G. Banta H. Southport I. Wicker J. County Line K. Fairview L. Smith Valley M. SR Pendleton N. I-465 SB ramp O. I-465 NB ramp P. 42nd Street Q. Franklin R. Esquire S. Post NA b NA b T. MBC group U. Mitthoeffer V. 56th Street W. Walmart X. Sunnyside Y. Oaklandon NA c NA c Note: WB = westbound; EB = eastbound; NA = not available; SB = southbound; NB = northbound. a This approach is unsignalized. b Some lanes had broken detectors, so this approach is excluded from the comparison. c No detector data available at this approach. logged by the controllers. Data from 1 week were aggregated on each corridor to support the optimization. Virtual detector offsets were determined by running the optimizer with arrival profiles from trajectory data and green times logged by the controllers. The same green time distributions were used as for the physical detector offsets. The physical detector offsets and the virtual detector offsets each ran for 1 week on each corridor. Travel time data were extracted from an analysis of minute-by-minute segment speeds obtained from the same data vendor that provided trajectory data; these data have been used for arterial travel time analysis in previous studies (11, 12). The methodology described by Remias et al. was applied in the present study, with the main difference being that the segment definitions used were the smaller XD rather than the longer Traffic Message Channel (11). Results of that exercise are presented in Figure 8, which shows two directions on each corridor for the midday time period. Each chart shows a cumulative frequency distribution of the travel times with existing offsets, physical detector offsets, and virtual detector offsets. On SR-37 inbound, the physical detector offsets reduced travel time by approximately 1 minute at the 5th and 75th percentiles (Figure 8a); the virtual detector offsets also improved travel time over the existing offsets but not as much. Travel times also were more reliable, as shown by the more vertical slopes of the curves. On SR-37 outbound, travel time was almost the same for the three data sets (Figure 8b). On Pendleton Pike inbound, very little difference was observed between the existing offsets and the physical detector offsets (Figure 8c). However, the virtual detector offsets reduced travel time by approximately.5 minute at the 25th percentile. On Pendleton Pike outbound, both the physical detector offsets and the virtual detector offsets reduced travel time by approximately 1 minute at the 25th percentile and slightly less than 1 minute at the 5th percentile (Figure 8d). Above the 75th percentile, the cumulative frequency distribution for the physical detector offsets exhibits a long tail, indicating that some travel times increased under physical detector offsets. Overall, the travel time results show that the virtual detector offsets can provide results that are similar to physical detector offsets. On SR-37, the physical detector offsets outperformed the virtual detector offsets, but the virtual detector offsets still yielded worthwhile improvement. Reduced travel time and improved reliability would have been welcome, for example, if analysis from physical detection had not been possible on the corridor. This result had been anticipated, given that the physical detectors provide more complete information. In contrast, on Pendleton Pike, the virtual detector offsets yielded results that were slightly better than the physical detector offsets, which may be attributable to a few factors. One is that a few of the Pendleton Pike approaches had poorly performing detection; the

12 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock 65 Existing offsets Physical detector offsets Virtual detector offsets Cumulative Frequency Cumulative Frequency Travel Time (min) Travel Time (min) Cumulative Frequency Travel Time (min) (c) Cumulative Frequency Travel Time (min) (d) FIGURE 8 Cumulative frequency distributions for travel time: SR-37 inbound, SR-37 outbound, (c) Pendleton Pike inbound, and (d) Pendleton Pike outbound. outbound approach at Intersection S had only one working detector, so arrival profiles captured by physical detection may have been poor at that location (Table 1). In a more urban environment, with lower speeds (hence shorter distances of the advance detector from the stop bar) and longer queues, physical detection might not have captured the true arrival patterns on some approaches. However, by interpolating between reported vehicle movement across a detection line rather than the rising edge of detector occupancy that creates a detector on event in the high-resolution data, virtual detection might have better characterized the arrival patterns. Shortening the Sampling Period Results from two corridors where offsets were improved with the use of cyclic flow profiles generated from virtual detection demonstrate that the virtual detection concept is feasible and can improve arterial travel times reasonably. For this study, 6 weeks of data were analyzed, which begs the question of whether such a long sampling period is necessary for such an analysis. To answer that question, a sensitivity analysis of the goodness of fit with respect to the duration of the sampling period was performed. Figure 6 shows the raw arrival profiles for various sampling periods (1 day to 6 weeks) for a particular approach. These profiles were smoothed, normalized, and converted to cumulative frequency diagrams. Then they were compared with detector data aggregated over the same time periods, and the Kolmorogov Smirnov test was performed for each comparison; results are shown in Figure 9, with D-statistic goodness of fit given for each interval. The D-statistic for the 6-week result (Figure 9g) differs from that in Table 1 because the detector data were aggregated across all 6 weeks rather than 1 representative week (data were not available from all 25 intersections across the entire 6-week period). Even though the cumulative distributions for even 1 day of data exhibit good visual agreement, only data sets with data from 2 weeks or longer pass a statistical goodness-of-fit test at a 9% confidence level. However, the D-statistic was lowest with 4 weeks of aggregated data and then started to increase as more data were added, indicating that differences in arrival profiles were accumulating over time. This finding demonstrates that an upper bound exists beyond which additional data aggregation becomes counterproductive because traffic pattern changes associated with Memorial Day weekend introduce noise into the data set. This brief analysis demonstrates that about 2 weeks may be an appropriate data-sampling period for many corridors. However, this period could be reduced with increased market penetration of probe vehicle data. The arrival profiles measured tomorrow probably will be more accurate than those that were measured yesterday. Also, the availability of true CV data from vehicles with dedicated short-range communication or other such means (which soon may be a substantial amount of the overall vehicle fleet) likely would increase the accuracy of arrival profiles and decrease the sampling period required to characterize them. Indeed, more active, real-time control schemes may become possible when the penetration rate is sufficiently high. Privacy concerns may limit the ability of agencies to collect trajectory information by this means. If few vehicles decide to opt in (i.e., to provide those data within the envisioned CV environment), then private-sector data might be a valuable resource for obtaining anonymized trajectories at a network level. The results in this paper indicate that early improvements are possible with conventional types of control that use private-sector data at low levels of market penetration.

13 66 Transportation Research Record day Detector week Detector Cumulative Frequency weeks Detector (c) weeks Detector (d) weeks Detector FIGURE 9 Comparison of virtual detector data from different sampling intervals and detector data from same date ranges (data for inbound approach at Intersection Q): 1 day, D =.1125; 1 week, D =.1126; (c) 2 weeks, D =.447; (d) 3 weeks, D =.57; and (e) 4 weeks, D =.36. (continued) (e)

14 Day, Li, Richardson, Howard, Platte, Sturdevant, and Bullock weeks Detector.5 Cumulative Frequency.25. (f) weeks Detector (g) FIGURE 9 (continued) Comparison of virtual detector data from different sampling intervals and detector data from same date ranges (data for inbound approach at Intersection Q): (f ) 5 weeks, D =.38 and (g) 6 weeks D =.453. Data in f and g are statistically significant at the 9% level. Summary and Future Work This study examined the feasibility of offset optimization that uses CV data at a low level of market penetration. Vehicle trajectory data were obtained from a private-sector vendor. Geometric analysis was performed on the trajectory splines to determine the times when vehicles would have crossed lines defined as arrival detectors. These results were considered virtual detections, from which arrival profiles were created. Data were collected for two corridors that comprised 25 coordinated signalized intersections. After the data were sampled and filtered, penetration rates were between.9% and.8%, with variation by approach (Table 1). Two tests were used to analyze the arrival profiles. First, a statistical goodness-of-fit matching test was made between arrival profiles aggregated over 6 weeks and detector data were aggregated over 1 representative week to determine whether the arrival profiles determined with virtual detection closely matched those measured from physical detectors. Most approaches exhibited statistically significant goodness of fit between the arrival profile distributions from virtual and physical detection, as determined with a KS test at a 9% confidence level (Table 1). Some approaches did not have a good statistical fit, especially at intersections with freeway ramps. Next, arrival profiles were used to optimize offsets. The performance of these offsets was compared with that of offsets determined with arrival profiles obtained from physical detectors. Corridor travel times were calculated for the existing offsets, the physical detector offsets, and the virtual detector offsets. On one corridor, the offsets determined with both physical detection and virtual detection improved; travel times were slightly lower with physical detection. On the other corridor, virtual detection reduced travel times slightly. Results demonstrate that virtual detection is feasible for optimizing offsets with current penetration rates of probe data. Then, a sensitivity analysis of the sampling period was conducted to determine whether intervals could be shorter than 6 weeks. Results indicated that a 2-week sampling period may be sufficient for current market penetration rates and that data quality (in terms of statistical goodness of fit for arrival profiles) does not necessarily increase linearly as the sampling period increases in response to shifts in traffic patterns. Results of the study have demonstrated that probe vehicle data can be used as a proxy for CV data in optimizing offsets. Future work in this area could refine the geometric analysis further to better filter erroneous data (e.g., vehicles traveling on freeway overpasses or underpasses near interchanges) and conduct additional comparisons of match quality over different sampling periods to fine-tune the requirements for data collection. Another potential area of study would consider multimodal extensions of the methodology. The present study assumes that each data point represents a vehicle; however, probe data could capture bicycles and pedestrians, particularly in urban environments. Investigating the impact of the operating environment (e.g., urban versus rural) on the data characteristics also would be worthwhile. Finally, a potential application for the proposed methodology is on corridors that lack physical detection (e.g., fixed-time operation in a central business district area). Acknowledgments This work was supported in part by the Joint Transportation Research Program and the Pooled Fund Study led by the Indiana Department of Transportation and supported by the state transportation agencies of California, Georgia, Kansas, Minnesota, Mississippi, New Hampshire, Pennsylvania, Texas, Utah, and Wisconsin; the FHWA Arterial Management Program; and the Chicago Department of Transportation. Probe vehicle data were provided by INRIX. References 1. Hill, C. J., and J. K. Garrett. AASHTO Connected Vehicle Deployment Analysis. FHWA-JPO FHWA, U.S. Department of Transportation, 211.

15 68 Transportation Research Record Kaths, J., E. Papapanagiotou, and F. Busch. Traffic Signals in Connected Vehicle Environments: Chances, Challenges, and Examples for Future Traffic Signal Control. In Proceedings, IEEE 18th International Conference on Intelligent Transportation Systems (ITSC 215), IEEE, Piscataway, N.J., 215, pp Day, C. M., and D. M. Bullock. Detector-Free Signal Offset Optimization with Limited Connected Vehicle Market Penetration: A Proofof-Concept Study. Transportation Research Record: Journal of the Transportation Research Board, No. 2558, 216, pp dx.doi.org/1.3141/ Day, C. M., R. Haseman, H. Premachandra, T. M. Brennan, Jr., J. S. Wasson, J. R. Sturdevant, and D. M. Bullock. Evaluation of Arterial Signal Coordination: Methodologies for Visualizing High-Resolution Event Data and Measuring Travel Time. Transportation Research Record: Journal of the Transportation Research Board, No. 2192, 21, pp Schrank, D., B. Eisele, and T. Lomax. 215 Urban Mobility Scorecard. Texas A&M Transportation Institute, College Station, Tex., Wünsch, G., F. Bölling, A. von Dobschütz, and P. Mieth. Bavarian Road Administration s Use of Probe Data for Large-Scale Traffic Signal Evaluation Support. Transportation Research Record: Journal of the Transportation Research Board, No. 2487, 215, pp dx.doi.org/1.3141/ Argote-Cabañero, J., E. Christofa, and A. Skabardonis. Connected Vehicle Penetration Rate for Estimation of Arterial Measures of Effectiveness. Transportation Research Part C: Emerging Technologies, Vol. 6, 215, pp Li, H., C. M. Day, and D. M. Bullock. Virtual Detection at Intersections Using Connected Vehicle Trajectory Data. In Proceedings, IEEE 19th International Conference on Intelligent Transportation Systems (ITSC 216), IEEE, Piscataway, N.J., 216, pp doi.org/1.119/itsc Day, C. M., and D. M. Bullock. Computational Efficiency of Alternative Algorithms for Arterial Offset Optimization. Transportation Research Record: Journal of the Transportation Research Board, No. 2259, 211, pp Hillier, J. A. Appendix to Glasgow s Experiment in Area Traffic Control. Traffic Engineering & Control, Vol. 7, 1965, pp Remias, S. M., T. M. Brennan, A. M. Hainen, C. M. Day, and D. M. Bullock. Characterizing Urban Mobility and Travel Time Reliability Along Signalized Corridors Using Probe Data. Presented at International Scientific Conference on Mobility and Transport, Munich, Germany, June 18 and 19, Hu, J., M. D. Fontaine, and J. Ma. Quality of Private Sector Travel-Time Data on Arterials. Journal of Transportation Engineering, Vol. 142, No. 4, The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented here, and do not necessarily reflect the official views or policies of the sponsoring organizations. These contents do not constitute a standard, specification, or regulation. The Standing Committee on Traffic Signal Systems peer-reviewed this paper.