THE EFFECTS OF DATA AGGREGATION ON MEASURING ARTERIAL PERFORMANCE MICHAEL JOSEPH WOLFE

Transcription

1 THE EFFECTS OF DATA AGGREGATION ON MEASURING ARTERIAL PERFORMANCE by MICHAEL JOSEPH WOLFE A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in CIVIL AND ENVIRONMENTAL ENGINEERING Portland State University 2009

2 ACKNOWLEDGEMENTS This thesis represents a jump by an order of magnitude over the size, scope, and rigor of previous research that I have done. It would not have been possible without the patient support of my two advisors, Dr. Robert L. Bertini and Dr. Christopher Monsere, who gave ample encouragement along the way, reassured me that there would indeed be an end, and let me know when I had gotten there. I d like to thank them for that, and to thank them and Dr. Miguel Figliozzi for serving on my thesis defense committee. I am also thankful to the civil engineering and urban planning faculty at Portland State University for their first- rate instruction. Their classes constantly challenged me and fed my enthusiasm for transportation engineering. I came to PSU without any background in engineering and leave it feeling confident and prepared to contribute what I have learned to my community. I am also grateful to my fellow students, who elevated the discourse both in and out of class, and from whose diverse backgrounds and perspectives I have deeply benefited. i

3 Thanks are due to Steve Boice and Jim Peters at DKS Associates for their friendly assistance parsing the SCATS data. Thanks also to Rafael Fernandez- Moctezuma, Alex Bigazzi, and Hau Hagedorn for their encouragement and their generous assistance with various pieces of software. Finally, I d like to thank my father Kirke, my sister Maia, and my fiancée Allison for their patience and understanding in the long months that I was consumed in this research. Their loving support was vital to keeping up my spirits when my enthusiasm was waning. This thesis is dedicated to them, and to the memory of my mother Marjorie, who was there at the beginning when I took on this project to become a transportation engineer, and who I think would have been proud of how it turned out. ii

4 TABLE OF CONTENTS Acknowledgements... i List of Tables... iv List of Figures... v 1.0 INTRODUCTION Problem Statement Research Objectives Project Scope Experimental Design Organization LITERATURE REVIEW DATA Study Location Simulation Configuration Simulation Data METHODOLOGY Visualizations Travel Time Estimation Methods ANALYSIS AND RESULTS Delay Analysis Travel Time Estimation CONCLUSION REFERENCES APPENDIX REGRESSION SCATTERPLOTS iii

5 LIST OF TABLES Table 1 Arterial performance measures 3 Table 2 Simulation green times by movement 22 Table 3 Vehicle volumes 24 Table 4 Comparison of simulated vs. probe travel times 25 Table 5 Summary of estimated delay 70 Table 6 Delay summary for increased detector density 75 Table 7 Summary of delay estimates for missing middle detector 77 Table 8 Travel time estimate distribution summary 81 Table 9 Linear regression between estimated and actual travel times 86 Table 10 Analysis of Variance results 87 iv

6 LIST OF FIGURES Figure 1 Burnside Street, SCATS implementation 5 Figure 2 Freeway performance method applied to an arterial 13 Figure 3 Burnside (simulated area) 20 Figure 4 Simulation layout 21 Figure 5 Figure 6 Time- Space diagram for simulated peak hour and schematic of Burnside Street 27 Example time- space diagram (left) and input/output diagram (right) 28 Figure 7 time- space diagram, Kelly to Eastman (westbound) 29 Figure 8 Example input/output diagram, Kelly to Fairview 31 Figure 9 The Midpoint Method 34 Figure 10 Speed 1 and speed 2 35 Figure 11 The constructed trajectory estimate 36 Figure 12 The Vehicle Matching Method 37 Figure 13 Best case arrival times for each entering vehicle 39 Figure 14 trajectories using the vehicle matching method 40 Figure 15 The Saturation Matching Method 41 Figure 16 Initial vehicle match 44 Figure 17 Matching the second vehicle 45 Figure 18 The second vehicle matched to the first exit plus one saturation headway 46 Figure 19 The Phase Matching Method 47 Figure 20 Best case arrival times for each entering vehicle 49 Figure 21 Departures evenly distributed in each green phase 50 v

7 Figure 22 The Vehicle Synchronization Method 51 Figure 23 Best case arrival times for each entering vehicle 53 Figure 24 Matching enumerated arrivals and departures 54 Figure 25 The Average Departure Method 55 Figure 26 Ground truth input/output diagram, Kelly to Fairview 59 Figure 27 Midpoint method time- space and input/output diagrams 61 Figure 28 Vehicle matching time- space and input/output diagrams 62 Figure 29 matching time- space and input/output diagrams 64 Figure 30 matching time- space and input/output diagrams 65 Figure 31 Input/Output diagram showing cumulative curve for cycle- aggregated data 67 Figure 32 Saturation matching applied to cycle aggregated data 69 Figure 33 Bar chart summary of estimated delay 71 Figure 34 Ratio of saturation matched travel times to actual travel times 80 Figure 35 Ratio of saturation matched to actual average travel times 80 Figure 36 Figure 37 Figure 38 Figure 39 Cumulative plot of the ratio of estimated to actual travel times, based on event- based data 82 Cumulative plot of the ratio of estimated to actual travel times, based on cycle aggregated data 83 Saturation matching estimates vs. actual average travel times (event based data) 85 Saturation matching estimates vs. actual average travel times (cycle aggregate data) 85 vi

8 1.0 INTRODUCTION The proliferation of information technology in the transportation field has opened up opportunities for communication and analysis of the performance of transportation facilities. The Highway Capacity Manual relies on empirical observations, traffic flow theory, and small data samples to generate levels of service to assess performance, but modern detection technology gives us the opportunity to better capture the dynamism of these systems and examine their performance from many perspectives. Travelers, operations staff, and researchers can benefit from measurements that provide information such as travel time, delay, number of stops, and effectiveness of signal coordination. In particular, point- based detectors can be leveraged to collect the data necessary to generate such information. But while their use for this purpose on restricted access facilities is well understood, a great many challenges remain in using loop detectors to measure the performance of arterials. 1.1 Problem Statement Methods for measuring the performance of restricted access facilities have been broadly implemented; however, in the U.S., over 40% of vehicle miles are 1

9 traveled on arterials. This leaves a large gap in the information that is available about transportation system performance. Arterials present far more options than freeways do for travelers in choosing a route, so information about the relative levels of congestion of alternatives would be quite valuable to users. Furthermore, making archived arterial performance data available to researchers and planners would have benefits in allowing them to quantify the impacts of changes in the system. However, using inductive loop detectors to monitor vehicle performance on arterials is complicated by many factors. Most prominently, there is no vehicle conservation between detectors and traffic control devices (i.e., signals) interrupt the flow of vehicles in order to encourage the development of platoons. Couple these considerations with the realities of loop detectors that are separated by great distances and detector management software that only makes data available in aggregate, and the challenges of generating arterial performance information from this data are apparent. 2

10 1.2 Research Objectives The objective of this research is to develop methods to measure arterial performance using existing detector infrastructure. Arterial performance may be measured in many different ways; Table 1 gives some examples. Measures include obvious measures like average and maximum speeds, travel time and travel time variance, delay, traffic volume, and vehicle density. Other measures include incidence of signal failure (i.e., failing to exhaust a vehicle queue in a single signal cycle), speed index (i.e., ratio of measured speed to Table 1: Arterial performance measures. An (A) indicates that the measure can be calculated from aggregated data, while an (E) indicates that event- based data is required. Speed Count Both Other Maximum Speed (E) Queue Length (E) Density (A) Incidents Travel Time Variance (E) Signal Failure (E) Congestion (A) Incident Duration Maximum Delay (E) Platoon Ratio (E) Number of Stops Average Delay (A) Average Speed (A) Speed Index (A) Travel Time (A) Volume (A) Average Delay (A) Average Speed (A) Speed Index (A) Travel Time (A) 3

11 posted speed limit), and platoon ratio (i.e., the number of vehicles that arrive during the signal s red phase). Additional measures such as fuel consumption and emissions are often computed from the basic performance measures. The table is organized based on the type of data that is required to calculate each measure, and each measure is labeled with an E or an A based on whether it requires event based data (describing the actions of individual vehicles) or it can be computed from aggregated data (describing the actions of collections of vehicles). While there are many metrics to measure arterial performance, vehicle travel time and delay are focused on in this research, as both are easily computed from data collected from inductive loop detectors. Methods to compute travel time and delay are proposed and compared. The effects of varying densities of detectors and levels of data aggregation are investigated. 1.3 Project Scope The study location is a 3- mile segment of East Burnside Road in Gresham, Oregon from Eastman Parkway to Powell Valley Road. Burnside Road is a major 5- lane arterial carrying 38,000 vehicles per day in 2007 (see figure 1). 4

12 Figure 1: East Burnside Street, SCATS implementation The corridor features 11 instrumented signalized intersections and is currently running TransCore s SCATS adaptive signal system. All intersections in the study area are signalized, though there are numerous other access points (i.e., driveways). Data collected by GPS units in probe vehicles from a previous 5

13 study and data archived by the SCATS system from the same time period was used to create a VISSIM simulation of the corridor. The model encompasses the first three intersections of the segment, from Eastman Parkway to Kelly Avenue, and simulates the afternoon peak hour. This simulation is used to compare different methods for measuring arterial performance and to assess the effects that variables such as detector spacing and data aggregation have on the quality of performance measures that can be generated. 1.4 Experimental Design The hypothesis that this research tests is that data from inductive loop detectors can be used to calculate vehicle travel time and delay. Once this question is answered, the secondary questions are: is there a method for estimating travel time that might be feasible to implement given current infrastructure and what effect does data aggregation and detector density have on the quality of our estimates? Travel time was considered because it is perhaps the most intuitive, broadly comparable, and easily applicable way to measure performance. In order to make a valid comparison between actual vehicle travel time and travel time 6

14 that is calculated from detector data, it is necessary to have both ground truth data and detector data. Probe data is expensive, and offers only a limited sample of the vehicles on the roadway. Therefore, a simulated corridor was designed, based on measurements of an actual arterial. This enabled us to compare simulated vehicle trajectories to trajectories generated from some set of data collected at discrete points ( detectors ). Vehicle delay was considered in addition to travel time because it is easily derivable from travel time and because it can be depicted visually in a very effective way. Delay can be shown by an input- output diagram, in which one curve shows the cumulative count of vehicles that enter a given road segment, and a second curve shows the cumulative count of vehicles that leave the road segment. The horizontal distance between the first curve and the second curve yields travel time, and that minus the free- flow travel time for the segment yields delay. Points where the two curves overlap indicate zero delay, while any gap is proportional to the system delay. This illustration can be created for both the ground truth trajectories and the estimated trajectories, giving us the actual delay and the estimated delay, and a clear way to compare the two. Quantifying this comparison lets us evaluate the accuracy 7

15 of estimation methods and the impacts of detector density and data aggregation. 1.5 Organization The section 2 of this document discusses some of the prior work done on the problem of arterial performance. It establishes the context for this research. Section 3 describes the data used in the research, including the measurements taken from East Burnside Road, the process used to construct and calibrate the simulation, and the data read from the simulation for reference and to construct arterial performance estimates. Section 4 talks about the methodology employed in this research, describing the methods used to make estimates and the tools used to evaluate them. A detailed, step- by- step process for implementing each method is given, including a list of data items and parameters needed for each. In section 5, two types of analysis are performed: first, estimated delay is compared actual delay both visually and in aggregate; then, travel time estimates are compared to the reference travel times, and estimation methods are evaluated based on how accurately they predict travel time. Finally, the results of the research are summarized in section 6, along with some suggestions for future research. 8

16 2.0 LITERATURE REVIEW The problem of assessing freeway performance has been studied by many authors and implemented widely in municipalities around the world. The consensus appears to be that using loop detectors or other sensors to measure speed and spatially extrapolating that speed to areas not covered by detectors is a reasonable method for measuring freeway performance as shown, for example, in a study of I- 4 in Florida (D Angello et al., 1999). When translating the problem of assessing traffic performance to arterials, using loop detectors to collect data remains a valid approach. This is in addition to other methods, such as probe vehicles, magnetic signature matching, radio frequency identification, and cell phone tracking. Arterial performance information is obtained from probe vehicles by extrapolating it from the performance of some subset of vehicles. The other three methods uniquely identify vehicles at different locations on the roadway and from that determine travel time. While each of these methods could provide extremely accurate arterial performance information, each relies on expensive or unimplemented/unproven technology, however, and vehicle identification 9

17 methods raise privacy concerns. Data from loop detectors is widely available however, and if it can be used to generate useful information, offers a cheap, rapidly implementable solution to the problem of measuring arterial performance. The complexity of arterial operations calls into question the validity of extrapolating speed measurements made by loop detectors over arterials, however. In particular, loop detectors on arterials are most frequently located near traffic signals, which heavily impact the behavior of nearby vehicles but whose influence wanes with distance. One study at the University of Washington examined the feasibility of using stop bar detectors to monitor arterial performance (Hallenbeck et al., 2008). The authors tested several variables, including detector placement, traffic volume, and site specific factors (such as turning volumes and signal coordination). It was found that stop bar detectors taking readings during the green and amber phases yielded good information on the amount of congestion on the arterial. This supports the idea that data from stop bar detectors can be used to generate relevant information, but does not suggest how one might compute delay, speed, or other traditional measures from such data. The City of Bellevue, Washington 10

18 developed a method to communicate arterial performance simply by displaying colors that correspond to occupancy times on its detectors (Liang, 2006). This method was satisfactory as a traveller information tool and for use in the operations center, but required site- specific calibration and, again, lacked quantifiability. As the work in Bellevue implies, it might not be necessary to estimate travel time to achieve the goal of communicating the congestion status. One paper (Fu et al., 2001) made the case that the presence of an overflow queue, and hence signal failure, is highly influential on travelers experiences. The study posited a method for measuring queue overflow based on conservation of vehicles. It assumed detectors placed both on the signal approach and at the stop bar, capable of providing event- based data, however; making it potentially difficult to implement. If travel time/average speed are the desired outcome, though, travel on arterials consists of free- flow travel between signals, and travel within the area under signals influence. Approaches to generating travel time/average speed information either attempt to measure each of these components, or use traffic 11

19 flow theory to calculate the effects of signals on traffic. One study (Tarko et al., 1999) used cumulative counts to estimate median travel times. The proposed method used vehicle counts over several second blocks to total the vehicle input and output of roadway segments. The method was developed and tested in a simulation. Another study (Xie et al., 2001) in Singapore attempted to use speeds measured by loop detectors at signalized intersections to estimate travel time over the whole road segment. The model required no site- specific calibration, using measured speeds and signal timing as its inputs. This algorithm was also tested in a simulation, and found to be highly accurate when detectors were closely spaced. A study in Roseville, Minnesota (Zhang, 1999) was performed on an actual arterial using probe vehicles. It found a correlation between the speeds of probe vehicles and speed estimates derived from three pieces of data: critical lane volume to capacity ratio, volume, and detector occupancy. It was found that speed estimates correlated highly in heavy traffic and not at all in light traffic. It was also found that signal factors, such as green time and offset were vital in explaining travel time variations. 12

20 Figure 2: Freeway performance method applied to an arterial One paper attempted to leverage transit vehicles as probes to supplement loop detectors as sources of arterial performance information (Berkow et al., 2008). In that study, two approaches were tried. In the first, loop detectors were used much as they are on freeways: speeds were measured and then extrapolated halfway to the next detector location (see Figure 2). This yielded implausible results, in part because detector density (4 detectors on a 4.5 mile segment of arterial) was low. The second method limited the area that the detectors described to the segment of roadway immediately around them and used transit vehicles as probes to fill in the gaps. This method represented an 13

21 improvement, but there was reason to doubt the accuracy of speeds measured at the detector, and to question the usefulness of data that was aggregated into 5 minute blocks. A related study (Hellinga and Gudapati, 2000) attempted to address the question of fusing arterial performance data from disparate sources in more general terms. The study proposes a 4- model method, fusing loop detector data, probe vehicle data, and driver reports, with a separate model generating a travel time estimate for each data source, and employing a fourth model to produce a final estimate based on a dynamic weighting of each sub- model. A common approach to arterial performance has been to break the problem of travel time into discrete delay components. Typically, these have included signal delay, accelerations/decelerations at signals, shockwave propagation, signal failure, and platoon interactions. The interactions of vehicles between signals have been computed using platoon dispersion algorithms (Skabardonis and Geroliminis, 2005) or by iterative use of virtual probes (Liu and Ma, 2007). Arterial performance measurement methods of this type require calibration of a number of site- specific parameters (e.g., saturation headway, free- flow 14

22 speed), employ a great deal of computation, and are not effective when supplied with aggregated data, which makes them difficult to employ on a widespread basis. Smaglik has done extensive work on deriving arterial performance measures from loop detector data. In one paper (Smaglik et al., 2007), arrival type is calculated from this data. A vehicle s arrival type describes when it arrives at an intersection during the signal cycle, and is used by the Highway Capacity Manual to evaluate signal coordination and calculate delay at an intersection. Because a vehicle s arrival type is based on the point in the cycle that it arrives at the signal, it is necessary to collect individual vehicle (event- based) data in order to calculate it. The authors show in a field study that with traffic controllers that are equipped to provide this output, Arrival Type can be easily and usefully calculated, to the benefit of anyone trying to evaluate/improve a corridor s signal timing plan. Another paper (Sharma et al., 2008) investigated two methods for estimating signal delay using inductive loop detector data: the Input- Output (IO) technique and the Hybrid technique. Both counted the number of vehicles 15

23 entering the queue at the signal with an advance detector, and both computed their delay estimates based on available queue storage and signal phase data. In the IO method, queue egress was estimated by using the intersection s saturation headway. The hybrid method used a stop bar detector and vehicle signature identification to more directly measure queue egress. Delay was calculated by superimposing the arrival and departure profiles and finding the area under the curve. These techniques again required event based data. The IO technique performed even better than the Hybrid technique in that study, suggesting its default use in this application, though the Hybrid technique would be useful in situations where saturation headway tended to change due to weather, or where there were a large number of access points between the advance detector and the stop bar. In conclusion, it is clear that there is a great deal of interest in measuring arterial performance. Most of the research to date that has looked at measuring arterial performance with point observer data has assumed event- based data and detectors at every intersection data of this quality is often not available. Studies that use lower quality data have not investigated the effects of varying data quality on estimates, and often required site- specific 16

24 calibration. There is a need for a method for estimating arterial performance that is easily implementable using current infrastructure, with full understanding of how data aggregation and varying detector density affects output. This research attempts to address that need. 17

25 3.0 DATA The comparisons that this study makes between vehicles actual performance and estimated performance are made with data collected from a carefully calibrated simulation. In order to make data from the simulation as realistic as possible, it was created and calibrated with extensive data from an actual arterial corridor. Data was used from a previous study undertaken to assess the SCATS signal management system on the East Burnside corridor in Gresham, Oregon (Peters, et al., 2008). This data included signal timing information, cycle- by- cycle traffic volumes, and GPS data from probe vehicles. Ground- truth trajectories were generated by the simulation for comparison purposes. Data used to estimate performance were limited to what could be gleaned from inductive loop detectors in the field, including vehicle volumes, occupancy (percentage of time a vehicle is detected), and speed. Data for estimates was aggregated at different intervals, including event based, per cycle, and per 5 minutes. Finally, for determining the effects of detector density, detectors were placed 1 per segment (at stop bars), 1 per 2 segments (at stop bars), and 3 per segment (at the stop bar, just past the intersection, and 18

26 at the back of the signal queue). Data were collected for 1 simulated peak hour. 19

27 3.1 Study Location The section of East Burnside considered in this study is 900 meters long, from Eastman Parkway to Kelly Avenue. Signalized intersections include Eastman Parkway, Fairview Drive, and Kelly Avenue. In this segment, Burnside has 5 lanes; 2 travel lanes in each direction and a center turn lane, plus bicycle lanes in each direction. All intersections are signalized, but there are numerous access points onto Burnside between intersections. Typical left turn movements at all three signals off are protected. See Figure 3 for an aerial view. Figure 3: East Burnside (simulated area) 20

28 3.2 Simulation Configuration A simulation was constructed using VISSIM 5.0 with intersections and lane configurations identical to this section of roadway. Access points outside of intersections were ignored and all turning movements were assumed to take place at intersections. Data collection points ( detectors ) were placed every 5 meters near intersections, and every 10 meters mid- block, as shown in Figure 4. Figure 4: Simulation layout 21

29 Table 2: Simulation green times by movement, in seconds Eastman Fairview Kelly EBT EBL WBT WBL NBT NBL N/A SBT SBL N/A Signal timing was taken directly from the SCATS strategic monitor records. SCATS is an adaptive system; to simplify the experiment, timings from the peak hour were averaged in the simulation (see Table 2). To obtain input volumes, the readings from stop bar detectors at Burnside and Eastman (eastbound) and Burnside and Kelly (westbound) were totaled for the peak hour. Input volumes for the cross streets were taken from stop bar detectors on Eastman, Fairview, and Kelly. Left turn volumes were taken from left turn lane detectors, while right turn volumes fit the following equation: Vt2 + Vl2 = Vt1 + Vlon1 Vroff1 + Vron1 (1) Where Vt2 is the through volume at intersection 2, Vl2 is the left turn volume at intersection 2, Vt1 is the through volume at intersection 1, Vroff1 is the right turn 22

30 volume off of the segment at intersection 1, Vlon1 is the cross- street left turn volume onto the segment at intersection 1, and Vron1 is the right turn volume onto the segment at intersection 1. All of these are known quantities except for Vroff1 and Vron1, which were estimated in proportion to the cross street volumes. The measured volumes and simulated volumes are compared in Table 3. Note that simulated volumes are slightly below those measured on the corridor, but follow a trend consistent with the measured volumes, except for the westbound Kelly to Fairview segment. The discrepancy here is due to the fact that one of the westbound loop detectors at the stop bar of the Burnside- Fairview intersection was inoperative the actual volume reading should be roughly double this number. 23

31 Table 3: Vehicle volumes Eastbound Actual Simulated Entering Eastman - Fairview Fairview - Kelly Exiting N/A 965 Westbound Entering Kelly - Fairview 425* 834 Fairview - Eastman Exiting N/A 802 Cross streets Eastman SB Eastman NB Fairview SB Fairview NB Kelly SB Kelly NB * indicates an inoperative detector at this location Having constructed the model with these parameters, the next step was to calibrate it. To calibrate the model, signal offsets were adjusted, and travel times for individual segments and for the whole corridor were recorded. Offsets were set to minimize total delay for vehicles traveling on Burnside in either direction. Neither the distribution of simulated travel times nor the distribution of probe travel times was normal, and there was no known equation governing either. Thus, a Wilcoxon Rank- Sum test was applied to 24

32 compare the distribution of simulated travel times to the distribution of probe travel times. The null hypothesis of this test is that the simulated travel times and the probe travel times are drawn from the same population, which the test evaluates by listing the travel times from both sets ordinally and observing whether either the simulated or probe travel times are prone to clustering. In the eastbound direction, this test yielded a p- value of 0.21, and in the westbound direction, it gave a p- value of A summary of the travel time distributions can be seen in Table 4. Table 4: Comparison of simulated vs. probe travel times Min 1st Q Median Mean 3rd Q Max Wilcoxon Rank- Sum Test p- value Eastbound Simulation Eastbound Probes Westbound Simulation Westbound Probes The model s visualization was observed to verify that the simulated corridor was operating in a plausible manner (e.g., no persistent queues, etc.). Simulated speeds were compared to both the posted speed limit and the average speed of probe vehicles. Simulated vehicle speeds were found to be 25

33 consistent with probe vehicle speeds and the speed limit the average speed of eastbound probe vehicles was 28.5 mph versus 29.6 mph for simulated eastbound vehicles, and westbound probe vehicles went 28.3 mph compared to 30.7 mph for simulated westbound vehicles. The posted speed limit for this segment of East Burnside is 35 mph, and the maximum speed recorded in the simulation is 38 mph. 3.3 Simulation Data Data were collected from the simulation by way of data collection points. Data collection points were placed every 5 to 10 meters on the roadway, and functioned as idealized inductive loop detectors. Data available from collection points included arrival time, departure time, and speed, which were easily translated into the count, occupancy, and speed that loop detectors can provide. In addition, collection points also provided data such as acceleration, vehicle length, vehicle type, and a unique vehicle ID. This last was used to create ground truth trajectories to which later estimates were compared. Figure 5 shows the trajectories that the simulation generated for the whole peak hour. 26

34 Distance (m) :00 20:00 30:00 40:00 50:00 60:00 Time Figure 5: Time- Space diagram for simulated peak hour and schematic of Burnside Street 27

35 4.0 METHODOLOGY Several methods for estimating travel time on an arterial are tested against simulated ground truth travel times and each other: the midpoint method, the vehicle matching method, the saturation matching method, the phase matching method, the vehicle synchronization method, and the average departure method. In order to make these comparisons, two diagrams are employed: time- space diagrams and input/output diagrams (see Figure 6). These diagrams allow visual comparison of estimation methods to ground truth and to each other, and quantitative comparisons are easily derived from them. Figure 6: Example time- space diagram (left) and input/output diagram (right) 28

36 4.1 Visualizations Figure 7 is an example of a time- space diagram. The x- axis represents time, while the y- axis represents a vehicle s linear position on the roadway segment. Each trajectory completely describes a vehicles movement on the roadway segment. Travel time between two points is the horizontal distance between Distance (m) :00 20:00 21:00 22:00 Time (s) Figure 7: Example time- space diagram, Kelly to Eastman (westbound) 29

37 the time the vehicle departs from the first and the time that the vehicle arrives at the second. The average speed between two points is the slope of the line between them. Delay is the horizontal distance between the time a vehicle would arrive at a point at free flow speed and the actual arrival time. The second diagram that is employed is the input/output diagram. Figure 8 shows an example. The x- axis once again represents time, and the y- axis represents a cumulative count of vehicles. This diagram can be created from the time- space diagram in the following way. Establish an input point and an output point. At any time that a vehicle trajectory crosses the input point, increment the input curve by one. Do the same for the output point. This will generate two cumulative vehicle curves. The gap between the curves represents the total time vehicles spent on the roadway segment between the input point and the output point. If the output curve is moved to the left by a time equal to the free- flow travel time between the input and output points (a constant), then the horizontal distance between the two curves at any point represents that vehicle s delay, and the total gap between the two curves represents the system s delay for that segment of road. 30

38 Number of Vehicles Input Output 45:00 50:00 55:00 60:00 Time Figure 8: Example input/output diagram, Kelly to Fairview Using these diagrams, estimation methods are compared on the basis of average delay, travel time per vehicle, and average travel time per signal cycle. Average delay is computed as described above, for both estimates and ground truth data. Travel times are computed as above; comparisons are 31

39 made by examining the distribution of the ratio of estimated to actual travel times. Estimation methods where this ratio shows a mean value near 1 and a low variance are optimal. 4.2 Travel Time Estimation Methods The methods for estimating travel time that this research evaluates can be applied in two different ways. The first is in a predictive capacity: the travel times of vehicles that enter a segment can be predicted as they enter. Note that the ability to do this on a real- time basis is constrained by the fact that many of the estimation methods require foreknowledge of the times that vehicles are detected at the exit detector. Furthermore, many of the methods require the signal phase information at the exit detector as one of their parameters, which makes implementing those methods on a real- time basis impossible in the case of free- running or actuated detectors. The second way that these travel time estimation methods may be applied is analytically, after the fact. This can be done on either an archive of detector data or on the data acquired by detectors in the previous signal cycle. Generating travel time estimates from archived data can be useful for 32

40 analyzing the evolution of arterial performance in response to changing conditions, or for establishing the segment s baseline historical performance. Analysis of data from the previous signal cycle can be used in a predictive capacity, under the assumption that generally, conditions on the arterial don t change drastically between consecutive cycles. All of the methods described may be applied in this way. The methods for estimating travel time under consideration include the midpoint method, the vehicle matching method, the saturation matching method, the phase matching method, the vehicle synchronization method, and the average departure method. This section describes each in detail. 33

41 Figure 9: The Midpoint Method The midpoint method (Figure 9) is essentially the same method currently used to measure freeway performance with loop detectors, applied to an arterial environment. To estimate a vehicle s travel time over a roadway segment at a given point in time, the most recent speed readings are taken at each detector in the segment. The vehicle is assumed to travel over the section of road from half the distance to the previous detector to half the distance to the next detector at the measured speed. 34

42 Implementing the midpoint method requires the following data/parameters: length of the segment time of vehicle detection vehicle speed Step 1: For each vehicle detected at the entrance to the segment, find the vehicle s speed at the detector (speed 1). Step 2: Find the speed of the last vehicle to cross the exit detector (speed 2). See Figure 10. Figure 10: Speed 1 and speed 2 35

43 Step 3: Construct a trajectory, starting at the vehicle s detected entrance time and traveling half the distance to the next detector at speed 1. From that point to the exit detector, construct a trajectory the rest of the way to the exit detector at speed 2. See Figure 11. Figure 11: The constructed trajectory estimate In this way, a predicted trajectory can be constructed over any instrumented section of road. It is hypothesized that this method will perform poorly on arterials, as arterial operations are characterized by frequent changes in speed. 36

44 Figure 12: The Vehicle Matching Method The vehicle matching method (and subsequent methods) takes advantage of two facts: first, detectors on arterials are most commonly located near signals, and second, signals tend to group vehicles into platoons. To estimate travel time, the vehicle matching method (Figure 12) starts with the departure time for each detector in the roadway segment. Then vehicles entering the segment are matched to vehicles exiting the segment, based on each vehicle s 37

45 calculated best case arrival time. Travel time is estimated to be the difference between the entrance time and the exit time. Implementing the vehicle matching method requires the following data/parameters: 90 th percentile speed on the segment (in the absence of this, some estimate of the maximum realistic speed on the segment will do) length of the segment AND event- based detector data OR cycle- by- cycle detector data length of green and yellow time for each signal signal offset for each signal The vehicle matching method assumes a segment of road with a detector on each end (or a series of such segments). The method calculates travel time by subtracting the departure time from the entering detector from a matched departure time from the exit detector. The step- by- step procedure follows. 38

46 Step 1: If using aggregated data, assume that vehicle departures are evenly spaced throughout the green time at each detector. Step 2: Calculate the travel time from the entering detector to the exit detector at 90 th percentile speed. Step 3: Add the 90 th percentile travel time to each departure time at the entering detector to find the best case arrival time at the second detector for each vehicle. See Figure 13. Figure 13: Best case arrival times for each entering vehicle 39

47 Step 4: For each entering vehicle, from first to last, find the first exit time after the best case arrival time, and match the entering vehicle to that exiting vehicle. Note that this may result in multiple entering vehicles being matched to a single exiting vehicle. See Figure 14. Figure 14: Estimated trajectories using the vehicle matching method Thus, a travel time estimate is generated for each vehicle entering the arterial segment. It is hypothesized that this method of estimation will give a lower bound on vehicle delay, and to give the best estimates in highly under- saturated conditions. 40

48 Figure 15: The Saturation Matching Method The saturation matching method (Figure 15) is a refinement of the vehicle matching method. The saturation matching method seeks to address the fact that the vehicle matching method often matches multiple departures from the first detector to a single departure at the second detector. The saturation matching method is the same as the vehicle matching method, but instead of matching to the next departure at the second detector, it matches to the greater 41

49 of the next departure time or the last matched departure time plus some delta equal to the saturation headway. Implementing the saturation matching method requires the following data/parameters: 90 th percentile speed on the segment (in the absence of this, some estimate of the maximum realistic speed on the segment will do) saturation headway length of the segment length of green and yellow time for each signal signal offset for each signal AND event- based detector data OR cycle- by- cycle detector data The saturation matching method assumes a segment of road with a detector on each end (or a series of such segments). The method calculates travel time by subtracting the departure time from the entering detector from an 42

50 estimated departure time from the exit detector. The step- by- step procedure follows. Step 1: If using aggregated data, assume that vehicle departures are evenly spaced throughout the green time at each detector. The saturation match (explained in step 5) means that this will change for the exit detector. Step 2: Calculate the travel time from the entering detector to the exit detector at 90 th percentile speed. Step 3: Add the 90 th percentile travel time to each departure time at the entering detector to find the best case arrival time at the second detector for each vehicle. See Figure 16 43

51 Figure 16: Initial vehicle match Step 4: For each entering vehicle, from first to last, find the first exit time after the best case arrival time, and match the entering vehicle to that exiting vehicle. See Figure

52 Figure 17: Matching the second vehicle Step 5: Now, compare this matched exit time to the last matched exit time. If they are the same or if the matched time is less than the previous matched exit time, match the current entering vehicle to the previous matched exit time plus one saturation headway. See Figure

53 Figure 18: The second vehicle matched to the first exit plus one saturation headway Step 6: If matching to the previous matched exit time plus 1 saturation headway puts the estimate past the end of the exit green + yellow, match to the first exit in the next green phase. In this way, travel time is estimated for each vehicle entering the road segment. From this, an average estimated travel time is easily computed. 46

54 Figure 19: The Phase Matching Method The phase matching method (Figure 19) seeks to account for platoon dispersion by distributing vehicle arrivals evenly throughout the green phase. The method assumes that each road segment has a detector at each end, and that each detector is located at the stop bar before a traffic signal. The phase matching method is hypothesized to give an upper bound on vehicle delay, and to perform best in saturated conditions. 47

55 Implementing the phase matching method requires the following data/parameters: 90 th percentile speed on the segment (in the absence of this, some estimate of the maximum realistic speed on the segment will do) saturation headway length of the segment length of green and yellow time for each signal signal offset for each signal event- based detector data OR cycle- by- cycle detector data The phase matching method assumes a segment of road with a detector followed by a signal on each end (or a series of such segments). The method calculates travel time by subtracting the departure time from the entering detector from an estimated departure time from the exit detector. The step- by- step procedure follows. Step 1: If using aggregated data, assume that vehicle departures are evenly 48

56 spaced throughout the green time the entering detector. Step 2: Calculate the travel time from the entering detector to the exit detector at 90 th percentile speed. Step 3: Add the 90 th percentile travel time to each departure time at the entering detector to find the best case arrival time at the second detector for each vehicle. See Figure 20. Figure 20: Best case arrival times for each entering vehicle 49

57 Step 4: Compare the best case arrival time to the end of the green phase at the exit detector to determine which green phase each vehicle is projected to depart the segment. Add up the number of projected departures for each green phase. Step 5: Evenly distribute the projected departures in each green phase at the exit detector. See Figure 21. Figure 21: Departures evenly distributed in each green phase 50

58 Once again, travel time is estimated for each vehicle entering the road segment. From this, an average estimated travel time is easily computed. Figure 22: The Vehicle Synchronization Method The vehicle synchronization method (Figure 22) takes advantage of closely- spaced detectors to assume that vehicle conservation more- or- less holds. Detectors are not necessarily assumed to be placed at signals; however, the green times for nearby signals are an important parameter, as the synchronization counts are reset at the end of each green phase. 51

59 Implementing the vehicle synchronization method requires the following data/parameters: 90 th percentile speed on the segment (in the absence of this, some estimate of the maximum realistic speed on the segment will do) length of the segment length of green and yellow time for nearby signals signal offset for each signal event- based detector data The vehicle synchronization matching method assumes a segment of road with a detector on each end (or a series of such segments). The method calculates travel time by enumerating entering and exiting vehicles, and matching them to each other. The step- by- step procedure follows. Step 1: Calculate the travel time from the entering detector to the exit detector at 90 th percentile speed. Step 2: Add the 90 th percentile travel time to each departure time at the 52

60 entering detector to find the best case arrival time at the second detector for each vehicle. See Figure 23. Figure 23: Best case arrival times for each entering vehicle Step 3: Compare the best case arrival time to the end of the green phase at the next downstream signal to determine which green phase each vehicle is projected to depart the segment. Step 4: Enumerate the entering vehicles whose best case arrival time puts them at the downstream signal for each green phase. For example, if 5 53

61 vehicles enter the road segment and have a best case arrival time in the same green phase, label them vehicle 1, vehicle 2, and so on, to vehicle 5. Step 5: Repeat steps 1 4 for the exiting detector. Step 6: For each green phase, match entering vehicle 1 to exiting vehicle 1, entering vehicle 2 to exiting vehicle 2, and so on. Discard extraneous vehicles (these are assumed to be vehicles that turn on or off the segment between detectors). See Figure 24. Figure 24: Matching enumerated arrivals and departures 54

62 The result is a travel time estimate for each vehicle entering the arterial segment. From this, an average estimated travel time is easily computed. Figure 25: The Average Departure Method Finally, the average departure method (Figure 25) takes advantage of some mathematical properties of the average travel time equation to offer a way to compute average travel time and delay without computing any individual travel times. The average departure method can be derived as follows: Consider a road segment with a detector on each end. The entry detector 55

63 detects two entering vehicles, at times A1 and A2, while the egress detector detects two departing vehicles, at times B1 and B2. If A1 and B1 are the same vehicle, and A2 and B2 are the same vehicle, then the average travel time is this: Average Travel Time = (B1 A1) + (B2 A2) (2) 2 However, a little algebra yields: (B1 A1) + (B2 A2) = (B2 A1) + (B1 A2) (3) 2 2 Which is the same as saying, in terms of computing average travel time, that it doesn t matter which entering vehicle is matched to which egress. Furthermore, after a little more algebra: (B1 A1) + (B2 A2) = (B1 + B2) (A1 + A2) (4) Thus, in theory, the average travel time is simply the average time of entry subtracted from the average time of egress. In applying this method, it is assumed that each detector is located at the stop bar before a traffic signal. The arrival time at the second detector assuming 90 th percentile speed is used to determine which green phase cohort each 56

64 vehicle belongs to. Of particular interest in the analysis of this method are the effects of imperfect vehicle conservation. 57

65 5.0 ANALYSIS AND RESULTS To assess the effectiveness of estimation methods, comparisons to ground truth are made both visually, with input/output diagrams, and quantitatively, by examining the distribution of the ratio of estimated travel times to actual travel times. Input/output diagrams are examined to test whether an estimation method seems to capture the general nature of traffic behavior. Methods that appear to reflect the same trends that govern ground truth are then quantitatively evaluated. The vehicle synchronization method is treated separately, as part of the analysis of increased detector density. The average departure method is discussed in the travel time section, as the input/output analysis relies on discrete inputs and outputs. 58

66 5.1 Delay Analysis Figure 26 shows the ground truth input/output diagram for the westbound segment from Kelly to Fairview for the simulated peak hour. For the whole hour, the average delay per vehicle is 20.1 seconds. For illustrative purposes, comparisons between these curves and those of estimation methods will be made in detail view. Number of Vehicles Input Output 0 10:00 20:00 30:00 40:00 50:00 60:00 Time Figure 26: Ground truth input/output diagram, Kelly to Fairview 59