Queue Length Estimation using Conventional Vehicle ...

Queue Length Estimation using Conventional Vehicle Detector and Probe Vehicle Data* Brian E. Badillo, Hesham Rakha, Member, IEEE, Thomas W. Rioux, and Marc Abrams, Member, IEEE

Abstract— The paper presents IntelliFusion, an algorithm that fuses inductive loop detector data with real-time vehicle probe data obtained from Connected Vehicles to enhance back of the queue estimates. The work also presents an evaluation of the data fusion algorithm using datasets produced by eTEXAS, a microscopic traffic simulation model for signalized intersections. Results of the evaluation show queue length estimates produced by the IntelliFusion algorithm are accurate to within the length of a single vehicle even at low levels of market penetration (e.g., LMP = 20%).

I. INTRODUCTION Increasing the effectiveness of adaptive traffic signal controllers can reduce driver delays, vehicle emissions, and accidents. We present a novel software algorithm entitled IntelliFusion which attempts to improve safety and mobility at intersections by enhancing the measurement and estimation of queue length (as well as various other Measures of Effectiveness (MOEs) for use in adaptive traffic signal control). This work is spurred by the advent of the Federal Highway Administration’s Connected Vehicle (CV) program, which enables communication between vehicles and roadway infrastructure. Our unique contribution as a result of this work is improving queue length estimation through the fusion of traditional vehicle detector data and CV sensor data. Improving the estimation of the location of the back of the queue is critical in the design of left turn and right turn pocket lanes, in the timing of traffic signals to prevent queue spillback to upstream intersections, in the timing of ramp meters, and in queue warning systems (Q-WARN). In addition the benefit of using queue length and delay are substantiated in the National Cooperative Highway Research Program (NCHRP) projects NCHRP 3-66 Signal Transition Logic [11] and NCHRP 3-79 Arterial Performance Measures [12]. Past research in the field has not addressed the benefits of combining data from CVs with data already existing in the transportation infrastructure such as loop detector data or video detectors. Our work is instrumental in accelerating the benefits of CVs by integrating CV sensor data with data *This work was supported by the US DOT Small Business Innovation Research (SBIR) program, Contract No: DTRT57-11-C-10033. B. Badillo, T. Rioux, and M. Abrams are with Harmonia Holdings Group, LLC, Blacksburg, VA 24060 USA. Phone: 540-951-5900x255; E-mail: [email protected]. H. Rakha is with the Department of Civil and Environmental Engineering at Virginia Tech and the Virginia Tech Transportation Institute, Blacksburg, VA 24060 USA.

produced by the existing infrastructure (e.g., vehicle detectors) even at low CV levels of market penetration (LMPs). We will demonstrate the use of shockwave analysis to combine CV sensor data with conventional detector data in our IntelliFusion algorithm. Then we present an evaluation of the IntelliFusion algorithm using data sets produced by the eTEXAS software, a microscopic traffic simulation model for signalized intersections. We discuss the results of the evaluation, which show queue length estimates produced by IntelliFusion to be accurate to within the length of a single vehicle even at low levels of market penetration considering homogenous traffic (e.g., LMP = 20%). To conclude, we identify several MOEs that might be derived from finding the front and back ends of the queue including queue length, cycle failure (or when a green phase does not fully serve vehicles stopped in the queue), stopped delay, travel time, and vehicle fuel consumption levels. II. BACKGROUND AND MOTIVATION With emerging technologies that provide positional data of vehicles (e.g., CV supporting technologies) comes a greater ability to analyze traffic conditions, and a greater need for data analysis techniques. There has been some exploration into the use of mobile sensors for freeway traffic [3]. However, because of “discontinuities” introduced by signal timings at intersections, this research may not be completely suitable [3]. Some literature has considered whether queue length is sufficient as an MOE. The literature is divided on this point. For example, Cai et al. [4] argue that using queue lengths for adaptive traffic signal control is not as suitable as using measured travel times because queue lengths are “ambiguous”. They point out that queue lengths represent only free-flow and standstill traffic and therefore lose some traffic information. Thus in their research they utilize travel times obtained from CVs to perform adaptive traffic signal control. In contrast, a paper by Ban et al. [3] cites several sources that highlight the importance of queue length estimation for traffic control. Given this division, we show in the conclusion of our research how to derive several MOEs in addition to queue length using our approach. Liu et al. [10] use high resolution vehicle change events and signal phase change events to queue lengths in real-time using a shockwave technique. Our approach is similar except for the

detector estimate analysis fact that

we enhance the shockwave analysis with CV sensor data. Skabardonis and Geroliminis [16] estimate intersection queue lengths in real-time using detector data that has been aggregated over 20 or 30 second intervals. Our work differs from this in that we assume fine-grained vehicle detection information as well as probe vehicle information from CV sensor data. Foundational work was conducted to develop methods of determining the extents of queues using mobile sensors. For example, Comert and Cetin [6] presented preliminary work to estimate the number of vehicles in queue given the position of the last vehicle with a mobile sensor in the queue. In their work, they presented a formulation that required the marginal distribution of the number of queued vehicles at a particular intersection. Using this distribution together with the position of the last vehicle with a mobile sensor, and the percentage of vehicles on the road equipped with mobile sensors they compute an expected value for the actual number of vehicles in the queue along with a method of measuring error. In effect, they make queue length estimates by reducing the sample space of possible queue lengths using the last known position in the queue and the percentage of vehicles for which a position is known. With their work, queue length estimates can be made at any time as long as there is at least one queued vehicle, which means that estimates can be made while a queue is forming or discharging. Also of note in this work is the possibility to account for roadways with multiple lanes and lane changes before vehicles join queues, because the formulation is dependent on a marginal arrival distribution (which would effectively marginalize vehicle lane changes). In later work, Cetin and Comert consider the time at which the last vehicle joins the queue [5]. Another more recent method of estimating queue extents using mobile sensors is presented in the Ban et al. [3]. In this work, travel times from vehicles equipped with mobile sensing devices are used to calculate the front and back of queues at intersections. However, this work assumes a uniform distribution of vehicle arrivals, and in addition does not consider supplemental data that may be obtained from fixed-point detectors. Still more recent methods of estimating the queue extents using mobile sensors involve reconstructing vehicle trajectories. Sun and Ban [17] present a method of finding queuing shockwave boundaries using limited vehicle trajectories and travel times obtained from mobile sensors, but they do not consider using fixedpoint vehicle detector information. Goodall et al. [8] present a method to augment the effective percentage of vehicles with mobile sensing capabilities using a car-following model. They supplement this method with fixed-point detector information. However, the vehicle trajectory reconstruction methods [8, 17] and queue length estimation method [3] do not consider vehicles changing lanes before joining queues. Other data fusion efforts include Ivan and Sethi [9], who have used neural networks and statistical prediction methods to monitor traffic conditions using sensor fusion

between vehicle detectors and vehicle probe data. They, however, do not apply their method to finding queue lengths. Neumann [13] provides a very flexible data fusion approach which uses both vehicle detector and vehicle probe data with success to determine queue lengths at intersections. The approach is even successful at very low probe vehicle penetration levels (e.g., less than 1%). However, this approach requires the use of weights that are known a priori. Our work goes further than the state-of-the-art cited because we use vehicle trajectory data available from CVs; the previous work preceded the advent of CVs. Information obtained from CVs use a transient vehicle ID to protect vehicle identities and address privacy concerns regarding tracking vehicle positions. Although previous work has assumed vehicle trajectory limitations due to privacy concerns, our work relaxes this constraint and utilizes vehicle trajectory data throughout single intersections. We can also exploit the assumption that CVs will transmit a single position for the vehicle (as opposed to using Smartphones for mobile sensing which may introduce multiple sensors for a single vehicle due to passengers carrying these devices). Standard messages transmitted by CVs also carry vehicle speed, vehicle length, vehicle heading, and vehicle braking information. Thus the mobile sensors provide more reliable information obtained from the vehicle itself (previous work did not have access to vehicle lengths and would not have been able to rely upon finegrained vehicle speeds). Vehicle steering wheel angle and braking information would also be useful to differentiate a vehicle slowing down to join a queue from a vehicle slowing down simply by not accelerating or from a vehicle that is changing lanes. Additionally, the CV program provides standard messages for signal timing information which provides red and green interval times; this information is helpful in determining queue growth and discharge. Lane information is also available to help with the assignment of vehicles to specific lanes. We also point out that NTCIP standards (NTCIP 1202 and NTCIP 1209) [1] provide a means to obtain finegrained vehicle detector information. Thus, we do not limit our solution to using aggregated data such as flow over coarse periods of time. Rather we assume that we can detect individual vehicles within short intervals. Consequently, the unique contribution of this effort is combining CV and spot sensor data to make better estimates of spatiotemporal queue propagations. III. INTELLIFUSION In this section we demonstrate how the integration of CV sensor and conventional detector data can be used to produce more accurate estimates of the front and rear end of the queue, the queue length, and the total delay incurred at a signalized intersection approach.

A. Real-Time Macroscopic Modeling We devised a method in IntelliFusion to estimate the back and front end of the queue based on real-time macroscopic modeling using vehicle detector data at an upstream vehicle detector (e.g., 228.6 meters (750 feet) from the intersection). We use a triangular fundamental diagram (or linear car-following model: Pipes or GM-1 model); however the approach is general and does not require a specific fundamental diagram. Fig. 1 shows the queuing situation, where the x-axis represents time and the y-axis represents the distance to the intersection (the stop line at the intersection being labeled at the top of the diagram). The figure shows stationary traffic (or traffic stream behavior with constant flow and density over space and time) trajectories for vehicles arriving upstream from the intersection. The dotted line in the figure shows a single car travelling towards the intersection over the period of time shown. In the first period of time (T1), the signal indication is

• A red signal indication gives a point of reference to start the computation of queue growth. • A green signal indication gives a point of reference to start queue discharge. • Distance between the intersection and the front of the queue (queue-front) can be modeled using a backward recovery shockwave. • Distance between the intersection and the back of the queue (queue-back) can be modeled using a backward forming shockwave. We assume that we can obtain the signal state through CV communications. Thus we will be able to start calculations for queue growth and discharge using these parameters. Given the properties above, we then must calculate the speed of the forming and recovery shockwaves for queue growth and discharge. We use the formulation in (1) which relates the velocity of a shockwave (vs) to the differences in traffic flow (q1 and q2) and density (k1 and k2) at both ends of the wave [7]: vs = (q1 – q2) / (k1 – k2)

(1)

In the following paragraphs we will discuss how we obtain values for flow and density in order to calculate the shockwave velocities. We note that shockwave analysis has been demonstrated to be consistent with queuing theory [14]. Further refinements to the computation of the speed of the waves can be achieved by optimization using probe

Figure 1. Time-Space Diagram of Queue Shockwaves

green and vehicles enter the intersection at the arrival rate (represented by the area labeled A). The next period of time (T2) shows the time period when the traffic signal is red. Here, we see vehicles begin to queue at a constant rate, creating a backward forming shockwave (shown as the red line in the figure). When the signal turns green again at the beginning of the next time period (T3) we see that vehicles discharge from the queue at another constant rate. A backward recovery shockwave is formed between the flow recovery and jam density (shown as the green line in the figure). Note that when the backward forming and backward recovery shockwaves meet, the queue has fully discharged. In addition, the area labeled B in the figure represents vehicles that are in queue and thus traffic within this area can be characterized as having zero discharge flow and operating at jam density. In this model, we also show when the last vehicle in the queue has been serviced (shown in the thick blue line in the figure). All vehicles in front of the last vehicle in the queue (i.e., vehicles in area C of the figure) are subject to saturation flow and density. It is only after the last vehicle discharges that traffic in the lane fully returns to its original state (or area A in figure). Using the traffic model above we consider the following properties to enable our queue length MOE calculation:

Figure 2. Time-Space Diagram Showing Look Ahead Interval

vehicle data or by calibrating the model to field conditions prior to its application. Using vehicle detectors upstream of the intersection we compute the flow arriving at the signalized intersection. Given that the vehicles are being detected at a known distance from the intersection, we compute a moving average flow of vehicles per second using a look-ahead time. The look-ahead time allows the computed flow to represent vehicle arrivals within the segment of roadway in which the vehicles will accumulate in a queue. Fig. 2 illustrates this concept in a time-space diagram where the xaxis represents time and the y-axis represents the distance

in meters to the intersection. In the figure, the current time is highlighted with an orange bar and the look-ahead is highlighted in the orange box. Vehicle trajectories accounted for by the look-ahead time are shown as dashed lines in the figure. We can see that the first vehicle trajectory (dashed line on far left) reaches the intersection just before the current time frame. Additionally we note that all other vehicle trajectories are contributors to a growing queue shockwave. In effect, the flow calculated within the look-ahead interval represents the upcoming traffic characterization and will be used to predict queue growth in the upcoming time frames. The formulation in (2) shows how to calculate the look-ahead interval (tL) using the roadway free-flow speed which is assumed to be the speed limit (s) and the distance of the upstream vehicle detector (d): tL = d / s

(2)

To complete the example, we could calculate flow in the figure by counting the number of vehicles crossing the upstream detector within the look-ahead (9 vehicles) and dividing by the look-ahead interval. The merit of using this approach allows us to expand our algorithm to more general traffic situations (e.g., more than one lane of traffic). Given that the approach only uses flows and densities, the existence of multiple lanes has no impact on the approach because we do not necessarily need to know the lane in which particular vehicles travel. With the look-ahead flow we then compute the traffic stream density using the method presented by Rakha and Zhang to compute the space-mean speed [15]. We then use this to find the density of arriving vehicles given the fundamental relation between density, flow, and velocity. We note here that the space-mean speed that we derive from the time-mean speed observed by a single loop detector (as described in [15]) will produce an estimation error of up to one percent. It would be advantageous to use CV data where possible to correct this estimation error to improve estimates produced by our real-time macroscopic model. This is an improvement which we plan to make in future work. Now that we have the arrival flow and density, we can compute the backward forming shockwave speed (Vg) using formula (3): Vg = (qa – qj) / (ka – kj)

(3)

In formula (3), qa and ka represent the arrival flow and density, respectively. The flow in the queue (or jam flow, qj) is zero. In this study, we also assume a queue density (or jam density, kj) using the average length of vehicles that would be obtained from CV sensor data plus an average spacing between vehicles when stopped. Next, we can compute the growth of the queue in realtime given the current distance between the back of the queue and the intersection. At the beginning of each red interval in each cycle we assume that no vehicles are in the

queue. Thus, as soon as the signal turns red, we begin accumulating queue growth from the stop line at the intersection at a rate dictated by the computed backward forming shockwave velocity. When the traffic signal turns green, we begin to calculate the distance between the intersection and the front of the queue, which we assume to start at 0 meters from the intersection. For the purpose of our comparative study, we used an observed average shockwave speed of 2.3 m/s (based on empirical observations) while allowing a start loss time as prescribed by Akçelik and Besley [2]. Further refinements to the approach would involve computing the speed of the recovery shockwave by calibrating the discharge saturation flow rate using CV sensor data. B. Enhancing the Real-Time Macroscopic Model with Connected Vehicle Sensors Our IntelliFusion algorithm enhances the real-time macroscopic model with actual microscopic data from CVs. With CV sensor data we can obtain the position of vehicles with respect to lanes at the intersection, thus we can compute the vehicle’s distance to the intersection. We can also obtain vehicle speeds. Since we are computing the distance to the front and back of the queue, we attempt to use the CV sensors to provide actual data about the front and back of the queue when it is available. Using the actual data we can then correct the error that has accumulated in the macroscopic model, thus increasing the accuracy of the estimate. We correct the error in queue-back calculations using the distance to intersection of vehicles that have just joined the back of the queue. We can sense that a vehicle is joining the back of the queue given the following: • The vehicle in question has stopped in the current time frame (defined by a speed less than 1.2 m/s, which is the speed of a walking pedestrian). • There are no stopped probe vehicles behind the vehicle in question. • The previous queue-back value is closer to the intersection than the candidate value. (Note: this logic prevents a bottleneck that has not yet compressed into a tight queue from corrupting the queue-back value). We correct error in queue-front calculations using the distance to intersection of vehicles that have just left the front of the queue. We can sense that a vehicle is leaving the front of the queue given the following: • The vehicle in question is accelerating from a stop in the current time frame. This is defined as a speed increase from less than 1.2 m/s to a speed greater than 1.2 m/s. • There are no stopped probe vehicles in front of the vehicle in question. We expect the fusion of both data sources to result in better estimates of queues, given that we are receiving

additional information from CV sensors. The following cases demonstrate the short-comings of using the real-time macroscopic model without CV probe data:

• The traffic in the lane consisted of vehicles that are all the same length (just less than5 meters) and turn neither right nor left.

• Heterogeneous traffic will be challenging to model using macroscopic methods.

We used a single simulation run with a startup time of 5 minutes and a simulation time of 15 minutes to study the effects of varying CV LMP. With this simulation data we studied 100 different permutations of CV assignment (the assignment of particular vehicles in the dataset to act as CVs) to study variations at LMP. Additionally, 99 eTEXAS model replicate simulation runs were performed to study the variance of traffic in the intersection. Replicate simulation runs essentially produce new datasets using the same original simulation parameters (e.g., vehicle arrival distributions, traffic volume, vehicle lengths, etc.) but a different random number seed.

• Cycle failure will lead to spillover of vehicles in subsequent cycles which will lead to erroneous queue statistics calculated using macroscopic methods. • Intersection approaches with multiple lanes makes queue length detection using macroscopic methods unreliable because it is difficult to predict the lane in which a vehicle will choose to queue. • Right turning lanes that may discharge even during a red signal will result in queue estimate errors. • Left turning lanes with a permissive left turning signal may discharge at a slower rate depending on oncoming traffic, which would also introduce significant error in queue statistic calculations. When available, CV probes can correct queue-back and queue-front estimates, resulting in a reduction in error introduced by the real-time macroscopic model in the situations listed above. IV. EVALUATION In this section we present an evaluation we conducted on the accuracy of queue length MOE estimates produced by the proposed IntelliFusion algorithm. We used the open source eTEXAS model (www.etexascode.org) to produce a simple intersection in which we studied a single lane of traffic. The model produced a stream of traffic data that modeled the growth and discharge of a queue at a signalized intersection. In addition, the traffic volume for the lane was such that, given the phase length, all vehicles were serviced during the green phase and the lane discharged at the arrival rate before turning to red. For discussion we will call this the eTEXAS dataset. The eTEXAS model simulation had the following configuration: • Four-leg intersection, with 335.3 meters (1100 ft.) single-lane inbound and outbound lanes per approach. • 48.3 k/h (30 mi/h) speed limit on all intersection approaches. • Pre-timed traffic signal controller with traffic volumes of 450 veh/h, 250 veh/h, 550 veh/h, and 600 veh/h for approaches 1, 2, 3, and 4, respectively. • 44 second traffic signal phase lengths with a 3 second yellow interval and a 1 second all-red interval. • Random traffic arrivals using a shifted negative exponential distribution inter-arrival headway.

We simulated vehicle detector sensors on the lane at 228.6 meters from the intersection (although IntelliFusion could utilize detectors at any distance from the intersection). These sensors produced a pulse for each vehicle (allowing us to count vehicles at the detector) and returned the speed at which the vehicle was travelling when it was detected. We used a look-ahead interval of 20 seconds which is calculated using the 228.6 meter vehicle detector distance and a speed limit of 40.2 k/h (25 mi/h). Note that we chose to use a speed limit value in the look-ahead interval calculation that is lower than the simulated speed limit so that we could include in our flow calculation the vehicles that travel slower than the speed limit in the simulation. We simulated CVs ranging from a LMP of 0% (no CVs) to 100 percent (all vehicles were CVs), at 10 percentage point increment. CV sensors produced a location for each CV over the course of its travel. From the vehicle's current and previous locations we could also compute the speed at which that vehicle was travelling. We obtained the following simulated values for our comparative study from vehicle positions in the eTEXAS simulation model: • Front of queue (distance in meters to the intersection where vehicle speeds increased to a speed above the speed of a pedestrian of 1.2 m/s) • Back of queue (distance in meters to the intersection at which vehicle speeds were reduced below a speed of 1.2 m/s) • Length of queue (distance in meters between the front and back of the queue) computed every second for the entire simulation run Using the queue length estimates, the total queued delay incurred during each cycle in the simulation was computed simply by summing up all of the queued time for each vehicle within a cycle. The eTEXAS dataset was created from a 20-minute (1200 second) simulation that contained 14 cycles. Fig. 3 shows a graph of the 14 cycles for the eTEXAS dataset (a queue only formed in 13 of the cycles). The figure depicts

the time-space diagram with the x-axis representing time (in seconds) and the y-axis representing the distance (in meters) from the intersection stop line. The blue lines represent the back end of a queue of vehicles and the red lines represent the front end of the queue. Logically, each cycle begins at each point that the blue line starts at 0 in the case that the cycle is under-saturated. V. RESULTS In this section we present an analysis of the degree to which our queue length calculations are correct. In these results we show average queue length error and total queue delay for individual cycles at the intersection. The chart in Fig. 4 shows average queue length estimation error per cycle for various LMPs. Average queue length error is defined as the summation of the errors between actual queue length values and estimated queue

no vehicles were in queue in the first cycle. Each bar in a group represents average queue length estimation error for a particular LMP. The darkest bar on the far left represents 0 percent (LMP = 0%) and each bar to the right represents 10 percentage points more than the previous one up until the light colored right-most bar which represents 100 percent (LMP = 100%). In addition to showing the mean error for each cycle using bars, Fig. 4 uses error bars (whiskers) to represent the standard deviation of the error metric resulting from each of the 100 simulation runs. It is interesting to note that the variance of the 100 replicate runs increases as the LMP approaches 50 percent and decreases to 0 at both 0 and 100 percent LMPs. This is expected because at both 0 and 100 percent there is only one CV assignment possible; for LMP = 0% no vehicles are CVs, and for LMP = 100% all vehicles are CVs. Therefore these replicate runs will produce the same results. From Fig. 4 we note that it seems that performance of sensor fusion degrades linearly as the LMP decreases. We also note that in the eTEXAS dataset, all vehicles were just less than 5 meters (16 feet) in length. This fact makes the average queue length calculation a successful estimate within a single vehicle length (5 meters) for all LMPs ranging from 20 to 100%.

Figure 3. Time-Space Diagram of the eTEXAS Dataset

length values each second in the simulation, divided by the total number of seconds in the cycle. Effectively, each average queue length error statistic represents the average error for the entire cycle. Because the average queue length error metric is based on a set of CVs that are randomly chosen, we calculated the values shown in the chart using a stochastic process involving 100 different simulation runs so that we could obtain a mean value of the metric. Each bar represents the mean value (y-axis) of the average queue length error for the 100 simulations. Each constituent simulation run of the mean statistic is a simulation of the same intersection with the exact same traffic. The only difference is that a different permutation of randomly assigned CVs is used for each simulation run. For example, suppose that in the first LMP = 20% simulation run there was a queue of 5 vehicles in one of the cycles. Further suppose that the first vehicle in the queue was selected to be a CV and provides that information to the IntelliFusion algorithm (one vehicle in five satisfies the LMP = 20% requirement). Now, in the second simulation run (of the 100 total), the new CV assignment permutation may select the last vehicle in the queue of 5 to be a CV. The chart shows 13 bar groupings along the x-axis, each of which represents a specific cycle in the eTEXAS dataset. However, only cycles 2-14 of the dataset are shown because

To further understand these results we have characterized each cycle in the simulation by counting the number of vehicles in queue when the signal changed from red to green. From this characterization we saw some correlation between the number of vehicles in queue, and queue error magnitudes at a 0% LMP. For example, cycle 12 had only 1 vehicle in queue when the signal changed to green. Consequently, in the average queue error chart above, the magnitude of error is very low. Also, it seems cycles with a lower number of vehicles in queue (cycles 2, 6, and 12) tended to also have lower queue length error, while cycles with a higher number of vehicles in queue (cycles 3, 7, 11, and 14) tended to also have high queue length error.

In our study, we also calculated the total queue delay per cycle using the queue lengths that were calculated for the queue length error statistic. The chart in Fig. 5 is setup in the same way as the chart above, except that it shows the cumulative queue lengths over the entire cycle (instead of average queue length error). Like the chart above, it is also representative of 100 simulation runs using different permutations of CVs at a variety of LMPs. Cycles 2 through 14 are shown along the x-axis, mean values of queue delay are shown against the y-axis, and error bars (whiskers) show the standard deviation of the queue delay statistic over the 100 CV assignment permutations.

margin of error at a LMP of 60%. This fact confirms trends shown in the chart in Fig. 5 visually showing larger estimation errors for LMPs below 50%. The histogram in Fig. 6 shows a distribution of actual queue delay values for a population of red-to-green cycles computed for a single lane. We simulated the cycle population using the eTEXAS model by running 99 replicate simulation runs of the eTEXAS model. A replicate simulation run is a dataset produced by eTEXAS that uses the same traffic conditions and simulation parameters as the first simulation run, but has varied vehicle trajectory data through a different random distribution of vehicles entering

Figure 5. Cumulative Queue Length per Cycle

the simulation. This effectively means that we are showing a distribution of how the actual Figure 4. Average Queue Length Estimation Error per Cycle queue delay From the chart we see a curved degradation of the queue varies each cycle under the same traffic conditions. The delay estimate as the LMP decreases. Presumably, this is population size represents queue delay values from a total of due to the fact that the error in the queue delay statistic is 1188 cycles. an accumulation of the average queue error statistic Using the Kolmogorov-Smirnov test we found the compounded over time. We note here that the LMP = 100% Pearsons-6 (4P) distribution to have the best fit with the bar on the far right of each grouping represents the actual total queue delay sampling in the chart in Fig. 6 (with a Pvalue of the total queue delay of the statistic, and Value of 0.99976). We calculate a margin of error for our furthermore that we can measure the error introduced at total queue delay statistic using two standard deviations other LMPs using this actual value. around the mean of the distribution above. This margin of The LMPs for which the expected value of total queue error represents the variability of the total queue delay delay estimates for each cycle were within one standard under similar conditions. With this margin of error we deviation of the actual value of total queue delay were could accept all of the estimations shown in Fig. 5 (except found. This means that for each cycle, the LMP gave an for the LMP of 0% estimate in Cycle 4). estimate of total queue delay that was within the margin of error of randomized CV assignments. We saw that all but one cycle produced total queue delay estimates within the

a single vehicle (under the specific conditions of our evaluation presented earlier in the paper).

VI. CONCLUSION It is evident from this study that we can obtain accurate queue length MOE estimates that greatly improve on the use of spot measurements (e.g., measurements made using conventional vehicle detectors) through the use of our data fusion approach. The study also shows that the LMP greatly affects the accuracy of estimates. In the charts above, we showed that the estimation error increased linearly the LMP decreased. However, we note here that there are several important additional MOEs that we can derive from our queue length MOE. These include cycle failure, queue delay, travel time, and fuel consumption. All are discussed in the following paragraphs.

Dataset

One MOE which IntelliFusion could be extended to estimate is cycle failure, which is the case when one or more vehicles which were queued for service at an intersection are not served at the time the signal changes to red. We could implement the detection of cycle failure by using the calculated queue-front and queue-back values (or distances of the first and last vehicles in the queue from the intersection, respectively) by assuming that a cycle failure has occurred if the queue does not completely discharge (e.g., queue-front is less than queue-back) at the time that the signal turns red again. In this case, a queue exists and therefore there is a cycle failure. However, there is also the case where a queue does not exist at the beginning of the red phase, but the last vehicle in the queue has not yet entered the intersection, which again indicates a cycle failure. We could apply the IntelliFusion algorithm to determine if and when the last vehicle is served to make our detection of cycle failure more accurate. In addition to simply determining when cycle failure occurs, we would also have the ability to estimate with accuracy the number of vehicles that were not served in the cycle. We could then use this value in subsequent cycles to improve queue length calculations under low LMPs. In order to compute queue delay, we could simply calculate the length of the queue at the intersection over time within a cycle. Pictorially, this is the area in Fig. 1 labeled B. If there is no cycle failure, this is an accurate estimate of queue delay. Given cycle failures, however, we would still be able to calculate queue delay using this method by using the number of vehicles that were not served from the previous cycle and tracking separate queue lengths for these vehicles. In future work we will need to investigate the sensitivity of our algorithm to the distance of vehicle detectors from the intersection. We would also like to field test the proposed algorithm to quantify the impact of vehicle detector measurement errors on the algorithm. Future work aside, from our results and observations from our study we draw the following conclusions: • By using known modeling techniques we can produce queue length estimates accurate to within the length of

• We can expand the applicability of our data fusion algorithm to other traffic situations simply by using known modeling techniques to account for complex interactions in traffic. With these results we show that with IntelliFusion we enable CV sensor data to be used effectively even at low LMPs. IntelliFusion enhances existing data from actuated controllers (e.g. – loop detectors) with additional data that provides benefits (such as more accurate estimates of the queue length MOE) that will allow traffic controllers to optimize timings for increased mobility through the intersection. ACKNOWLEDGMENT Special thanks to David Gibson with the US DOT Federal Highway Administration (FHWA) and Donald MacGee with the US DOT Research and Innovative Technology Administration (RITA) for making this paper possible. REFERENCES [1]

AASHTO, ITE, and NEMA. Welcome to NTCIP. 2012 [cited 3/6/2012]. http://www.ntcip.org/ [2] Akçelik, R. and M. Besley. Queue Discharge Flow and Speed Models for Signalised Intersections. In Proceedings of the 15th International Symposium on Transportation and Traffic Theory. 2002. Adelaide, Australia: Pergamon. p. 99 - 118. http://www.sidrasolutions.com/Documents/Akcelik_ISTTT15_2002_Pa per.pdf [3] Ban, X., P. Hao, and Z. Sun, Real Time Queue Length Estimation for Signalized Intersections using Travel Times from Mobile Sensors, Transportation Research Part C: Emerging Technologies, 2011. 19(6): p. 1133–1156. DOI: 10.1016/j.trc.2011.01.002. [4] Cai, C., Y. Wang, and G. Geers. Adaptive Traffic Signal Control using Wireless Communications. In Transportation Research Board 91st Annual Meeting. 2012. Washington D.C. [5] Cetin, M. and G. Comert. Estimating Queues at Signalized Intersections: Value of Location and Time Data from Instrumented Vehicles. In Intelligent Vehicles Symposium, 2007 IEEE. 2007. Istanbul. p. 1138 - 1143. DOI: 10.1109/IVS.2007.4290271 [6] Comert, G. and M. Cetin, Queue length estimation from probe vehicle location and the impacts of sample size, European Journal of Operational Research, 2009. 197(1): p. 196-202. [7] Daganzo, C., Fundamentals of Transportation and Traffic Operations, Illustrated ed. 1997, Pergamon. 339 pages. ISBN: 9780080427850 [8] Goodall, N., B. Smith, and B. Park. Microscopic Estimation of Freeway Vehicle Positions Using Mobile Sensors. In TRB 91st Annual Meeting. 2011. http://amonline.trb.org/1sgj7q/3 [9] Ivan, J. and V. Sethi. Data Fusion of Fixed Detector and Probe Vehicle Data for Incident Detection. In Computer-Aided Civil and Infrastructure Engineering. 2002. 13(5): p. 329-337. [10] Liu, H., X. Wu, W. Ma, and H. Hu. Real-Time Queue Length Estimation for Congested Signalized Intersections, Transportation Research Part C: Emerging Technologies, 2009. 17(4): p. 412-427. DOI:10.1016/j.trc.2009.02.003. [11] National Academy of Sciences. NCHRP 03-66 [Active]. Transportation Research Board (TRB); 2012 [cited 3/6/2012]. http://apps.trb.org/cmsfeed/TRBNetProjectDisplay.asp?ProjectID=820 [12] National Academy of Sciences. NCHRP 03-79 [Completed]. Transportation Research Board (TRB); 2012 [cited 3/6/2012]. http://apps.trb.org/cmsfeed/TRBNetProjectDisplay.asp?ProjectID=835

[13] Neumann, Thorsten. Efficient Queue Length Detection at Traffic Signals Using Probe Vehicle Data and Data Fusion, Intelligent Transportation Systems World Congress, 2009. Stockholm (Sweden). [14] Rakha, H. and W. Zhang, Consistency of Shock-wave and Queuing Theory Procedures for Analysis of Roadway Bottlenecks, 2005. Transportation Research Board 84th Annual Meeting, Washington, DC., http://filebox.vt.edu/users/hrakha/Publications/Shockwave%20&%20Qu euing%20Delay%20Estimates%20-%20Ver6.pdf [15] Rakha, H. and W. Zhang, Estimating Traffic Stream Space-Mean Speed and Reliability from Dual and Single Loop Detectors, Transportation Research Record: Journal of the Transportation Research Board, No. 1925, 2005: p. 38-47. DOI: 10.3141/1925-05 [16] Skabardonis, A. and N. Geroliminis, Identification and Analysis of Queue Spillovers in City Street Networks, In IEEE Transactions on Intelligent Transportation Systems, 2011. 12(4): p. 1107-1115. [17] Sun, Z. and X. Ban. Vehicle Trajectory Reconstruction for Signalized Intersections Using Mobile Traffic Sensors. In TRB 91st Annual Meeting. 2012. Washington, D.C. http://amonline.trb.org/1spkk0/1spkk0/1