Systematic Identification of Freeway Bottlenecks

We present an algorithm that identifies bottleneck locations, the times for which each bottleneck is active and the delay it causes. The bottlenecks are ranked in terms of their frequency of recurrence and the magnitude of their delay impact. The algorithm works with five-minute loop detector data. It uses speed difference as an indicator of bottleneck activation. The algorithm is applied to three months of data from 270 miles of seven freeways in San Diego. It identifies 160 locations whose bottlenecks cause 64 percent of the total delay on these freeways. The ‘top’ ten account for 61 percent of the delay from all bottlenecks. The method can be used in any area where large amounts of data are available. Transportation authorities may use it to identify bottlenecks and to track their impact over time. Chen, Skabardonis, Varaiya 2 INTRODUCTION Certain freeway locations experience congestion at nearly the same time almost every day. They are often called (recurring) bottlenecks. Bottlenecks may be caused by merging and diverging traffic, lane drops, and grade changes, for example. The Highway Management Handbook views bottleneck analysis and removal a key element of congestion relief (1). Bottlenecks like the Bay Bridge in San Francisco and the I-5/I-805 split in San Diego are familiar to area motorists. However, without measurements we cannot tell where all the bottlenecks are in a region nor the severity of the delay they cause. A transportation engineer asked to find the bottlenecks on an unfamiliar freeway might drive along the freeway for several days and at different times, noting locations downstream of which traffic is free flowing, but upstream of which traffic is significantly slower. He might further investigate his list of bottleneck locations and their activation times in order to figure out the most severe bottlenecks. This is a time-consuming way to identify bottlenecks and assess their impact. We present an automatic method that mimics our traffic engineer. The method relies on the availability of traffic data (flows and speeds) at freeway locations over many days. The method systematically processes all the data, locates bottlenecks by speed differentials, determines how frequently each one is activated and calculates the average delay it causes. To illustrate the efficacy of the method, we apply it to three months of data from 263 loop detector stations in 270 miles of seven San Diego freeways. The method identifies 160 bottleneck locations, accounting for 64 percent of total delay on the seven freeways; the ten worst bottlenecks account for 61 percent of the delay caused by them all. The virtue of the method is that it can be used with no familiarity with the freeway. Its limitation is that it does not diagnose the cause of the bottleneck. As explained in a later section, information about the freeway geometry at the identified bottleneck can help to determine its cause and suggest corrective action. Identification of bottlenecks and estimation of their activation times and delay impact can aid the transportation agency in focusing and prioritizing relief efforts. Applying the method routinely over time allows the identification of new bottlenecks and monitoring of existing ones to discern congestion trends. BACKGROUND The notable Twin Cities, Minnesota study by Zhang and Levinson (2) follows a strategy similar to that adopted here. However, their objectives are different. They identify bottlenecks locations and their activation times on the basis of occupancy differentials. Based on frequency of recurrence, and some other criteria, they select 27 bottlenecks for further investiation. For each of these, they use flow data to determine average pre-queue and queue flow rates, and the percentage flow drop. They propose a capacity measure based on these flow rates. Although they illustrate the freeway geometry at each of the 27 bottlenecks, this plays no role in the analysis. This Minnesota study follows several earlier smaller scale studies, also intent on finding indicators of bottleneck activation. For example, Banks measured 30-second speeds upstream of the bottleneck locations and used a drop in speed as an indicator of congestion onset at four San Diego locations (3). Hall and Agyemang-Duah used a threshold on the ratio of 30-second occupancy to flow because speed data were not available (4). Bertini suggests other signals that may be used to detect bottleneck activation, such as the variance of 30-second counts (5). These studies and others conclude that flow rates drop after a bottleneck is activiated (6, 7, 8). They suggest that reducing bottleneck activation by, say, ramp metering, may increase flow. Our method evaluates the impact of a bottleneck in terms of the delay it causes, rather than by the reduction in flow. Chen, Skabardonis, Varaiya 3 BOTTLENECK DETECTION ALGORITHM FROM LOOP DETECTOR DATA Given a pair of upstream-downstream detector station locations, we want to determine the times (if any) when there is an active bottleneck between them. Bottlenecks are clearly visible features in two-dimensional speed contour maps. Figure 1 is an example. It shows constant-speed contours on a time vs. distance plane. The time is between 5:50 and 9:30 AM on 1 May, 2003. The distance is along I-15 SB; the direction of travel is in order of decreasing postmiles. A speed gradient persists near postmile 26 between 5:50 and 9:30 AM. Speed is low upstream of the bottleneck. The region extending five miles upstream remains congested while the bottleneck is active. Figure 2 shows the speed contour plots on I-15 SB over four weeks in May, 2003. Lower speeds are represented by darker colors. The bottleneck at postmile 26 is visible on 15 out of 20 days. There is an equally frequent bottleneck at postmile 15, but it appears to be causing less delay. The algorithm is inspired by this visual analysis of speed contours. It requires 5-minute averaged speed and flow (count) measurements by freeway loop detectors. For the application, we use the data from the California freeway performance measurement system, PeMS. PeMS receives real time 30-sec loop detector flow and occupancy measurements from throughout the state. PeMS processes these data and computes 5-minute speed averages, and makes available online both the real time and historical data (9). The algorithm uses the presence of a sustained speed gradient between a pair of upstream-downstream detectors to identify bottlenecks. Other signals of bottleneck activation have been used, including occupancy differentials (2); drop in upstream speed (3); ratio of occupancy to flow as speed surrogate (4); and variance in 30-sec counts (5). Because speed changes much more sharply than occupancy when a bottleneck is activated, speed differentials provide a more sensitive indicator than occupancy-based signals. We consider a freeway with n detectors indexed by i = 1, · · · , n, each of which provides speed and flow measurements, averaged over 5-minute intervals indexed by t = 1, 2, · · ·. Detector i is located at postmile xi; vi(t) = v(xi, t) is its measured speed (miles per hour, mph) and qi(t) = q(xi, t) is its measured flow (vehicles per hour, vph) at time t. If xi < xj , it is understood that xi is upstream of xj . The algorithm has three steps. First, the algorithm declares an active bottleneck at certain locations and times if the data meet criteria (1)—(4). Second, it includes additional time periods as part of bottleneck activation, provided nearby time intervals are selected in the first step. The criterion for this is (5). Lastly, it calculates the delay caused by a bottleneck, using (9). The algorithm declares that there is an active bottleneck between two locations xi, xj , with xi < xj , during period t if the following four inequalities hold: xj − xi < 2 miles (1) v(xk, t)− v(xl, t) > 0 if xi ≤ xk < xl < xj (2) v(xj , t)− v(xi, t) > 20 mph (3) v(xi, t) < 40 mph (4) Location xi is upstream of xj , but there may be other detectors at xk, xl between these locations. The thresholds in (1)—(4) are selected to best match visual evaluations of contour plots. Extensive analysis of data in Los Angeles shows that free flow speed is close to 60 mph and, when a bottleneck is activated, speed drops rapidly to below 40 mph (10). Hence the 20 mph minimum speed differential (1) and 40 mph congestion speed threshold (4). (However, for non-California freeways, different threshold speeds may be more appropriate.) The maximum separation of 2 miles in (1) is designed to include locations where speed continues to rise as we go downstream, but the difference between each neighboring pair is small. The Chen, Skabardonis, Varaiya 4 constraint (2) that speed should drop continuously is of course the distinctive characteristic of an active bottleneck. Recurring bottlenecks are sustained over periods longer than five minutes. Let Ai(t) = 1 if there is an active bottleneck at location i and time period t. We declare a bottleneck to be sustained between times t1 and t2 if t+N−1 ∑ τ=t Ai(τ) ≥ qN, ∀ t1 ≤ t ≤ t2 −N + 1, (5) where N = 7 and q = 57 . That is, a sustained bottleneck has at least five active bottleneckperiods (or 25 min) within every seven consecutive periods (or 35 min). The definition is somewhat arbitrary. It is formulated in response to situations shown in Figure 1, in which at postmile 26 the bottleneck is continuously sustained between 7:00 and 8:00 except for several five-minute periods. The notion of sustained bottleneck allows us to treat this as a single bottleneck rather than two or three bottlenecks. It is customary to define the most downstream location of a sustained bottleneck as the location of an active bottleneck. Figure 1 shows the result of applying the algorithm to data from I-15 SB on 9/18/2002, between 5 and 11 AM. The locations and times of detected bottlenecks are the squares superimposed on the speed contours. The contours visually suggest one bottleneck between 5:45 and 9:45 at postmile 26, and another between 6:45 and 8:30 at postmile 15, and indeed both bottlenecks are identified by the algorithm. Calculating Delay We now describe how the algorithm estimates the delay caused by a bottleneck. The speed contour in Figure 1 shows regions of congestion upstream of each bottleneck location. We assign the delay in vehiclehours represented by these regions to their associated bottlenecks and compute its value as follows. The n detectors divide the freeway into n segments. In the PeMS database, a segment is typically one half to one mile long. We say that a segment is congested at time t if its speed is below 40 mph. We define the congested region associated with a bottleneck as the contiguous group of congested segments immediately upstream of the bottleneck location. For an active bottleneck just downstream of segment j at time t, the congested region is the set of segments Bj(t), Bj(t) def = {i : vk(t) < 40 mph, for all i ≤ k ≤ j} . (6) The delay Dj(t) associated with the bottleneck during this period is the sum of the delays in Bj(t):