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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations
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Publication Number: FHWA-HRT-10-043
Date: September 2010
Effects of Yellow Rectangular Rapid-Flashing Beacons on Yielding at Multilane Uncontrolled Crosswalks
Figure 1. Screenshot. SSAM's color-coded conflicts. This screenshot from the Federal Highway Administration (FHWA) Surrogate Safety Assessment Methodology (SSAM) shows the software's display of the location of conflicts on a network map, with icons of different shapes and colors assignable to different conflict types or severities. The sample is a complex intersection marked with green, red, and yellow areas where SSAM identified conflicts. The colors represent varying time to collision (TTC), with green marking TTC less than or equal to 0.5 s, red marking TTC less than or equal to 1.0 s, and yellow marking TTC less than or equal to 1.5 s.
Figure 2. Chart. Operational concept of SSAM. This flow chart shows the simple workflow for using Surrogate Safety Assessment Methodology (SSAM). The chart begins with a simulation model, which leads to several event files. The event files are then imported into SSAM. A table of all identified conflicts and their corresponding surrogate measures of safety is summarized as an output of SSAM. In the flowchart, the output is represented by a table icon and a pie graph.
Figure 3. Illustration. SSAM's zone grid. Surrogate Safety Assessment Methodology (SSAM) constructs a zone grid to cover a rectangular analysis area. This illustration shows a grid of individual, square zones that cover 50 ft by 50 ft (15.25 m by 15.25 m) areas. Clockwise from the top left corner, the corners of the grid are marked (MinX, MaxY), (MaxX, MaxY), (MaxX, MinY), and (MinX, MinY).
Figure 4. Illustration. Vehicle path. This illustration shows a set of three line segments (labeled S1, S2, and S3) connecting Vehicle A's future downstream locations (labeled X(t), X(t+1), X(t+2), and X(t+3)). The text in the illustration reads, "The path for vehicle A is composed of sequential segments (S1, S2, S3…), each with two points representing vehicle A's sequential locations X(t), X(t+1), …".
Figure 5. Illustration. DIS1 and DIS2. The illustration indicates that DIS subscript 1 equals V subscript 1 times MaxTTC. It also depicts the distance between a vehicle at location x subscript 2, y subscript 2 and vehicle A at location x subscript 1, y subscript 1. The gap between the two vehicles is marked DIS subscript 2, which equals the square root of the sum of the squared difference between x subscript 1 and x subscript 2 plus the squared difference between y subscript 1 and y subscript 2.
Figure 6. Illustration. Checking a conflict between two vehicles at MaxTTC. Two overlapping rectangles indicate that a future collision is projected for a pair of vehicles, and therefore, a potential conflict has been identified. This figure shows vehicle A, a blue rectangle pointing to the right, and vehicle B, a red rectangle pointing to the left, on a grid. The vehicles overlap about halfway at a slight angle to show a future collision at MaxTTC. The illustration indicates that MaxTTC equals 1.5.
Figure 7. Illustration. Checking a conflict between two vehicles at TTC = 1.3 s (vehicles no longer in conflict). In this figure, the time to collision (TTC) values have reduced from the maxTTC value of 1.5 s (illustrated in figure 6) to a TTC value of 1.3 s. Vehicle A is a blue rectangle pointing to the right, and vehicle B is a red rectangle pointing to the left. Instead of the large overlap in figure 6, the vehicles in figure 7 have just barely come into contact.
Figure 8. Illustration. Conflict types by angle. This figure shows the angles at which a conflict is the result of a rear-end, lane-change, or crossing movement. The conflict is classified as a rear-end conflict if ||ConflictAngle|| less than 30 degrees, a crossing conflict if ||ConflictAngle|| greater than 85 degrees, or otherwise a lane-changing conflict.
Figure 9. Illustration. Lane change conflict. This figure shows two vehicles that begin the conflict event in the same lane but change links over the course of the event. The illustration depicts a rear green car heading toward the lane to the left of a leading white car.
Figure 10. Illustration. Conflict angle. This illustration depicts the conflict angle, expressed in the perspective of the first vehicle to arrive at the conflict point and conveying the direction from which the second vehicle is approaching the first vehicle. The angle ranges from -180 to +180 degrees. A negative angle indicates approach from the left and a positive angle indicates approach from the right. An angle of ±180 degrees indicates a direct head-on approach, and an angle of ±0 degrees indicates a direct rear approach. The figure shows vehicle 1 in a circle with an arrow pointing to the topmost part of the circle, marked ±180 degrees. Angles are marked clockwise around the circle at +135 degrees, +90 degrees, +45 degrees, ±0 degrees, -45 degrees, -90 degrees, and -135 degrees. Vehicle 2 is at the +45-degree mark, pointing toward vehicle 1.
Figure 11. Illustration. Clock angle. This illustration is identical to figure 10, except with angles expressed in terms of clock-hand positions. Again, the angle is expressed in the perspective of the first vehicle, with the clock time indicating the angle from which the second vehicle is approaching. The 12:00 position is directly ahead of the first vehicle, and times are marked at 1:30, 3:00, 4:30, 6:00, 7:30, 9:00, and 10:30. Vehicle 2 is located at the 4:30 angle.
Figure 12. Illustration. Intersection configuration used in simulation tests. This figure shows the geometric configuration of the intersection used in the initial analysis. The intersection configuration includes two through lanes on the main street (depicted horizontally), with right-turn movements shared with the through lanes and an exclusive left-turn lane in each approach. The side streets (depicted vertically) have two through lanes, and left- and right-turn movements are shared with the through lanes.
Figure 13. Illustration. Arterial configuration used in simulation tests. This figure shows the geometric configuration of the three-intersection arterial used in the initial analysis. The intersection configuration includes a main street (depicted horizontally) and three side streets (depicted vertically) marked 1, 2, and 3.
Figure 14. Illustration. Typical intersection layout. This figure shows the intersection layout for the base condition, reflecting the average conditions at a typical urban arterial intersection on a four-lane roadway with left-turn pockets. The intersection configuration includes two through lanes on the main street (depicted horizontally), with right-turn movements shared with the through lanes and an exclusive left-turn lane in each approach. The side streets (depicted vertically) have two through lanes, and left- and right-turn movements are shared with the through lanes.
Figure 15. Illustration. Intersection traffic volumes. This figure shows demand volumes at an intersection. The main street is horizontal and includes the numbers 50, 350, and 95 leading up to the intersection on the left and the same numbers leading up to the intersection on the right. The side street runs vertically and includes the numbers 190, 930, and 170 leading up to the intersection from above and the same numbers leading up to the intersection from below.
Figure 16. Illustration. Three-intersection arterial. This figure depicts the base condition, intended to reflect the average conditions at a typical urban arterial with three intersections on a four-lane roadway with left-turn pockets at the intersections. The intersection configuration includes a main street (depicted horizontally) and three side streets (depicted vertically) marked 1st, 2nd, and 3rd.
Figure 17. Illustration. Detail of intersection in three-intersection arterial. This figure depicts the details of a particular intersection on the arterial. The figure indicates the level of detail that is modeled for each geometric condition, including the turning-pocket lengths, lane widths, approach geometry, and signal timings. The specific yellow plus all red (Y+AR) signal timings are shown on the main and side street approaches, with 4.5 s yellow and 1 s all-red for the main street through movements, 3 s yellow and 1 s all-red for the main street left-turn movement, and 3.5 s yellow and 2 s all-red for the side street movements.
Figure 18. Illustration. Demand volumes for 50-s cycle (vehicles per hour). This figure shows the demand conditions for the 50-s cycle (volume to capacity ratio = 0.85). As in figure 15, the main street runs horizontally and the side street runs vertically. The main street includes the numbers 180, 250, and 125 leading up to the intersection on both sides and the side street includes the numbers 200, 1145, and 200 leading up to the intersection on both sides.
Figure 19. Illustration. Demand volumes for 105-s cycle (vehicles per hour). This figure shows the demand conditions for the 105-s cycle (volume to capacity ratio = 1.00). As in figure 15, the main street runs horizontally and the side street runs vertically. The main street includes the numbers 180, 270, and 130 leading up to the intersection on both sides, while the side street has the numbers 200, 1300, and 175 leading up to the intersection on both sides.
Figure 20. Screenshot. Synchro™'s representation of flows impacted by offset changes. These three diagrams, generated by Synchro™, illustrate the magnitude of predicted flows and queues under different offset conditions. Three conditions are shown in the figure, each depicting the three intersections on the test arterial. Each graph shows time on the x axis and distance on the y axis. Red and blue lines are used to depict where traffic stops at red lights or continues during a green light. Red lines show queuing in the "down" direction (e.g., southbound), and blue lines show queuing in the "up" direction (e.g., northbound). The case on the left side shows when the offset at the intersection is adjusted to 30 percent earlier in the cycle than the case in the middle of the figure. In the left diagram, more red queuing is generated with a bit less blue queuing. The graph on the right side of the figure illustrates the effect on the predicted queues when the offset is moved 30 percent later than the current setting. This case shows both more blue queuing and more red queuing than the baseline case.
Figure 21. Screenshot. Typical summary of statistical distribution data. This screenshot from Surrogate Safety Assessment Methodology (SSAM) shows a typical summary of results. It is a chart listing each of the six runs in a single row along with a row for the total of all runs and a row for the average of the results. The first three columns are Total Conflicts, Total Number of Conflicts in Seeding Period, and Minus 900 s (Seeding Period). The remaining columns are under Conflict Type and Frequency and include a column for Unclassified, followed by three groups of three columns for Crossing, Rear End, and Lane Change, including columns for number of conflicts in seeding period and Minus 900 s (Seeding Period) for each type of conflict.
Figure 22. Screenshot. An excerpt of t-test statistical output from SSAM. Variations from the base scenario, such as a change in demand or a change in splits, were compared statistically to identify the significance of the difference from the base condition. An example of this comparison, as produced by Surrogate Safety Assessment Methodology (SSAM), is shown in this figure. The screenshot is a table with rows for SSAM measures TTC, PET, MaxS, DeltaS, DR, Max D, and MaxDeltaV as well as rows for conflict types Crossing, Rear-end, Lane-changing, and Total. The column headers are Mean, Variance, and Replications for V/C 1.00; Mean, Variance, and Replications for V/C 0.85; t value; t critical; Significant; and Mean Difference. In the significant column, cells are highlighted in yellow for NO and in red for YES.
Figure 23. Chart. Generic cycle time tuning algorithm to keep all intersections below 90 percent degree of saturation. This flow chart depicts a simple approach for tuning cycle times to keep all intersections below 90 percent degree of saturation. The first step is "Calculate x, the maximum degree of saturation over all approaches in the network." The chart then asks, "Is x > 0.90?" If yes, the chart advances to "C = C+1," then to "Report new cycle time to all signals in the network," and, finally, to "Done." If the answer to the first question is no, the chart asks "Is x < 0.90?" If yes, the chart advances to "C = C–1," then to "Report new cycle time to all signals in the network," and, finally, to "Done." If the answer to the second question is no, the chart advances to "Done."
Figure 24. Chart. Flow chart of cycle time tuning algorithm. This flow chart depicts an algorithm for adjusting cycle time that combines the effects of both safety and efficiency by including the evaluation of the safety performance function. First, it must be determined if all of the k highest saturation levels are above or below 90 percent. If they are above, an increase to the cycle time is considered. If this change improves safety by lowering total predicted conflicts, this direction is followed until safety performance begins to degrade or when one or more of the k highest saturation levels has fallen below 90 percent saturation. When the safety performance does not continue to reduce the total number of conflicts, a safety efficiency trade-off metric is computed to determine whether to continue to increase the cycle time at the expense of safety. If so, it is increased until the metric falls below the trade-off threshold, and then it is stopped. In the opposite direction, reducing the cycle time is considered if there are more than k' movements with saturation levels below 70 percent. If so, a reduction to the cycle time is considered and the system cycle time is reduced until the safety trade-off metric is violated or until there are no longer k' movements with saturation level below 70 percent.
Figure 25. Illustration. Typical flow profile detector locations on coordinated approaches. This figure illustrates the detector locations used for offset tuning. There is one detector station for each coordinated approach. Intersection 1, which is not shown in the illustration, is referred to as the upstream intersection, and intersection 2, which is at the center of the illustration, is referred to as the downstream intersection. Traffic volume and occupancy are measured at some point between 1 and 2 by a flow profile detector in each lane. These flow profile detectors can be located where typical advance detectors are located, 200–300 ft from the intersection.
Figure 26. Illustration. Example of volume and occupancy data from a typical advance detector. This figure illustrates plots of the flow profile data (volume and occupancy observations) as a function of the local cycle time of the controller. Time is on the x axis. The magnitude of the volume and occupancy is indicated by the height of the corresponding bars in each row of the chart. Occupancy is shown by blue bars, and volume is shown by red bars. Each row on the chart is one cycle at the intersection. Six cycles of data are shown in the figure. The height of the bars in each row is scaled by the maximum value observed in that row. Equal heights in different rows do not necessarily indicate the same volume or occupancy value. These profiles indicate that it is typical for traffic to arrive near the beginning of the local cycle time over the last few cycles for this approach. Secondary platoons and individual vehicles also show up randomly throughout the cycle, possibly due to turning flow on the cross-street phases of upstream intersections and/or early return to green due to side street gap outs.
Figure 27. Illustration. Example of phase timing for each of the last several cycles. This figure illustrates an example of phase timing history observed over the last several cycles at an intersection. Time is shown on the x axis. Nine pairs of rows are depicted to illustrate how the phase timing data can vary from one cycle to another. Each pair of rows shows the active phase interval on a second-by-second basis for both rings of a typical North American-style traffic controller. The number and color of each column in the timeline corresponds to the active phase interval (green, yellow, and red) displayed by each ring at that time in the cycle. The top pair of rows depicts what the cycle would look like if all phases serve to their maximum demand. All subsequent cycles shown below the first row are actual data recorded from a field test controller with the most recent data at the top and progressing back in time down the display. Each cycle begins at the local zero time, which is labeled on the left.
Figure 28. Illustration. Example of cyclic volume and occupancy profiles averaged over the last several cycles. This figure shows a single, cyclic representation of the percent of time that the progression phase was green during the several cycles since the last offset adjustment control decision. Red bars indicate volume, purple bars indicate occupancy, and green bars indicate phase green probability. The height of the green bar in the display denotes a range of 0 to 100 percent. The figure shows that during a portion of the cycle, the progression phase is green 100 percent of the time, starting at local time 50 and ending at local cycle time 0 (or 80). The figure illustrates an early return to green behavior with the tapering percent-green bars prior to the programmed start of the main street green split (local time 50 s). As shown, this progression phase started as early as local cycle time 27 in at least one cycle during the last ~10 cycles. This figure also displays the detector data from the flow profile detector shifted to account for the unimpeded travel time from the upstream detector location to the theoretical "green point," where a driver would likely decide to stop if the light were yellow and continue if the light were green. The flow profile scenario shown is an example of the performance of a good offset for one-directional travel. The arriving platoons are indicated by the cluster of relatively tall occupancy bars between local cycle time 40 and local cycle time 75, which corresponds to the green portion of the service phase.
Figure 29. Chart. Offset adjustment algorithm flow chart. This flow chart depicts an algorithm for tuning offset that includes the evaluation of the safety impact of the adjustment. The algorithm will use the safety performance regression equation as the performance calculator. The general approach is to identify the capture efficiency performance of moving the offset either forward or backward. If one or the other improves performance over the "no change" situation, the safety impact of the proposed change is checked. If this change is deemed to improve both safety and efficiency, the algorithm will continue exploring this direction of change for additional improvements. If the change is deleterious to safety, the algorithm checks if the trade-off value is satisfied, asking if the effect on safety is not significant enough to disallow exploration in this direction. The algorithm continues until the effect on safety is deleterious or no longer improves the capture efficiency.
Figure 30. Diagram. Ring diagram with barriers denoted by bold vertical lines. This diagram depicts a typical phase-barrier sequence, with barriers explicitly labeled. The diagram includes "b" in between bold vertical lines on each side and "A" in between bold vertical lines in the center. In between the first b and A are the numbers 1, 2, 5, and 6. The numbers 3, 4, 7, and 8 are between A and the second b. There are four ring groups: (1, 2), (3, 4), (5, 6), and (7, 8). There are also two barrier groups (1, 2, 5, 6) and (3, 4, 7, 8).
Figure 31. Screenshot. A complete utilization-detector layout for ACS Lite. This screenshot illustrates a typical detector layout for measuring phase utilization with a detector placed at the stop bar for each lane. Each detector is associated with the phase that serves traffic flowing through its corresponding lane. The screen capture is taken from the Traffic Visualization (TRAFVU) tool that is part of Traffic Software Integrated System-Corridor Simulation (TSIS-CORSIM). An aerial view of an intersection with four approaches is shown, with the phase-sequence diagram shown in the upper left corner of the display. Each lane of each approach is marked with a directional arrow indicating the allowable movements from that lane. Each approach has left-turn, through, and right-turn lanes. A blue rectangle is shown in each lane extending approximately 30 ft upstream from the stop line.
Figure 32. Illustration. Measuring phase utilization for coordinated-actuated controllers. This figure illustrates an example where 10 s of green is served, during 7 s of which the detector is occupied. For a fixed-time controller, this corresponds to 70 percent utilization. However, in the context of a coordinated, actuated controller, the capacity of the phase is measured as the amount of available green time. In this case, the phase started timing green 2 s early due to a prior phase gapping out early. It could serve up to 12 s of green until it is forced off, but it gaps out after 10 s of green. The figure shows that this service time corresponds to 58 percent green utilization.
Figure 33. Graph. Utilization of phases before split adjustment. This graph, depicting phase on the x axis and utilization on the y axis, is an example of utilization estimates for a dual-ring, eight-phase controller where the utilization of phase 3 is very high. The phase 3 utilization is 100 percent and marked with a red arrow.
Figure 34. Graph. Utilization of phases after split adjustment. This graph, depicting phase on the x axis and utilization on the y axis, is an example of the estimated utilization of phases after the algorithm has adjusted the splits to minimize the maximum utilization of any phase on the controller. Phase 3 utilization, marked with a red arrow, is now at 72 percent.
Figure 35. Chart. Flow chart of the split optimization process including safety analysis. This flowchart shows the algorithm for the optimization of splits that includes an evaluation of safety. First, the reallocation algorithm is run to identify the set of splits that optimizes only efficiency. This set of splits is then evaluated for safety impact. The safety/efficiency trade-off is also calculated for each split. If the reallocated splits improve total safety, then the splits that have positive safety trade-offs are identified for biasing. Since those phases were found to have a positive correlation with improving safety, additional time would be considered to improve safety further. The reallocation algorithm is then run with the biased utilization values. If this solution further improves total safety—the negative impacts from shortening the other phases is not enough to cancel out the positive returns—the process is repeated until additional biasing does not result in further safety improvements. Similarly, if the initial reallocation decreases total safety, the phases that have the highest negative trade-off impacts are identified. This process identifies the phases that were shortened in the initial reallocation and boosts their utilization values so that a subsequent reallocation will provide additional split for that phase. That reallocation is then tested again for an improvement to the total safety. If the result is positive, the algorithm stops. If the result is a further detriment, the most negatively impacted phases are biased and the process is repeated.
Figure 36. Chart. Flow chart of algorithms execution sequence. This flow chart shows the five optimization stages, which are executed independently but in sequence and with feedback steps. In step 1, the split reallocation algorithm is executed for each intersection in the system. After this reallocation, the offset adjustment algorithm is executed in step 2 to identify any modifications to the offsets to improve progression. After the splits and offsets are calculated, modifications to the phase sequence (step 3) are evaluated with the new split values calculated in step 1. If any phase sequence modifications are identified that adjust the offset, the offset calculation must be re-executed to determine if this change is of further benefit and can be retained. Next, potential changes to the protected/permitted settings for left turns are evaluated (step 4) using the phase sequence selected in the previous step. If any left-turn settings are deemed beneficial, the split reallocation algorithm may have to be recalculated. In turn, if the splits are reallocated at this step, the offsets, phase sequence, and protected/permitted settings are reevaluated as well. Finally, the cycle time adjustment algorithm is evaluated (step 5). As with the phase sequence and protected/permitted settings, if it is deemed beneficial to modify the cycle time, all other algorithms must be reevaluated within the new value for the cycle.
Equation 1. Crashes 1. Crashes equals a times CMF1 times CMF2 times CMF3 times open parenthesis Vcross to the power b close parenthesis times open parenthesis Vmain to the power c close parenthesis plus d.
Equation 2. Crashes 2. Crashes equals CMF1 times CMF2 times CMF3 times exp open parenthesis negative a plus b times ln parenthesis Vcross close parenthesis plus C times open parenthesis Vmain close parenthesis close parenthesis.
Equation 5. Format for fractional designs. Y equals A1 times x1 plus A2 times x2 plus … plus An times xn plus A12 times x1 times x2 plus A13 times x1 times x3b plus … plus An, n-1 times xn times xn-1.
Equation 6. Non-linear regression equation. Y equals a1 times x1 plus a2 times x2 plus … plus … plus an times xn plus a11 times x1 to the power 2 plus a12 times x2 to the power 2 plus … plus a1n times xn to the power 2 plus b.