Performance Evaluation of Coordinated-Actuated Traffic Signal Systems Gary E. Shoup and Darcy Bullock

Transcription

1 ABSTRACT Performance Evaluation of Coordinated-Actuated Traffic Signal Systems Gary E. Shoup and Darcy Bullock Arterial traffic signal systems are complex systems that are extremely difficult to analyze due to the stochastic properties associated with vehicular traffic and actuated controllers. Currently, the most common method for analyzing traffic signal systems is based on fixed-time highway capacity manual procedures. Unfortunately, this methodology does not provide procedures for analyzing the performance of coordinated-actuated traffic signal systems. A literature review indicates that there is no accepted practice for analyzing the performance of coordinated-actuated traffic signal systems. This paper describes a procedure that will be particularly useful to practicing engineers analyzing coordinated-actuated arterial signal systems. The proposed analysis procedure produces graphical performance summaries that quantify the performance of an arterial traffic signal system. We believe this procedure will provide a more accurate prediction of how a proposed coordinated-actuated system (or a new adaptive control system) will perform before it is deployed in the field. Further, the evaluation methodology is independent of the design process and can be used for validating the viability of a new signal timing strategy. The additional engineering analysis time this process requires can be justified by reducing the amount of field tuning typically required when coordinated-actuated systems are deployed. CURRENT METHODS OF ARTERIAL ANALYSIS Traditionally, methods for analyzing traffic signal systems have been based upon procedures that do not account for many of the properties associated with vehicular traffic and actuated signal control systems. Typically, engineers conducting an arterial analysis use the analysis procedures outlined in Chapter 11 of the 1997 Highway Capacity Manual Update (HCM) and/or utilize a computer methodology that is designed to measure the aspects of vehicle arrivals and bandwidths for a fixed-time signal system. (1, 2) Of these two procedures, Chapter 11 of the HCM is most often used by practicing engineers to evaluate the impact that modified signal timings have on the level of service for an arterial. A detailed discussion of the limitations of the HCM procedure follows. The HCM analysis procedure quantifies arterial performance by following the seven-step process shown in Figure 1. The basis for determining the performance of an arterial using this procedure is to calculate the average travel speed for the arterial and then assign a level of service for the arterial based upon the average travel speed. However, prior to determining this average travel speed and the resultant arterial level of service, the running time per mile of the arterial must be computed using another HCM table, and an estimate for the intersection delay times along the arterial must be calculated using several HCM equations. Once both these items are calculated, the analyst can quantify the performance of an arterial section using the average travel speed.

2 Unfortunately, subjective analysis procedures are included in the arterial analysis procedure. Subjective values are required for determining the arterial classification, as well as for the vehicle progression classifications provided in HCM Table Table 1a and Table 1b show the HCM tables in which subjective values are required. Table 2 provides the HCM definitions for the progression adjustment factors (PF) for different arrival types. These subjective requirements are explicitly acknowledged in the HCM, and the manual states that if knowledge of the intended signal timings and quality of progression are not available, no meaningful estimation of arterial level of service is possible, even on a planning level. (1) The sensitivity of the HCM procedure to the subjective value for quality of progression and other stochastic variables present in actuated traffic controllers can best be explained through a discussion and a quantitative example incorporating the HCM arterial analysis equations. EXAMPLE HCM ARTERIAL ANALYSIS PROCEDURE One of the main components in determining the arterial running speed, and thus the arterial level of service, is the average intersection control delay equation. The HCM defines the average intersection control delay equation as shown in Figure 2. This delay equation is intended to estimate the average control delay per vehicle at a signalized intersection based upon average green splits. However, the delay equation does not account for how variations in green splits affect the start of green times in modern coordinated-actuated controllers. Such variations in the start of green times directly impact the quality of progression (HCM PF Factors shown in Table 1) and the amount of delay experienced. Furthermore, determining the quality of progression factor for the PF term of the HCM average intersection delay equation is a difficult task, even if observed in the field by an engineer. For existing arterial conditions, one analyst may conclude that current arterial signal timings are not facilitating progression and assign an arrival of type-2 (Table 2). But, another analyst may conclude that because of platoon dispersion, vehicle progression for the exact same arterial resembles random arrivals and assign an arrival of type-3 (Table 2). Both of these arrival types are subjective values and are difficult to distinguish between one another in the field by technicians typically employed to do so. To analyze how arterial progression will occur in the future for a new set of signal timing plans, the HCM suggests that an analyst should review the time-space diagrams for the new arterial signal timing plan. Unfortunately, many of the time-space diagrams created with current traffic signal design software packages are based on fixed-time systems and do not represent the time-space diagrams which occur in the field for coordinatedactuated systems. The reason for this discrepancy in time-space diagrams is because of the early return to green phenomena associated with actuated controllers. The early return to green has been identified by several researchers, and signals operating with this

3 condition often release vehicles prior to the desired release time required for coordination purposes. (3, 4, 5, 6) An early release of vehicles at signals often leads to platoons stopping at adjacent arterial signals downstream and resulting in poor arterial progression. Thus, engineers often erroneously award a higher value to the quality of progression for new signal timing plans then is warranted because of reviewing time-space diagrams based on fixed-time traffic signal systems. An example of how slight discrepancies with both of the discussed issues impact an arterial level of service is provided. Table 3 and Table 4 show the quantitative calculations used to compute an arterial level of service for a hypothetical 0.2 mile suburban arterial section with slightly different values assigned to the g/c ratios and the quality of progression factors. The results show that minor changes in the g/c ratio and/or platoon arrival type can vary the arterial LOS by as much as two performance letter grades. Case 3 with a g/c ratio equal to 0.6 and an arrival type-2 yields an arterial level of service of E while Case 5 with a g/c ratio equal to 0.7 and an arrival type-3 yields an arterial level of service of C. This small discrepancy in g/c ratios and arrival types resulted in a significant disparity in the arterial level of service reported and could have easily arisen due to actuated traffic control hardware not being accounted for properly in the analysis procedure. The arterial level of services provided in this table were intended to show quantitatively how slight discrepancies in the discussed values can affect the arterial level of service being reported and why actuated traffic controller hardware must be accounted for in an arterial analysis procedure. Although the HCM now includes procedures for estimating average green times for actuated controllers, it is unlikely closed form analytical models will be developed for accurately modeling the multitude of coordinated-actuated control parameters now in use on most modern traffic signal systems. Stochastic properties affecting the HCM arterial analysis procedure are not limited to traffic controller hardware operations but also include vehicular traffic flows. Vehicle flows vary over time and may result in short term oversaturated conditions that impact the arterial being analyzed. Such saturated conditions may result in left turn storage lanes spilling back and impeding through movements, and/or result in spillback to adjacent intersections and affect upstream intersections. The current form of the HCM arterial analysis procedure does not account for arterials experiencing saturated conditions. Thus, while the HCM arterial analysis procedure is quite systematic in providing an arterial analysis procedure, it is limited in its analysis capabilities due to subjective observations analytical models being unable to account for stochastic traffic variations and the impact on actuated controller logic.

4 PROPOSED MICROSIMULATION ANALYSIS PROCEDURES To overcome the limitations associated with deterministic empirical formulas and accurately account for the stochastic properties of an arterial signal system, the option of using a microscopic simulation package is becoming more attractive. (7, 8, 9, 10) The HCM manual indicates that traffic simulation models can be used to estimate the level of service for an arterial; however, at this time, the manual does not provide procedures for analysts to follow. HCM sanctioned simulation analysis procedures would be of great benefit to practicing engineers because they would provide practitioners a standard analysis procedure for the analysis of advanced signal systems, such as coordinatedactuated and real-time adaptive signal systems, which are not able to be analyzed with current empirical methods. Microscopic simulation traffic models, such as CORSIM, SimTraffic, and VISSIM, facilitate the analysis of these advanced systems by supplying large amounts of data on arterial performance ranging from the percentage of stops at the arterial intersections to the travel time for the arterial. (7, 8, 9) In addition to providing a wealth of traffic simulation data, microscopic simulation models are also able to analyze traffic control systems consisting of complex attributes such as actuated controllers, short duration oversaturated conditions, signal pre-emption events, and cycle transition algorithms. This paper presents an arterial analysis procedure that addresses the issue of accounting for the stochastic properties present in vehicular traffic and signal controller systems and outlines a step-by-step approach for compiling insightful graphical summaries that compare arterial signal timing plans under various alternatives. The proposed graphical reporting procedure presents cumulative delay and cumulative travel time for an arterial in relation to the locations of the signalized intersections for the corridor. Cumulative travel and delay times are calculated by compiling several traffic simulation runs and tabulating the average individual link delay and travel times for the arterial. These average values are then tabulated to calculate the arterial cumulative delay and travel times with respect to intersection locations. Plots of these cumulative delay and travel times can provide insight on the performance of the system. The cumulative travel time plot is intended to represent the time a typical motorist experiences travelling through the arterial and in the authors opinion is often the most insightful plot. This analysis procedure can be generally viewed as a simulation based floating car study. To demonstrate the usefulness of such plots, the proposed graphical procedure was applied to a four-lane arterial signal system in Lafayette, Indiana (Figure 3). Examples of the resultant cumulative performance graphs for the mid-day, existing signal timing plan are shown in Figure 4 and Figure 5. As shown in these figures, the graphs indicate the eastbound cumulative arterial travel and delay times for an existing coordinated-actuated signalized arterial. These graphs are designed to explicitly indicate where each signalized intersection is on the arterial and how the cumulative delay and travel times are impacted by each signalized intersection. Note in Figure 4 how the cumulative travel time at each arterial intersection node is indicated and graphed. This plot of average cumulative travel time versus distance for several random seed number runs permits the analyst to easily comprehend the cumulative travel time for the arterial. It also provides a tool for the

5 analyst to identify the critical locations on the arterial that have the most significant impact on the cumulative travel time. Critical locations can be readily located by looking for a steep slope on the graphs, indicating an abrupt change in the noted measure of effectiveness. Noting such critical locations is important to the analyst because it signifies a location that may warrant further investigation by the analyst for possible corrective measures in signal timing plans. See Figure 4 and Figure 5 for examples that identify critical locations along the arterial. Additionally, although the graphic procedure discussed is limited to cumulative delay and travel times, similar graphical presentations can be expanded to include the number of stops or emission estimates for HC, CO, and NOX. DATA REDUCTION PROCEDURES FOR ANALYSIS GRAPHS To construct the above-described graphic analysis procedure, a step-by-step data reduction process of CORSIM simulation data was conducted. The step-by-step process consisting of four steps is described as follows. STEP 1: Data Extraction Obtain simulation data from several simulation runs using different random number seeds. Travel time per link in seconds per vehicle and the delay time per link in person-minutes is tabulated for the through movement for each of the links along the arterial. STEP 2: Data Calculations Individual link values are then used to compute the cumulative values for link lengths, travel times, and delay times at each of the node locations on the arterial. After this cumulative data are compiled, the averages (Table 5, cols. 7 & 8) and standard deviations (Table 5, cols. 9 & 10) for the cumulative arterial measures of effectiveness (MOEs) are computed. STEP 3: Graphing of Results With the cumulative travel and delay times calculated for each node, the cumulative times are graphed on the y-axis for the corresponding node locations indicated on the x-axis. Node locations are provided by accumulating the link lengths over the distance of the arterial. Figure 4 and Figure 5 illustrate these plots. STEP 4: Statistical Evaluation and Comparison Standard deviation error bars at the individual nodes and lines connecting the cumulative times are drawn on the graph creating the graphic performance summary (Figure 4 and Figure 5). A variation on the ±1 standard deviation bar

6 can be calculated, to show the 90% or 95% confidence interval, using a t-statistic. If more than one arterial control strategy is to be shown on the same graph, differentiating symbols are drawn to represent different cumulative times for each arterial timing strategy. Figure 4 and Figure 5 show an example arterial performance summary graph that can be used to evaluate an arterial. The above data reduction steps can be easily automated with the use of macro functions contained in popular word processing and spreadsheet packages. IMPLEMENTATION POTENTIAL The proposed CORSIM performance evaluation procedure can be used to graphically quantify the performance of a traffic signal system. This ability to evaluate a traffic signal system is extremely important when designing a new signal timing strategy and can be used to validate the viability of a new signal timing strategy, compare alternatives, or document anticipated problems due to heavy traffic or constrained geometry. Currently, comparisons of existing and proposed timing plans are conducted by comparing quantitative values at each intersection with no graphics that provide insight into how the signal system operates as a whole. In contrast to current methods, this proposed performance evaluation procedure can provide a graphic comparison of different system plans to validate new proposed signal timings. As shown in Figure 6 through Figure 9 and Table 6, a proposed timing plan can be compared with an existing timing plan through graphical and tabular analysis procedures to quantitatively illustrate that the proposed arterial timing plan accomplishes the design objective of reducing the delay and travel times. This comparison of existing versus proposed signal timing plans provides engineers and decision makers a graphical interpretation tool that illustrates the improvement of the proposed arterial signal timing plan over the existing signal timing plan. With this tool, the existing versus proposed signal timing graphs and tables can be easily evaluated to ensure that the proposed signal timing plan is superior to the existing signal timing plan. CONCLUSION The proposed simulation performance evaluation procedure of traffic signal systems provides an analytical tool that accounts for the stochastic traffic characteristics present in modern coordinated-actuated traffic control systems. It is an analytical method that is able to graphically depict the quantitative performance of an arterial under many different alternative strategies. This method provides a formal but feasible procedure to evaluate the benefits associated with arterial signal improvements. Secondly, a much needed evaluation methodology, independent of the design process can now be used for validating the viability of a new signal timing strategy. Although the authors believe these procedures are superior to the HCM analytical model for analyzing modern coordinated-actuated systems, we also recognize that underlying

7 traffic simulation models deserve scrutiny. Future research should be devoted to ensuring that simulation models effectively model signalized intersection lane group capacity and platoon dispersion between intersections. Finally, although CORSIM was used for illustrating the procedure, other simulation packages such as VISSIM or SimTraffic could be used. ACKNOWLEDGEMENTS This work was supported in part by the Louisiana Department of Transportation and Development, the Indiana Joint Transportation Research Program, and the Federal Highway Administration. The views expressed in this paper do not necessarily reflect those of the sponsors.

8 REFERENCES 1. Highway Capacity Manual, Transportation Research Board Special Report 209, 3 rd Edition, TRB, Washington, D.C., Avery, D. J. Jr., Courage, Kenneth G. Method for reviewing and assessing PASSER II and TRANSYT 7-f signal timing optimization outputs. In Microcomputers in Transportation: Proceedings of 4 th International Conference on Microcomputers in Transportation. ASCE, New York, NY, 1993, pp Ficklin, N.C. For and Against Semi-actuated Signals. Traffic Engineering, March Skabardonis, A. Determination of timings in signal systems with traffic-actuated controllers. In Transportation Research Record 1554, TRB, National Research Council, Washington, D.C., 1996, pp Chang, E. C. P. Guidelines for actuated controllers in coordinated systems. In Transportation Research Record 1554, TRB, National Research Council, Washington D.C., 1996, pp Kuzbari, Ray. Early green start analysis for time-of-day signal coordination. In ITE Journal, August Husch, David. SimTraffic 1.0 User Guide. Trafficware, Berkeley, CA, Kaman Sciences Corporation. CORSIM User s Manual. Version Colorado Springs, CO, 1997B. 9. Bauer, Thomas. VISSIM User Manual. Innovative Transportation Concepts, Corvallis, OR, Shoup, G. Traffic Signal System Offset Tuning Procedure Using Travel Time Data. Master s Thesis, Purdue University, West Lafayette, Indiana, 1998, pp

9 AUTHORS INFORMATION Gary E. Shoup Engineer Dunn Engineering Associates 66 Main Street Westhampton Beach, NY Phone: (516) Fax: (516) Darcy Bullock Associate Professor Purdue University 1284 Civil Engineering Building West Lafayette, IN Phone: (765) Fax: (765) Internet Web Site:

10 Step 1 Establish location and length of arterial to be considered Step 2 Determine arterial classification and free-flow speed Step 3 Define arterial sections Step 4 Compute running time Step 5 Compute intersection total delay for arterial through movements Alternative Existing conditions on existing facilities can also be assessed using field data Step 6 Compute average travel speed (a) by section and speed profile (b) over entire facility Step 7 Assess level of service Figure 1: Highway Capacity Arterial Level of Service Method (adapted from Figure 11-2 in (1))

11 d = d + 1 PF + d2 d3 d C[1 - ( g / C)] = 1- ( g / c)[min( X,1.0)] 2 d 2 = 900T[( X -1) + ( X -1) + 8kIX / Tc] d = control delay (sec/veh), d 1 = uniform delay (sec/veh), d 2 = incremental delay (sec/veh), d 3 = residual demand delay (sec/veh) (defined in HCM Appendix 9-VI), PF = uniform delay adjustment for quality of progression, c = capacity of lane group (veh/hr), X = v/c ratio for lane group with v representing demand flow rate, C = cycle length (sec), g = effective green time for lane group, T = duration of the analysis period (hr) k = incremental delay adjustment for actuated control, and I = incremental delay adjustment for filtering and metering by upstream signals Figure 2: Highway Capacity Manual Average Intersection Control Delay Equation (1)

12 W 410 vph E N vph 12 S 924' vph 100 vph 8 15 vph 2078' 1741' 792' 1584' vph 260 vph vph 670 vph vph 786' 1188' 674' 618' 3033' 130 vph 170 vph 235 vph 1070 vph vph 370 vph 30 vph 1165 vph 410 vph vph vph Figure 3: State Route 26 link-node diagram

13 Cumulative Travel Time S.R. 26 Eastbound (THROUGH VEHICLES ONLY) Critical location indicated by a steep slope Time (s) Posted speed limit slope Linear Distance Along Corridor (ft) Signal Location Existing Timing Plan Posted speed limit Figure 4: Cumulative travel time graph for State Route 26, Lafayette, Indiana. Cumulative Delay S.R. 26 Eastbound (THROUGH VEHICLES ONLY) Critical location indicated by a steep slope Delay (veh-min) Linear Distance Along Corridor (ft) Signal Location Existing Timing Plan Figure 5: Cumulative delay graph for State Route 26, Lafayette, Indiana.

14 Cumulative Travel Time S.R. 26 Eastbound (THROUGH VEHICLES ONLY) Time (s) % Reduction in Cumulative travel time Posted speed limit slope Linear Distance Along Corridor (ft) Signal Location Existing Timing Plan Proposed Timing Plan Posted speed limit Figure 6: Comparison of signal control plans based upon cumulative travel time, State Route 26 Eastbound Cumulative Delay S.R. 26 Eastbound (THROUGH VEHICLES ONLY) Delay (veh-min) % Reduction in Cumulative delay time Linear Distance Along Corridor (ft) Signal Location Existing Timing Plan Proposed Timing Plan Figure 7: Comparison of signal control plans based upon cumulative delay time, State Route 26 Eastbound

15 Cumulative Travel Time S.R. 26 Westbound (THROUGH VEHICLES ONLY) % Reduction in Cumulative travel time 400 Time (s) Posted speed limit slope Linear Distance Along Corridor (ft) Signal Location Existing Timing Plan Proposed Timing Plan Posted speed limit Figure 8: Comparison of signal control plans based upon cumulative travel time, State Route 26 Westbound Cumulative Delay Route S.R. 26 Westbound (THROUGH VEHICLES ONLY) Delay (veh-min) % Reduction in Cumulative delay time Linear Distance Along Corridor (ft) Signal Location Existing Timing Plan Proposed Timing Plan Figure 9: Comparison of signal control plans based upon cumulative delay time, State Route 26 Westbound

16 HCM TABLE ARTERIAL CLASSIFICATION ACCORDING TO FUNCTIONAL AND DESIGN CATEGORIES PRINCIPAL ARTERIAL FUNCTIONAL CATEGORY MINOR ARTERIAL DESIGN CATEGORY High Speed design And control I Not Applicable Typical suburban design and control II II Intermediate design II III or IV Typical urban design III or IV IV (a) Arterial classification subjective values HCM TABLE RELATIONSHIP BETWEEN ARRIVAL TYPE AND PLATOON RATIO (R P ) ARRIVAL TYPE RANGE OF PLATOON (R P ) DEFAULT VALUE (R P ) PROGRESSION QUALITY Very Poor 2 >0.50 and Unfavorable 3 >0.85 and Random Arrivals 4 >1.15 and Favorable 5 >1.50 and Highly Favorable 6 > Exceptional HCM TABLE UNIFORM DELAY (d 1 ) PROGRESSION ADJUSTMENT FACTOR (PF) GREEN RATIO ARRIVAL TYPE (AT) (g/c) AT-1 AT 2 AT 3 AT 4 AT 5 AT Default, f P Default, R P NOTES: 1. PF = (1 P) f P /(1 - g/c). 2. Tabulation is based on default values of f P and R P 3. P = R P * g/c (may not exceed 1.0). 4. PF may not exceed 1.0 for AT 3 through AT 6. (b) Arterial progression subjective values Table 1: Highway Capacity Manual tables requiring subjective values (1)

17 HIGHWAY CAPACITY MANUAL DESCRIPTIONS FOR PROGRESSION ADJUSTMENT FACTORS ARRIVAL TYPE DESCRIPTION FOR PROGRESSION ADJUSTMENT FACTOR Dense platoon containing more than 80 percent of the lane group volume and arriving at the start of the red phase. This arrival type is representative of arterials that experience very poor progression quality as a result of conditions such as lack of overall network signal optimization. Moderately dense platoon arriving in the middle of the red phase or dispersed platoon containing 40 to 80 percent of the lane group volume arriving throughout the red phase. This arrival type is representative of unfavorable progression quality on a two-way arterial. Random arrivals in which the main platoon contains less than 40 percent of the lane group volume. This arrival type is representative of operations characterized by highly dispersed platoons at isolated and noninterconnected signalized intersections. It may also be used to represent coordinated operation in which the benefits of progression are minimal. Moderately dense platoon arriving in the middle of the green phase or dispersed platoon containing 40 to 80 percent of the lane group volume arriving throughout the green phase. This arrival type is representative of favorable progression quality on a two-way arterial. Dense to moderately dense platoon containing more than 80 percent of the approach volume and arriving at the start of the green phase. This arrival type is representative of highly favorable progression quality, which may occur on routes that have a low to moderate number of side street entries and receive high priority in the signal timing plan design. This arrival type is reserved for exceptional progression quality on routes with nearly ideal progression characteristics. This arrival type is representative of very dense platoons progressing over a number of closely spaced intersections with minimal or negligible side street entries. Table 2: Highway Capacity Manual Definitions for Progression Adjustment Factors (1)

18 SUMMARY OF ARTERIAL INTERSECTION DELAY ESTIMATES Case Arterial Description: Cycle Length Green Ratio v/c Ratio 4 lane suburban arterial, 0.2 mile section, volume = 1500 vph, Adjusted Saturation flow rate = 3000 vph, Unit extension of 2.5 seconds to determine k, I = 0.5, T = 1 hour Lane Group Capacity Arrival Type Uniform Delay Filtering/ Metering Factor Incremental Delay Control Delay Through Movement C g/c X c AT d 1*PF I d 2 d(sec) LOS B B C A A B Table 3: HCM calculations for average control delay per vehicle on arterial approach 1 If analyst considers phases 2 and 6 to be non-actuated, k = 0.50 and resulting d 2 = 2.5 seconds and 1.1 seconds for X = and X = respectively. COMPUTATION OF ARTERIAL LOS WORKSHEET Case Arterial Description: 4 lane suburban arterial, 0.2 mile section, Volume = 1500 vph, Adjusted Saturation flow rate = 3000 vph, Unit extension of 2.5 seconds to determine k, I = 0.5, T = 1 hour 3600(sum of length) ART SPD = sum of time Freeflow Speed (mph) Running Time (sec) Control Delay (sec) Other Delay (sec) Sum of Time by Section Arterial Speed (mph) Arterial LOS by Section Length (mi) Arterial Class Section II D II 40 I D II E II C II 40 I C II D Table 4: HCM calculations for arterial level of service

19 MID-DAY TRAFFIC STRATEGY #1: EXISTING TIMING PLAN STATE ROUTE 26 LAFAYETTE, INDIANA CORSIM NODES EASTBOUND CORSIM VALUES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Cumm Cumm Link Link Cumm Cumm Stdev Stdev Cumm Travel Delay TT Delay Travel Delay Start End Length Length Time Time Time Time Time Time (ft) (ft) (s) (veh-min) (s) (veh-min) (s) (veh-min) Table 5: Cumulative delay and travel times used to construct Figure 4 and Figure 5 (number of simulation runs = 6)

20 Lane Group Movements Existing Delay (sec/veh) Proposed Delay (sec/veh) Existing Level of Service Proposed Level of Service D D NB D D A A B B EB B B E E SB C D D C WB D C Note: Standard deviations for delay can be included to conduct statistical comparisons. Due to limited space requirements for this paper, only one example of an individual intersection, lane group comparison is shown. Table 6: Lane Group Comparison of Delay per Vehicle at an individual intersection; State Route 26, Node 1