Minimum Merging Section Lengths for Triple Left-Turn Lanes with Downstream Lane Reductions

Transcription

1 Minimum Merging Section Lengths for Triple Left-Turn Lanes with Downstream Lane Reductions THIS PAPER, WHICH WON THE ITE STUDENT PAPER AWARD IN 2000, DISCUSSES TRIPLE LEFT TURNS, AN ALTERNATIVE TO HANDLING AT-GRADE SIGNALIZED INTERSECTIONS WITH SEVERE LEFT-TURN CAPACITY AND OPERATIONAL PROBLEMS. BY QIONG JOAN SHEN INCREASING TRAVEL DEMANDS on urban streets not only proportionately increase left-turn volumes, but also make left turns more difficult due to increased opposing traffic. Further, mid-block turning traffic will continue to be shifted to downstream intersections as both medians and median openings become more restrictive under stricter access control. With increasing left-turn demands and decreasing left-turn opportunities comes the need for higher left-turn capacities. Installation of triple left turns in lieu of double left turns has been introduced as a solution to relieving congestion at signalized intersections that serve heavy left-turn traffic. 1 A triple left turn allows three lanes of vehicles to turn left simultaneously during a usually protected left-turn phase. Studies have consistently shown that triple left turns significantly increased left-turn capacities. A study of five triple left-turn sites in California recorded a high average saturation flow rate of 1,928 vehicles per hour of green per lane (vphgpl). 1,2 A more recent Institute of Transportation Engineers (ITE) study of 17 triple left-turn sites reported an average saturation flow rate of 1,830 vphgpl. 1,3 In Florida, a study of two triple left-turn sites in Broward County recommended the use of triple left turns as a solution to inadequate left-turn capacities. 1,4 Since a triple left turn involves traffic from three left-turn lanes moving downstream simultaneously, its downstream roadway must have at least three lanes. Where the downstream roadway has only two lanes, a triple left turn may be installed by including a transitioning three-lane section on the two-lane facility, creating essentially a merging section with a lane-drop condition some place downstream. The length of this merging section is measured from the beginning of the departing approach downstream of the triple left turn to the beginning of the lane-drop location, excluding the lane-drop taper section. Figure 1 shows an example of such a geometric configuration and the associated merging section. In this case, the triple left turn is installed at a ramp terminal either to shorten the required left-turn green phase or to prevent traffic from backing up onto the freeway, or both. When the merging section is not sufficiently long, vehicles traveling on the lane being dropped will be forced to slow down, stop, or perform unsafe merging maneuvers, resulting in undesirable traffic operational and safety problems. The provision of sufficient merging distance is thus highly important. The most comprehensive guidelines to date for triple left turns have been developed by Ackeret based on data from triple left-turn sites in Las Vegas, NV, USA. 5 Ackeret s guidelines did not include minimum merging lengths at triple left turns with downstream lane reductions. This paper describes a study sponsored by the Florida Department of Transportation (FDOT) to address, among others, this particular need. The establishment of such guidelines would allow triple left turns to be properly designed and installed at locations where they are warranted. The next section provides an overview of the methodology applied in this study to develop models to determine the minimum merging section lengths based on data generated by simulation models. Critical variables considered in the simulation models are introduced in the two subsequent sections. The simulation modeling process is then described in detail, followed by the method used to determine tabulated guidelines for minimum merging section lengths. The last section summarizes and concludes this paper. 40 ITE JOURNAL / MARCH 2001

2 METHODOLOGY OVERVIEW The methodology designed to accomplish the objective of this study consists of the following five major steps: 1. Select the appropriate measure of effectiveness (MOE) (i.e., the dependent variable) for measuring the quality of traffic flow at the downstream merging section. 2. Identify the independent variables, including the design control variable (i.e., the merging section length) and other variables expected to have an impact on the MOE. 3. Develop simulation models to simulate the effects of the independent variables on the MOE. 4. Establish the mathematical relationships between the MOE and the independent variables. 5. Determine the minimum merging section lengths required for various traffic and signal conditions. The following sections describe each of these steps in detail. MEASURE OF EFFECTIVENESS Potential MOEs for measuring the quality of traffic flow at merging sections include average delay, vehicle stops and average speed. It is reasonable to assume that favorable MOE values will lead to better safety experience at the merging sections. Average delay in seconds per vehicle was selected over vehicle stops because the latter does not consider the effects of vehicular slowdowns on flow quality. Although both average delay and average speed can be used in this study, only one is needed since the two are highly correlated. Average delay was selected for its popularity as a MOE for urban street-design evaluation. INDEPENDENT VARIABLES The independent variables include both the design control variable (i.e., the merging section length) and other variables that significantly affect the average delay. As the merging section length increases, the average delay experienced by vehicles traveling on the section is expected to decrease. Variables expected to affect the average delay include the length of the left-turn green time, the percentage of heavy vehicles in the leftturning traffic stream and the design freeflow speed of the downstream roadway. The length of the left-turn green phase affects the size of the vehicle platoon moving downstream from the triple left turn. As the green time increases, longer merging section lengths will be needed to increase capacity to serve larger platoons. Heavy vehicles in the traffic stream will cause higher average delays due to their larger vehicle sizes and lower acceleration rates. The effects of design free-flow speed on average delay are less obvious. It is expected that, as the design free-flow speed increases to a certain level, heavy vehicles will be unable to accelerate fast enough to reach the design free-flow speed, causing delay not only to themselves but also other vehicles in the traffic stream. SIMULATION MODELING After the MOE and the potential contributing variables are identified, the next step is to determine the relationships among the variables. Since triple left turns with downstream lane reductions did not exist, no field data could be collected to synthesize these relationships empirically. Empirical modeling based on simulated data became the only logical and feasible approach to establishing the relationships. Simulation Tool CORSIM (CORridor SIMulation) was used as the traffic simulator to simulate the different scenarios and to obtain the corresponding MOE. Developed and supported by the Federal Highway Administration, CORSIM is a stochastic, microscopic simulation model consisting of the NETSIM and FRESIM submodels for modeling street and freeway networks, respectively. 6 The CORSIM model was designed to represent traffic flow on a roadway system using commonly accepted driver and vehicle behavior models. COR- SIM is well recognized for its sophisticated algorithms for car-following and lanechanging models and is able to analyze a wide range of traffic, geometric and control conditions. CORSIM also produces a rich set of MOEs that include delay, travel time, speed, stops, queue time, stop time, queue length and fuel consumption. In addition, CORSIM comes with the TRAFVU visualization program that can dynamically display the actual traffic operations of a simulation model. 7 Figure 1. Triple left-turn lanes serving heavy left turns at ramp terminal. Network Coding Roadway networks are represented in CORSIM by nodes and links. Each link represents one direction of a street, which is defined in terms of the node at each end. A node usually represents an intersection but can also represent a location where the roadway conditions change (in which case, it is referred to as a dummy node). Figure 2 shows the link-node diagram of the base network used in this study as displayed in ITRAF a graphical program designed to facilitate the creation of CORSIM input files. 8 In this network, node 1 is the main intersection with a triple left turn installed on the approach represented by link (2,1). Nodes 8001, 8002 and 8003 are entry nodes that are used to form entry links, which are used mainly to specify the approach volumes. Nodes 2, 3 and 5 are nodes that are used to define the various intersection approaches. To meet the specific needs of this study, the following model features were coded into the base network: 1. Since NETSIM does not explicitly model lane drops, a lane-drop condition was created by including a dummy node at the desired lane-drop location and dropping the number of lanes from three to two at the dummy node. The dummy node is shown as node 4 in Figure 2. Accordingly, links (1,4) and (4,5) are assigned with three and two lanes, respectively. 2. Since the required merging section lengths are minimum values, the triple left turn was coded with leftturn volumes that ensure no unused left-turn green times for all three left-turn lanes. 3. Since NETSIM outputs MOE values for individual links, links (1,4) and ITE JOURNAL / MARCH

3 Figure 2. Link-node diagram of base network. (4,5) were aggregated to obtain the combined average delay for the roadway segment represented by nodes 1 and 5. Note that the length of this (1,5) roadway segment remains the same for all simulation runs. The various merging section lengths were simulated by moving node 4 along the (1,5) roadway segment. 4. Only the triple left-turn lanes were assigned traffic volumes to ensure that the aggregated delay values from links (1,4) and (4,5) resulted from only the triple left-turn vehicles. Simulation Runs After the CORSIM input file for the base network was coded, simulation runs for different scenarios could be performed by modifying the base input file. Table 1 shows the independent variables and the corresponding iteration range and increment for each variable. As indicated, a total of 1,890 simulation scenarios were considered. Table 1. Simulation scenarios. Variable Lower bound Upper bound Increment Frequency Merging section length (ft.) Green time (s) Percentage of heavy vehicles Downstream free-flow speed (mph) Total scenarios 1,890 Because of the stochastic nature of simulation models, each simulation run may produce significantly different results, depending on the random number of seeds used. Most simulation studies have used between five to 10 simulation replications. For this study, 10 replications were performed for each scenario, resulting in a total of 18,900 simulation runs. The average delay values from the 10 replications were averaged to obtain the final average delay for each scenario. Each simulation run was based on a 30- minute simulation time. Due to the large number of simulation runs involved, a computer program was developed to repeat the following steps automatically: 1. Read the input file for the base network. 2. Modify the base input file for a (new) specific scenario. 3.Run CORSIM for the specific scenario. 4. Read the CORSIM output file and extract the aggregated average delay value. 5. Repeat steps 3 and 4 for 10 different random number seeds. 6. Average the average delay values resulting from the 10 replications. 7. Save the values for all dependent and independent variables to a file. 8. Repeat steps 2 through 7 until all scenarios are simulated. This automated procedure allowed the complete process to be repeated, which was important because several model finetunings were needed during the model development process. Note that in step 3, a shell program called RunCOR 9 was used to execute CORSIM in the batch mode (i.e., command-line executable). RunCOR allowed CORSIM to be executed without the original TSIS shell program. Although TSIS comes with the scripting feature that allows multiple CORSIM runs to be executed continuously, steps 4 through 7 cannot be included in the script. Simulation Outputs The final output file from the automated procedure contains simulated results for average delay, merging section length, percent of heavy vehicles, green time and downstream free-flow speed. To model the relationships among these five variables, data for three of the variables were plotted individually, resulting in a total of 18 plots. Figure 3 shows a line plot for average delay against merging section length for various percentages of heavy vehicles at 10-second (s) green time and 45-mile-per-hour (mph) downstream freeflow speed. The relationships show that, as expected, the average vehicle delay decreases as the merging section length increases, and increases as the percentage of heavy vehicles increases. MINIMUM MERGING SECTION LENGTHS It can be observed in Figure 3 that the decrease in the average delay diminishes and eventually reaches a plateau where increasing the merging section length no longer significantly reduces the average delay. This suggests that the logical minimum merging section length should be one that corresponds to the transition point (i.e., where the line begins to turn flat). 42 ITE JOURNAL / MARCH 2001

4 Curve Fitting To help identify the transition points for all the lines more accurately and consistently, a curve was fitted through each line using the SPSS statistical package. A number of fitting functions were attempted. The shifted inverse function, defined as follows, was found to fit the lines the best: Average Delay 1 = 0 + (MSL where MSL is the merging section length and β 0, β 1 and β 2 are the regression coefficients. Figure 4 shows the fitted curves for the lines in Figure 3. Since the minimum lengths to be adopted are not likely to occur at the lower range of the x-axis of which the average delays are relatively high, the lower-range portion of the lines were excluded from the curve fitting. The exclusion has the benefit of improving the overall goodness-of-fit of the curves. The fitted curve for the line for 0 percent heavy vehicles (HV) in Figure 4, for example, is described by the following fitted formula: Average Delay = (MSL ) 2 ) Average delay (s/vehicle) Figure 3. Line plot for average delay (green time = 10 s; downstream free-flow speed = 45 mph). Average delay (s/vehicle) Merging section length (ft.) for MSL 125 ft. Determination of Initial Minimum Merging Section Lengths After all the fitted curves were found, their knee (i.e., the area of which the slope of the curve changes from sharp to flat) can be identified more easily and a standard slope can be adopted and applied to all curves. For design purposes, a more conservative value that corresponds to the lower end of the knee area was used. Accordingly, the minimum merging section length for the 0 percent HV curve was determined to be at about 200 feet (ft.). The slope corresponding to this 200-foot merging section length was computed as This slope was then used as the standard slope to determine the corresponding minimum merging section length for each of the other curves. For example, the minimum merging section length for the 5 percent HV curve can easily be shown to follow this equation: Figure 4. Fitted curves for lines in Figure 3. 1 MSL = where β 0 and β 1 are the regression coefficients for the 5 percent HV curve. The minimum merging section lengths for other green times and downstream freeflow speeds were similarly determined. All of the minimum merging section lengths were first scatter-plotted, as are shown with dotted points in Figure 5 for 45 mph downstream free-flow speeds. The figure shows the minimum merging section lengths for combinations of green times and percentage of heavy vehicles for a specific downstream free-flow speed. Merging section length (ft.) Determination of Final Minimum Merging Section Lengths It was observed in Figure 5 that the minimum merging section lengths (for a specific percentage of heavy vehicles) exhibit a linear relationship with the green times. Accordingly, straight lines were drawn through the sets of points by carefully observing the overall trends within each set of points as well as among the different sets of points. This manual approach, as opposed to using the regression technique to find the bestfitted curves, is desirable for developing empirical lines that show a certain level of regularities among the lines. A good example of the use of this approach is in the development of the speed-flow ITE JOURNAL / MARCH

5 Minimum merging section length (ft.) Green time Percent of heavy vehicles (s) 0% 5% 10% 15% 20% 25% 30% Downstream free-flow speed = 35 mph Downstream free-flow speed = 45 mph Downstream free-flow speed = 55 mph curves in the Highway Capacity Manual 10 for basic freeway sections. The drawn lines are also shown in Figure 5. The final minimum merging section lengths were then determined from these lines and are tabulated in Table 2 as a look-up table. To use the table, for example, for a triple left-turn designed for a green time of 40 seconds, 10 percent left-turn heavy vehicles and 45-mph downstream free-flow speed, the look-up minimum Green time (s) Figure 5. Minimum merging section lengths (downstream free-flow speed = 45 mph). Table 2. Minimum merging section lengths. merging section length is 310 ft. It should be noted that the minimum values given in Table 2 are shorter than those for freeway merging because vehicles in this case move at a much lower average speed as they have to accelerate from a stop position. SUMMARY AND CONCLUSIONS Triple left turns have been introduced as an alternative to handling at-grade signalized intersections that have severe leftturn capacity and operational problems. However, comprehensive guidelines for the installation of triple left turns do not exist. This paper has presented a study that aims to determine the minimum merging section lengths for triple left-turn lanes with downstream lane reductions. Simulation models were successfully developed to estimate the effects of different merging section lengths on average vehicle delay under various traffic and control scenarios. The average delay experienced by vehicles traveling on the downstream roadway were modeled through curve fitting as a function of merging section length, left-turn green time, left-turn heavy vehicle percentage and downstream free-flow speed. A look-up table for determining the minimum merging section lengths was developed based on a set of linear relationships that show the minimum merging section length: Increases linearly with the left-turn green phase length; Increases at a decreasing rate with percentage of heavy vehicles; and Increases at a decreasing rate with downstream free-flow speed. Although the simulation models produce results that give very logical relationships among all of the variables considered, further studies are needed to attempt to validate the simulated results with field data when they can be collected. The safety experience of triple left turns is currently being investigated as part of the same project. All triple left-turn guidelines, including those presented in this paper, should be fine-tuned further based on findings from the safety study. ACKNOWLEDGEMENTS The Florida Department of Transportation sponsored this research through a subcontract from the University of Florida, Gainesville, FL, USA. The author would like to thank her advisor, Dr. Albert Gan, for his guidance and support. The author would also like to thank Dr. John D. Leonard of the Georgia Institute of Technology for the use of his useful RunCOR shell program. References 1. Gan, A.C., and C.E. Wallace. Effectiveness, Criteria and Guidelines of Triple Left-turn 44 ITE JOURNAL / MARCH 2001

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