Tutorial: Vehicle Entry Headway Distribution

Main Page > Tutorials > Vehicle Entry Headway Distribution Vehicle Entry Headway Distribution Two types of vehicle entry distributions can be specified: Uniform or Random. For a uniform distribution, each vehicle will enter at the same headway, i.e., 3600 s/h divided by the entry volume (in veh/h). For example, an entry volume 1800 veh/h will result in a vehicle entering the network every 2 seconds. If the ‘Random’ distribution type is selected, two different distributions will be used, as follows:
 * Entry flow rate < 900 veh/h/ln &#8594; Negative Exponential distribution
 * Entry flow rate ≥ 900 veh/h/ln &#8594; Normal distribution
 * The standard deviation for the Normal distribution is calculated as: (Average Headway × Number of Lanes - MinArrivalHeadway) / 2.5
 * The minimum arrival headway is calculated as: DesiredHeadwayMultiplier × 1.1 + (StopGap + MinVehLength) / DesiredSpeed

Average Entry Headway  Average entry headway is calculated from headway results from the Link_Lane_Detector output file to match the Average Headway given in Detector Aggregate output file. Average entry headway is calculated through the equation, the number of vehicles, $$ N $$, traversing link during simulation time is, $$ N=N'-1$$, $$ N'$$ is the total number of vehicles which has Actuation Time On (from Link_Lane_Detector output file) greater than warm-up time.

Entry Headway Distribution Entry headway distribution (random) is validated by counting frequencies of headways from the HeadwayDataOutput.csv file. First, filter out headway data of target entry node. Second, set up a series of bins with equal width (set lower bounds and upper bounds), count the number of headways within each bin (through countifs function in Excel). Finally, headway frequency distribution is plotted through Excel to validate the stated distribution (uniform, negative exponential or normal arrival). The target link/segment is shown in right figure.

Simulation Setup
 * Load network file under SwashSim &#8594; File &#8594; Project Properties, the network file MediumFreeway.nwf is downloaded from github.
 * Detectors can be added through Table View &#8594; Set Detector(s) for each segment. One detector (48.8 Position%, 48.8 Position (ft), 6 Length (ft)) is added to OnRamp segment (3, 602) to monitor entry vehicles pass through middle of link 3602 for average headway validation. The vehicle entry headway distribution is verified based on the vehicle headway at node 703 from HeadwayDataOutput file.
 * Change desired Entry flow rate and type of vehicle arrival distribution under Table View &#8594; Traffic Data. Average vehicle headway is validated for both uniform (2000 veh/h) and random (850 veh/h for negative exponential dist. and 2000 veh/h for normal dist.) arrival distribution. Entry headway distribution validation is conducted for both uniform and random arrival scenario.
 * Run simulation with 3 replications, 300s warm-up time and 1800s simulation time. Check Link Performance Measure Data, Detector Aggregate Measures Data, Detector Vehicle Actuation Data, Vehicle Headway Data under Output Options. Check Vehicle Time Step Data customized for LinkID 7033, 3602.

Results
 * Uniform Entry Headway
 * Simulation Environment: 300s warm-up time, 1800s simulation time, 3 replications, vehicle arrival distribution: uniform, entry flow rate: 2000 veh/h, target entry node for headway distribution verification: 703, target link for average headway verification: 3-602; Seed number: 1,0,1,3651,5999,3092,7165; 1,0,2,5480,5414,8474,9906; 1,0,3,7691,8869,3708,8947.
 * Average Headway Verification Calculate average headway from Link_Lane_Detector output file of detector locates in the middle of link 3-602, and match result with that from DetectorAggregateMeasures output file, see Table 1.
 * Entry Headway Distribution Verification There are 3502 vehicles enter the network through node 703. The minimum and maximum value of Revised Headway Value from HeadwayDataOutput file are both 1.8, indicates that entry headway is uniform/identical. For comparison, headway distribution of detector locates in the middle of link 3-602 is plotted, see figure Target link/segment. The headways are no longer identical.3602_headway_distribution.png
 * Negative Exponential Distributed Entry Headway
 * Simulation Environment: 300s warm-up time, 1800s simulation time, 3 replications, vehicle arrival distribution: random (exponential), entry flow rate: 850 veh/h, target entry node for headway distribution verification: 703, target link for average headway verification: 3-602; Seed number: 1,0,1,6114,5442,4665,8408; 1,0,2,3221,9936,6491,3901; 1,0,3,7003,3756,9738,7706.
 * Average Headway Verification Calculate average headway from Link_Lane_Detector output file of detector locates in the middle of link 3-602, and match result with that from DetectorAggregateMeasures output file, see Table 2.
 * Entry Headway Distribution Verification There are 1445 vehicles enter the network through node 703. The minimum and maximum value of Revised Headway Value from HeadwayDataOutput file are 0.77 and 37.41. See figure Entry Headway Distribution of 850 veh/h flow rate.
 * Normal Distributed Entry Headway
 * Simulation Environment: 300s warm-up time, 1800s simulation time, 3 replications, vehicle arrival distribution: random (normal), entry flow rate: 2000 veh/h, target entry node for headway distribution verification: 703, target link for average headway verification: 3-602; Seed number: 1,0,1,4044,317,2414,9722; 1,0,2,6613,6742,805,1763; 1,0,3,8801,9127,9346,7502.
 * Average Headway Verification Calculate average headway from Link_Lane_Detector output file of detector locates in the middle of link 3-602, and match result with that from DetectorAggregateMeasures output file, see Table 3.
 * Entry Headway Distribution Verification There are 4662 vehicles enter the network through node 703. The minimum and maximum value of Revised Headway Value from HeadwayDataOutput file are 1.32 and 2.29. See figure Entry Headway Distribution of 2000 normal veh/h flow rate. Standard deviation and average headway is 0.1852 and 1.8028 based on HeadwayDataOutput file. The DesiredHeadwayMultiplier is 1 from SwashSim &#8594; Setting &#8594; Drivers. Minimum vehicle length is 14.78 ft. Desired Speed is 95.69 by averaging desired speed in TSD files. Number of lanes is 1. Then minimum arrival headway is 1.254 and standard deviation by calculation is 0.2193, close to 0.1852.