58 sec no of vehicles 419 vph 10000 cumulative

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Unformatted text preview: 1 1 10 0 100 10 20 30 Actual Data OU Fitting Distribution Normal Distribution Actual Data 70 80 Normal Distribution 120.00% 100.00% 100.00% Cumulative Percentage Cumulative Percentage 60 d 120.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 419 vph 40.00% 80.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 419 vph 60.00% 40.00% 20.00% 20.00% 0 .00% 0 .00% 0.01 50 OU Fitting Distribution c 60.00% 40 Interarrival Time (sec) Interarrival Time (sec) 80.00% Negative Exponential Distribution Negative Exponential Distribution 0.1 1 10 100 0 20 Actual Data Actual Data OU Fitting Distribution 40 60 80 100 120 Interarrival Time (sec) Interarrival Time (sec) OU Fitting Distribution Pearson Type III Distribution Pearson Type III Distribution e f Figure 11: Comparison of Actual Inter-arrival Times, OU Fitting Distribution, and Negative Exponential Distribution (a (Logarithmic Scale), b), Normal Distribution (c (Logarithmic Scale), d), Pearson Type III Distribution (e (Logarithmic Scale), f) for 419 vehicles/hour/passing lane 49 120.00% 120.00% 80.00% Cumulative Percentage Cumulative Percentage 100.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 518 vph 100.00% 60.00% 40.00% 20.00% 80.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 518 vph 60.00% 40.00% 20.00% 0.00% 0.01 0.1 1 10 100 0.00% 1000 0 Interarrival Time (sec) Actual Data OU Fitting Distribution 20 40 60 Actual Data OU Fitting Distribution a 120 140 Negative Exponential Distribution 120.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 518 vph 100.00% Cumulative Percentage Cumulative Percentage 80.00% 100 b 120.00% 100.00% 80 Interarrival Time (sec) Negative Exponential Distribution 60.00% 40.00% 20.00% 80.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 518 vph 60.00% 40.00% 20.00% 0.00% 0.01 0.1 1 10 100 0.00% Interarrival Time (sec) 0 10 20 30 40 50 60 70 Interarrival Time (sec) Actual Data OU Fitting Distribution Normal Distribution Actual Data OU Fitting Distribution c d 120.00% 100.00% 100.00% 80.00% 60.00% Cumulative Percentage 120.00% Cumulative Percentage Normal Distribution N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 518 vph 40.00% 20.00% 0.00% 0.01 80.00% 60.00% N = 126 Average = 7.204 sec Standard Deviation = 9.402 sec No. of Vehicles = 518 vph 40.00% 20.00% 0 .00% 0.1 1 10 100 0 10 20 30 Interarrival Time (sec) Actual Data OU Fitting Distribution 40 50 60 70 80 90 100 Interarrival Time (sec) Pearson Type III Distribution Actual Data e OU Fitting Distribution Pearson Type III Distribution f Figure 12: Comparison of Actual Inter-arrival Times, OU Fitting Distribution, and Negative Exponential Distribution (a (Logarithmic Scale), b), Normal Distribution (c (Logarithmic Scale), d), Pearson Type III Distribution (e (Logarithmic Scale), f) for 518 vehicles/hour/passing lane 50 The comparison of the proposed cumulative IAT distribution fit the actual data better than the three distributions given for the IATs. It should also be noted that the given mathematical distributions provide probability tables from which you can get the probability of given inter-arrival time. In the proposed method for determining cumulative IAT distribution one can only enter the hourly traffic volume and get the inter-arrival times for the given cumulative percentage values. The validation shows that this method produces fairly accurate cumulative IAT distributions in the hourly traffic count range the data was taken in. The cumulative IAT distributions show a fairly close hyperbolic relationship between higher percentile values and hourly traffic counts, as shown by the higher R2 values in Table 3 and Table 4. As expected, a similar hyperbolic relationship holds between the average IAT and the hourly traffic counts, as seen in Appendix A. The conversion approach presented here, using a least squares fit to get the best relationship between cumulative IATs and hourly traffic counts and implemented in an easy to use Excel spreadsheet works quite well. The observed relatively strong hyperbolic relationships between the IAT averages and the hourly traffic counts indicate that even under fairly different traffic flows with all their randomness, a robust relationship appears to exist between the average IAT and the hourly traffic count. Additional work using a representative sample of other sites will be required to demonstrate that this conversion approach is generally valid. 51 3.2 3.2.1 Description and Design of ARENA (SIMAN) Simulation Program Description of ARENA (SIMAN) Simulation Program ARENA simulation software research version 7.01 by Rockwell Automation was used to model the traffic flow in construction zone. ARENA software is designed to model queues. The software program takes the inter-arrival time probability density functions and service time probability density functions as inputs [26]. And the ARENA software can model multiple lanes as multiple queues. The vehicles entering the work zone was...
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