k 0258 where t average of the sample t 520 seconds

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Unformatted text preview: onds, for 15 minute time interval where no. of vphpl was 698) α = 0.1 user selected parameter greater than or equal to zero that affects the shift of the distribution (IATs less than this value will have a 0 probability) e= constant parameter, 2.71828 Γ ( K ) = gamma function, equivalent to ∫ ∞ 0 e − x x K −1dx for all K ≥ 0 Cumulative IAT values used in Figure 9 e, f are given below in Table 13. The cumulative probabilities were obtained by numerically integrating the f(t), equation (3) using ∆t of 0.10 seconds (Matlab trapezoidal rule). 43 Table 13: Cumulative Percentage Values used for Pearson Type III Distribution in OU Fitting Distribution Comparison Graph (Figure 9 e, f) Cumulative Percentage 0.40% 4.75% 11.50% 18.60% 25.60% 32.32% 38.64% 44.53% 49.96% 54.95% 59.50% 63.64% 67.40% 70.80% 73.86% 76.62% 79.11% 81.34% 83.34% 85.13% 86.73% 88.16% 89.44% 90.59% 91.61% 92.52% 93.33% IAT (sec) 0.1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 Cumulative Percentage 94.05% 94.69% 95.77% 96.22% 96.63% 96.98% 97.30% 97.58% 97.83% 98.05% 98.25% 98.42% 98.58% 98.72% 98.84% 98.95% 99.04% 99.13% 99.20% 99.27% 99.33% 99.38% 99.42% 99.46% 99.50% 99.53% 99.56% IAT (sec) 13.5 14 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 Cumulative Percentage 99.58% 99.61% 99.63% 99.64% 99.66% 99.67% 99.68% 99.69% 99.70% 99.71% 99.72% 99.73% 99.73% 99.74% 99.74% 99.75% 99.75% 99.75% 99.75% 99.76% 99.76% 99.76% 99.76% 99.76% 99.77% 100.00% IAT (sec) 27.5 28 28.5 29 29.5 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 38 38.5 39 39.5 40 The comparison graphs for driving lane are given in Figure 7, Figure 8, and Figure 9, and the graphs for passing lane are given in Figure 10, Figure 11, and Figure 12. 44 1.2 1.2 0.8 Cumulative Percentage Cumulative Percentage 1 N = 117 Average = 7.509 sec Standard Deviation = 6.698 sec No. of Vehicles = 469 vph 1 0.8 N = 117 Average = 7.509 sec Standard Deviation = 6.698 sec No. of Vehicles = 469 vph 0.6 0.6 0.4 0.4 0.2 0.2 0 0.01 0.1 Actual Data 1 10 Interarrival Time (sec) OU Fitting Distribution 100 0 1000 0 Negative Exponential Distribution 20 40 Actual Data 60 80 Interarrival Time (sec) OU Fitting Distribution a 1 Cumulative Percentage Cumulative Percentage N = 117 Average = 7.509 sec Standard Deviation = 6.698 sec No. of Vehicles = 469 vph 0.8 0.8 N = 117 Average = 7.509 sec Standard Deviation = 6.698 sec No. of Vehicles = 469 vph 0.6 0.6 0.4 0.4 0.2 0.2 0 0.01 0 0.1 1 10 100 0 10 20 Interarrival Time (sec) Actual Data OU Fitting Distribution 30 40 50 Interarrival Time (sec) Normal Distribution Actual Data OU Fitting Distribution c Normal Distribution d 1.2 1.2 Cumulative Percentage 1 Cumulative Percentage 140 1.2 1 0.8 N = 117 Average = 7.509 sec Standard Deviation = 6.698 sec No. of Vehicles = 469 vph 0.4 0.2 1 0.8 0.6 N = 117 Average = 7.509 sec Standard Deviation = 6.698 sec No. of Vehicles = 469 vph 0.4 0.2 0 0.01 120 b 1.2 0.6 100 Negative Exponential Distribution 0 0.1 1 10 100 0 10 20 Interarrival Time (sec) Actual Data OU Fitting Distribution 30 40 50 60 70 Interarrival Time (sec) Pearson III Distribution Actual Data e OU Fitting Distribution Pearson III Distribution f Figure 7: 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 469 vehicles/hour/driving lane 80 45 120.00% 120.00% 100.00% 80.00% Cumulative Percentage Cumulative Percentage 100.00% N = 145 Average = 6.243 sec Standard Deviation = 4.897 sec No. of Vehicles = 581 vph 60.00% 40.00% 20.00% 80.00% 60.00% N = 145 Average = 6.243 sec Standard Deviation = 4.897 sec No. of Vehicles = 581 vph 40.00% 20.00% 0 .00% 0.01 0.1 1 10 100 0.00% 1000 0 Interarrival Time (sec) 20 40 60 80 100 120 Interarrival Time (sec) Actual Data OU Fitting Distribution Negative Exponential Distribution Actual Data OU Fitting Distribution a Negative Exponential Distribution b 120.00% 120.00% 100.00% Cumulative Percentage Cumulative Percentage 100.00% N = 145 Average = 6.243 sec Standard Deviation = 4.897 sec No. of Vehicles = 581 vph 80.00% 60.00% 40.00% 80.00% 60.00% N = 145 Average = 6.243 sec Standard Deviation = 4.897 sec No. of Vehicles = 581 vph 40.00% 20.00% 20.00% 0 .00% 0.00% 0.01 0 0.1 1 10 5 10 100 15 20 25 30 35 40 45 Interarrival Time (sec) Interarrival Time (sec) Actual Data Actual Data OU Fitting Distribution OU Fitting Distribution c d 120.00% 100.00% Cumulative Percentage Cumulative Percentage 120.00% 80.00% 60.00% N = 145 Average = 6.243 sec Standard Deviation = 4.897 sec No. of Vehicles = 581 vph 40.00% 20.00% 100.00% 80.00% 60.00% N = 145 Average = 6.243 sec Standard Deviation = 4.897 sec No. of Vehicles = 581 vph 40.00% 20.00% 0.00% 0 .00% 0.01 Normal Distribution Normal Distribution 0.1 1 10 100 0 10 20 Actual Data OU Fitting Distribution 30 40 50 60 Interarrival Time (sec) Interarrival Time (sec) Pearson III...
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This document was uploaded on 02/26/2014 for the course E 515 at University of Louisiana at Lafayette.

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