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 Interarrival 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 Interarrival 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 interarrival time. In the proposed method for determining
cumulative IAT distribution one can only enter the hourly traffic volume and get the
interarrival 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 interarrival 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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 Spring '13
 Mr.Kau
 Normal Distribution, ........., Cumulative distribution function, Driving Lane

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