PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
Publisher: WILEY
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Textbook Question
Chapter 5, Problem 27P
At a parking lot, vehicles arrive according to a Poisson process and are processed (parking fee collected) at a uniform deterministic rate at a single station. The mean arrival rate is 4.2 veh/min and the processing rate is 5 veh/min. Determine the average length of queue, the average time spent in the system, and the average waiting time in the queue.
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1. Estimate the queue dissipation time, maximum queue length, and total delay, given:
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Departure Rate (veh/hour/lane)
3:30 4:00 PM
4:00 8:00 PM
3:00 - 3:30 PM
1200
1800
1200
1200
900
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At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 1200
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Queue Analysis - Numerical
M/M/N
- Average length of queue
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- Average time waiting in queue
- Average time spent in system
A = arrival rate
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= departure rate
M/M/N - More Stuff
1
- Probability of having no vehicles
1
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pN
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n = n! N!(1-p/N)
- Probability of having n vehicles
p"Po
for n ≤N
n!
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P₁ =
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- Probability of being in a queue
PAN
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A = arrival rate
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P/N
The gate entrance to a park opens at 8:00 AM and there are 18 vehicles in the queue waiting to enter. Vehicles continue to arrive (from
8:00 AM onward) at a constant rate of 8 veh/min. The gate attendant processes vehicles at a constant rate of 1 vehicle every 6
seconds. Assume D/D/1 queuing for the vehicle arrival and departure processes at this gate. What is the average delay per vehicle
(min/veh) from 8:00 AM until the queue clears?
0.9
1.1
4.5
9
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81
Chapter 5 Solutions
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
Ch. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10P
Ch. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - The arrival rate at a parking lot is 6 veh/min....Ch. 5 - Prob. 16PCh. 5 - At the end of a sporting event, vehicles begin...Ch. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Vehicles begin arriving at a single toll-road...Ch. 5 - Vehicles begin to arrive at a toll booth at 8:50...Ch. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Vehicles begin to arrive at a parking lot at 6:00...Ch. 5 - At a parking lot, vehicles arrive according to a...Ch. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Vehicles arrive at a recreational park booth at a...Ch. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37PCh. 5 - A truck weighing station has a single scale. The...Ch. 5 - Prob. 39PCh. 5 - Prob. 40PCh. 5 - Vehicles leave an airport parking facility (arrive...Ch. 5 - Vehicles begin to arrive at a parking lot at 7:45...Ch. 5 - Prob. 43PCh. 5 - Prob. 44PCh. 5 - Prob. 45PCh. 5 - Prob. 46PCh. 5 - Prob. 47PCh. 5 - Prob. 48PCh. 5 - Prob. 49PCh. 5 - Prob. 50PCh. 5 - Prob. 51PCh. 5 - Prob. 52PCh. 5 - A theme park has a single entrance gate where...Ch. 5 - Prob. 54PCh. 5 - Prob. 55P
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