Principles of Highway Engineering and Traffic Analysi (NEW!!)
6th Edition
ISBN: 9781119305026
Author: Fred L. Mannering, Scott S. Washburn
Publisher: WILEY
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Chapter 5, Problem 38P
A truck weighing station has a single scale. The time between truck arrivals at the station is exponentially distributed with a mean arrival rate of 1.6 veh/min. The time it takes vehicles to be weighed is exponentially distributed with a mean rate of 2.1veh/min. When more than five trucks are in the system, the queue backs up onto the highway and interferes with through traffic. What is the probability that the number of trucks in the system will exceed 5?
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2.) Queuing Theory:
At a single toll booth, you were able to observe an average vehicle arrival rate of 10 vehicles per minute starting from 7:00 AM. 30 minutes later, average vehicle arrival rate has become 4 vehicles per minute and continues throughout the day at that rate. If the toll booth is able to process one vehicle every 10 seconds, how many minutes after 7:00 AM will the first queue clear up? What is the longest queue length, expressed in number of vehicles? Assume a D/D/1 queuing model.
10-Trucks begin to arrive at a truck weigh station (with a single scale) at 6:00 A.M. at a deterministic
but time-varying rate of 2(t)= 4.3-0.22t where (t) is in veh/min and t is in minutes. The departure
rate is a constant 2 veh/min (time to weigh a truck is 30 seconds). When will the queue that forms be
cleared, what will be the total delay, and what will be the maximum queue length?
At a toll booth, vehicles arrive with a mean arrival rate of 2 vehicles per minute and
they are processed with a mean rate of 6 vehicles per minute. Determine the
average length of queue, the average time spent in the toll booth, and the average
waiting time if the vehicles arrive according to a Poisson process and
they are processed at a uniform deterministic rate.
they are processed at an exponential rate.
a)
b)
Chapter 5 Solutions
Principles of Highway Engineering and Traffic Analysi (NEW!!)
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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