PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
PRIN.OF HIGHWAY ENGINEERING&TRAFFIC ANA.
7th Edition
ISBN: 9781119610526
Author: Mannering
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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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)
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?
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