Traffic and Highway Engineering
5th Edition
ISBN: 9781305156241
Author: Garber, Nicholas J.
Publisher: Cengage Learning
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Question
Chapter 6, Problem 27P
To determine
(a)
The average number of vehicles waiting to be served at the booth.
To determine
(b)
The length of the ramp to provide storage of all vehicles for
To determine
(c)
The average waiting time at the tollbooth before being served.
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The rate of arrival of vehicles at the expressway can be considered to be Poisson with a mean of 45 veh/hr, and the rate of service to vehicles can be assumed to be exponentially distributed with a mean of 1 min. (a) What is the average number of vehicles waiting to be served at the booth (that is, the number of vehicles in queue, not including the vehicle being served)? (b) What is the length of the ramp required to provide storage for all exiting vehicles 90% of the time? Assume the average length of a vehicle is 18 ft and that there is an average space of 10 ft between consecutive vehicles waiting to be served. (c) What is the average waiting time a driver waits before being served at the tollbooth (that is, the average waiting time in the queue)?
At the exit of a toll gate with a single booth, vehicles arrive at random at a rate of 20 vehicles per minute. The
service has an average rate of 22 vehicles per minute. However, due to variable toll fees, the service is also
random with an average rate of 22 vehicles per minute.
Estimate average waiting time of vehicles
O 0.45
0.35
O 0.65
0.55
At exactly 8:05AM, vehicles start to
enter a single toll gate at rate of
7veh/min following deterministic
distribution. Due to teller being late,
the toll booth opened at 8:20AM
having a service rate of 8.5veh/min.
Determine the time of queue dissipation,
total vehicles at queue dissipation, longest
vehicle delay, longest vehicle queue, total
vehicle delay, and average delay per vehicle.
Chapter 6 Solutions
Traffic and Highway Engineering
Ch. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3PCh. 6 - Prob. 4PCh. 6 - Prob. 5PCh. 6 - Prob. 6PCh. 6 - Prob. 7PCh. 6 - Prob. 8PCh. 6 - Prob. 9PCh. 6 - Prob. 10P
Ch. 6 - Prob. 11PCh. 6 - Prob. 12PCh. 6 - Prob. 13PCh. 6 - Prob. 14PCh. 6 - Prob. 15PCh. 6 - Prob. 16PCh. 6 - Prob. 17PCh. 6 - Prob. 18PCh. 6 - Prob. 19PCh. 6 - Prob. 20PCh. 6 - Prob. 21PCh. 6 - Prob. 22PCh. 6 - Prob. 23PCh. 6 - Prob. 24PCh. 6 - Prob. 25PCh. 6 - The arrival times of vehicles at the ticket gate...Ch. 6 - Prob. 27P
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