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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Question
Chapter 5, Problem 23P
To determine
The total delay and maximum queue length.
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Vehicles arrive at a single toll booth beginning at 7:00 A.M. at a rate of 8 veh/min. Service also starts at 7:00 A.M. at a rate of u(t)=6+0.2t where (f) is in vehicles per minute and it is in minutes after 7:00 A.M. Assuming D/D/1 queuing, determine when the queue will clear, the total delay, and the maximum queue length in vehicles.
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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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- 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)?arrow_forwardVehicles arrive at a single toll booth beginning at 8:00 AM. They arrive and depart according to a uniform deterministic distribution. However, the toll booth does not open until 8:10 AM. The average arrival rate is 8 veh/min and the average departure rate is 10 veh/min. Assuming D/D/1 queuing, when does the initial queue clear and what are the total delay, the average delay per vehicle, longest queue length (in vehicles), and the wait time of the 100th vehicle to arrive (arrow_forwardThe arrival rate at a parking lot is 6 veh/min. Vehicles start arriving at 6:00 P.M., and when the queue reaches 36 vehicles, service begins. The company policy states that the total vehicle delay should be equal to 500 veh-min. Assuming D/D/1 queuing and a constant service rate, determine the maximum queue length.arrow_forward
- At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of (t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of (t) = 2.1 + 0.3t ((t) and (t) are in vehicles per minute and t is in minutes after 8:00 A.M.). Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears?arrow_forwardAt 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of (t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of (t) = 2.1 + 0.3t ((t) and (t) are in vehicles per minute and t is in minutes after 8:00 A.M.). Assuming D/D/1 queuing, what is the maximum queue length, and what would the total delay be from 8:00 A.M. until the queue clears? (Also Draw the D/D1)arrow_forwardPassenger car arrive at the stop sign at an average rate of 280 per hour. Average waiting time at the stop sign is 12 sec. If both arrivals and departure are exponentially distributed, what would be the average delay per vehicle in minutes. Assume both arrival and departure rates are exponentially distributed.arrow_forward
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