At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of λ(t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of μ(t) = 2.1 + 0.3t [λ(t) and μ(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?
At 8:00 A.M. there are 10 vehicles in a queue at a toll booth and vehicles are arriving at a rate of λ(t) = 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being serviced at a rate of μ(t) = 2.1 + 0.3t [λ(t) and μ(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?
Traffic and Highway Engineering
5th Edition
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Garber, Nicholas J.
Chapter6: Fundamental Principles Of Traffic Flow
Section: Chapter Questions
Problem 26P: The arrival times of vehicles at the ticket gate of a sports stadium may be assumed to bePoisson...
Related questions
Question
At 8:00 A.M. there are 10 vehicles in a queue at
a toll booth and vehicles are arriving at a rate of λ(t)
= 6.9 − 0.2t. Beginning at 8 A.M., vehicles are being
serviced at a rate of μ(t) = 2.1 + 0.3t [λ(t) and μ(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?
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