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Civil Engineering
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 λ(t) = 4.3 − 0.22t [λ(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?

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 λ(t) = 4.3 − 0.22t [λ(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?

Traffic and Highway Engineering
Traffic and Highway Engineering
5th Edition
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Garber, Nicholas J.
Chapter12: Forecasting Travel Demand
Section: Chapter Questions
Problem 16P
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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 λ(t) = 4.3 − 0.22t [λ(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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