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10 December, 23:46

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 μ (t) = 6 + 0.2t where μ (t) is in vehicles per minute and t 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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  1. 11 December, 00:10
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    Queue will clear at 7:30 AM

    The total delay = 10.55 min

    The maximum queue length in vehicles = 54 Veh

    Explanation:

    Vehicles arrival rate = 8 Veh/min.

    vechicles deparature rate = 6.2 Veh/min

    Queue in one minute = 8-6.2

    = 1.8Veh/min

    Queue clear time = 8-6/0.2

    = 30 minutes

    Total delay time = 19/1.8

    =10.55 min

    Maximum queue length

    = 30x1.8

    =54 Veh

    Queue will clear

    by 7:30 AM
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