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.

Question

Leonidas Brady

Engineering

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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Fatty · Answer 1

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