Vehicles begin arriving at a single toll-road booth at, Ask an Expert

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Vehicles begin arriving at a single toll-road booth at 8:00am at a time-dependent deterministic rate of λ(t) = 2 + 0.1t (with λ(t) in veh/min and t in minutes). At 8:07 A.M. the toll booth opens and vehicles are serviced at a constant deterministic rate of 6 veh/min. Assuming D/D/1 queuing, what is the average delay per vehicle from 8:00 A.M. until the initial queue clears and what is the delay of the 20th vehicle to arrive?

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