The purpose of a shop drawing

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Chapter 1, Problem 8RQ

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The purpose of a shop drawing

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Vehicles arrive at a single park-entrance booth where a brochure is distributed. At 8 A.M., there are 20 vehicles in the queue and vehicles continue to arrive at the deterministic rate of λ(t) = 4.2 − 0.1t, where λ(t) is in vehicles per minute and t is in minutes after 8:00 A.M. From 8 A.M. until 8:10 A.M., vehicles are served at a constant deterministic rate of three per minute. Starting at 8:10 A.M., another brochure-distributing person is added and the brochure-service rate increases to six per minute (still

Vehicles arrive at a single park-entrance booth where a brochure is distributed. At 8 A.M., there are 20 vehicles in the queue and vehicles continue to arrive at the deterministic rate of λ(t) = 4.2 − 0.1t, where λ(t) is in vehicles per minute and t is in minutes after 8:00 A.M. From 8 A.M. until 8:10 A.M., vehicles are served at a constant deterministic rate of three per minute. Starting at 8:10 A.M., another brochure-distributing person is added and the brochure-service rate increases to six per minute (still at a single booth). Assuming D/D/1 queuing, determine the longest queue, the total delay from 8 A.M. until the queue dissipates; and the wait time of the 40th vehicle to arrive.

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?