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.
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.
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