Vehicles begin arriving at an amusement park 1 hour before the park opens, at a rale of four vehicles per minute. The gale to the parking lot opens 30 minutes before the park opens. If the total delay to vehicles entering the parking lot is 3600 vehicle-minutes, (a) how long after the first vehicle arrival will the queue dissipate and (b) what is the average service rate at the parking lot gate? Assume a D/D/l queueing system at the parking lot gate.

a) ≈ 30 mins

b) 8 vpm

Explanation:

a) Determine how long after the first vehicle arrival will the queue dissipate

The time after the arrival of the first vehicle for the queue to dissipate

= 29.9 mins ≈ 30 mins

b) Determine the average service rate at the parking lot gate

U = A / t

where : A = 240 vehicles , t = 30

U = 240 / 30 = 8 Vpm

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