The Palace of Auburn Hills is trying to determine an appropriate level of staffi

Question

The Palace of Auburn Hills is trying to determine an appropriate level of staffing in order to meet demand during arrivals for a series of concerts scheduled for this summer. Past experience has shown that traffic tends to begin arrive at a rate of approximately 40 vehicles per minute during the period 120 to 60 minutes before each show. In the hour immediately prior, this rate increases to 60 vehicles per minute. Finally, once the show has begun, vehicles continue to arrive at a rate of 20 per minute until one hour after the concert start time. As vehicles arrive, they are processed into the parking facilities through one of several lines, each of which has a processing time of 10 seconds per vehicle. Given this Information, determine at what point a queue will form, when the queue will dissipate, the total system delay, maximum queue length, and longest vehicle delay assuming (hat there are: (1)4 lines open and (2) 8 lines open. Determine how many lines would need to be open In order to ensure that no delay is experienced.

Explanation / Answer

a. If four lines are open:

Expected waiting time / customer in the system = 10 - 6.68 = 3.32 secs.

After 6.62 secs queue will form in the 1st line.

At the peak time i.e. before 1 hr mean arrival time = 6 vehicles/ 10 secs.

So we require at least 6 lines so that no delay is experienced.

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