Evaluate the waiting line properties of the following customer service operation

Question

Evaluate the waiting line properties of the following customer service operation. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with an average interarrival time of 20 minutes. The time to service for a customer is exponentially distributed with a mean of 15 minutes.

A) What is the total time in the system for this service?

B) Determine the average number of people waiting for the service.

C) If the server worked an 8 hour day, how many hours on average, would the server be busy?

You can use excel to solve this problem.

Explanation / Answer

This is a M/M/1 queque system with following parameters

Arrival rate, = 60/20 = 3 per hour

Service rate, = 60/15 = 4 per hour

A) Total time in system, W = 1/(-) = 1/(4-3) = 1 hour

B) Average number of people waiting for service, Lq = 2/(*(-)) = 32/(4*(4-3)) = 2.25

C) Utilization rate = / = 3/4 = 0.75

Average number of busy hours in an 8 hour day = 8*utilization rate = 8*0.75 = 6 hours

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