5. (10 points) You are assigned the task of modeling a single-server queuing sys

Question

5. (10 points) You are assigned the task of modeling a single-server queuing system as a simulation model. Historical data gives strong evidence that the arrival process is Poisson with a arrival rate of lambda= 2 per hour. Service time, however, is much more open to interpretation. The average service time is 24 minutes.

a. If you assume the service process is also a Poisson process, then the model you might consider is the M/M/1 model. Under this assumption, what are the steady-state (1) average number of customers in queue (LQ) and (2) average delay in queue for each customer (wQ).

b. You are uncomfortable with the Poisson process assumption for service times, so choose to model this part of the model with a general distribution, yielding the M/G/1 queuing model. If historical data for service times have an average of 24 minutes, and a standard deviation of 10 minutes, then what are the new calculated values for the steady-state parameters, LQ and wQ.

Explanation / Answer

Average customers = 60/24 = 2.5 per hour

Average delay in queue<= 24 minutes

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z = (x-24)/10 follows a normal distribution with (0,1) as parameters.

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