5 10 points You are assigned the task of modeling a singlese

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 (L_Q) and (2) average delay in queue for each customer (w_Q).

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, L_Q and w_Q.

Solution

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.