stat week 5

Customer Service (M/M/1)

A local fast food restaurant has a drive thru operation that has a single server. Customers arrive, on average, every 5 minutes and can be served, on average, every 4 minutes. The management has found that the arrival pattern follows the Poisson distribution while the service times tend to follow the exponential distribution. Assuming that the calling population size is infinite and the queue length is unrestricted, answer the following:

a. What is the server utilization? b. How many customers, on average, are waiting to be served? c. How long does it take the average customer to move through the system

(waiting plus service)? d. How many customers, on average, are in the system at any given time?