What is the utilization rate of this service system?

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A small suburban post office is frequented by customers at the rate of 15 per hour. The post office has a single employee who typically processes each customer’s request at an average rate of 3 minutes per transaction. Assume that arrival rate follows a Poisson distribution and servicetime follows an exponential distribution. To determine the efficiency of operations, the postmaster wishes to examine several queue operating characteristics. a. What is the utilization rate of this service system? b. What is the average number of customers in line? c. What is the average time that each customer spends in the queue? d. What is the average time that each customer spends in the queue and being serviced? e. What is the probability that the post office employee will be idle?

 

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