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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.
a) 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?
b) Refer to the information above. The postmaster has been receiving complaints from customers about long waiting time. The postmaster is considering hiring an additional employee who will also be able to process each customer's request at the same rate of 3 minutes per transaction. Assume that the post office pays its employees $12 per hour and that the cost of customer waiting time in terms of customer dissatisfaction and good will is $10 per hour. Assume that arrival rate follow a Poisson distribution and service time follows an exponential distribution. Should the post master hired an additional employee? Compare the total costs of this two employee system with the old single-server queuing system.
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