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9-2: The following data has been collected from a hospital pharmacy. This system operates as a single server, single channel system.

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                                        7-3pm                3-11pm               11-7am

Service rate per hr        200                     100                       50

Arrival rate per hr        60                       50                        40


The service rate can be increased or decreased in increments of 50 prescriptions per hour. The expense associated with each 50-prescription increment is $100. In other words, to be able to process 50 additional prescriptions will cost an additional $100 per hour. If the current rate of processing or service is lowered by 50 prescriptions per hour, the savings are $100 per hour. Using queuing theory, describe this service system. What is:


a. The probability that the clinic is idle—no patients waiting or being served?

b. The average number of patients in the system?

c. The average time (hours) a patient spends in the system (waiting + service time)?

d. The average number of patients in the queue waiting for service?

e. The average time (hours) a patient spends in the queue waiting?

f. The probability that a patient, upon arrival, must wait?


Given the associated costs, should the service rate be changed? What are the financial implications associated with your recommendations?