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For multiple server models please use the approximate formulae and check your answers using Excel software....

For multiple server models please use the approximate formulae and check your answers using Excel software. Students arrive at an administrative services office at an average of one every 15 minutes, and their requests take, on average, 10 minutes to be processed. The service counter is staffed by only one clerk who works eight hours per day. Assume exponential inter-arrival time and service times. a. What percentage of time is server idle? b. How much time, on average, does a student spend waiting in line? c. How long is the (waiting) line, on average?

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Answer #1

arrival rate = lambda =60/ 15 = 4 per hour

service rate = mu = 60/10=6 per hour

Proportion of the time server is busy = 4/6 =0.666

Proportion of idle time = 1-0.6666 =0.3333 =33.33%

Waiting time in line Wq = lambda / mu ( mu-lambda)

= 4/6 (6-4) =0.33 hour

Size of the line = Lambda x Wq

= 0.33 x4 = 1.32 persons

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