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