Problem 10-6 Students arrive at the Administrative Services Office at an average

Question

Problem 10-6

Students arrive at the Administrative Services Office at an average of one every 5 minutes, and their requests take on average 3 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

Students arrive at the Administrative Services Office at an average of one every 5 minutes, and their requests take on average 3 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

Explanation / Answer

arrival rate, lambda = 5 min = 12/hr

service time,mu = 3 min = 20/hr

only 1 clerk, M = 1

A)

% of time judy is idle = (1-rho) = 1-[lambda/(M*mu)] = 1-12/20 = 8/20 = 2/5 = 40%

B)

Wq = lambda/[mu*(mu-lambda)] = 12/(20*(20-12)) = .075 hr

C)

Lq = Wq*lambda = .075*12 = .9 student

D)

Arriving student will find atleast one student waiting in line means atleast 2 student in system,

= P(>2)=1-P(<2) = 1-(1-(lambda/mu)^2) = 12/20 = (3/5)^2 = .36

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