Students arrive at the Administrative Services Office at an average of one every 15 minutes, and...
- Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take, on average, 12 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. Use the Q.xls calculator to answer the following questions.
- What percentage of time is Judy idle?
- How long is the (waiting) line, on average (Lq)?
- How much time, on average, does a student spend waiting in line (Wq)?
Homework Answers
λ = Arrival rate = 60 / 15 = 4 per hour
μ = service rate = 60 / 12 = 5 per hour
A. Utilization = λ / μ = 4 / 5 = 0.8
Idle time = 1 - utilization = 1 - 0.8 = 0.2 or 20%
B. Lq = λ^2 / μ(μ - λ)
= (4 * 4) / 5 (5 - 4) = 3.2 customers
C. Wq = Lq / λ = 3.2 / 4 = 0.8 hours
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