SOLUTIONS MANUAL for Stochastic Modeling: Analysis and ...

It appears that there will be very little queueing even with the minimum of 2 forklifts.
31. We first approximate the drive-up window as an M/M/s/4 queue with λ 1 = 1/2
customer/minute and µ 1 = 1/1.8 customer/minute. (This approximation is rough
because the true service-time distribution is more nearly normal, and ε s < 1.)
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s π 4
1 0.16
2 0.03
π 4 is the probability that an arriving car will find the queue full and thus have to park.
Adding a window reduces this dramatically.
The rate at which customers are turned away from the drive-up window is λ 1 π 4 =
(1/2)π 4 . Therefore, the overall arrival rate into the bank is λ 2 =1+(1/2) π 4 customers
per minute. This process will not be a Poisson process, but we approximate it as one.
As a first cut we model the tellers inside the bank as an M/M/s 2 queue with µ 2 =1/1.4
customer/minute.
(s 1 ,s 2 ) λ 2 w q (minutes)
(1, 2) 1.08 1.9
(2, 2) 1.02 1.5
(1, 3) 1.08 0.2
The bank can now decide which improvement in performance is more valuable.
Comment: The approximation for the inside tellers can be improved by using the
GI/G/s adjustment. Clearly, ε s =1.0/(1.4) 2 ≈ 0.5.Theexactvalueofε a can also be
computed, but requires tools not used in this book, so set ε a = 1 for a Poisson process.
32. No answer provided.
33. No answer provided.
34. No answer provided.
35. No answer provided.