Summary: ISyE 6656 Exam # 2
Please be neat and show all your work so that I can give you partial credit.
(30) 1. Consider a single-server model with Poisson input and an average cus-
tomer arrival rate of 30/hr. Currently, service is provided by a mechanism that
takes exactly 1.5 min.
(a) Is the current system stable? Justify your answer.
(b) Now suppose that the system can be served instead by a mechanism that has
an exponential service time distribution. What must be the mean service time of
this mechanism to ensure the same long run average waiting time in the system?
(40) 2. The arrival process of customers at a taxi stand is Poisson with rate
and the arrival process of the of taxis at the stand is Poisson with rate µ.