# hmwk6 - ISyE 3232 J Dai and H Ayhan Stochastic...

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ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 J. Dai and H. Ayhan Homework 6 February 17, 2011 Please do not hand in; but you should have it done before the 1st test 1. A production line has two machines, Machine A and Machine B, that are arranged in series. Each job needs to processed by Machine A ﬁrst. Once it ﬁnishes the processing by Machine A, it moves to the next station, to be processed by Machine B. Once it ﬁnishes the processing by Machine B, it leaves the production line. Each machine can process one job at a time. An arriving job that ﬁnds the machine busy waits in a buﬀer. (The buﬀer sizes are assumed to be inﬁnite.) The processing times for Machine A are iid having exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the interarrival times of jobs arriving at the production line are iid, having exponential distribution with mean of 5 minutes. (a) What is the utilization of Machine A? What is the utilization of Machine B?
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