Consider an M/M/1 queue with an arrival rate and the service rate . We havederived the

Chapter 8, Problem 1

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Consider an M/M/1 queue with an arrival rate and the service rate . We havederived the distribution function of the response time R. Now we are interestedin deriving the distribution function of the waiting time W. The waiting timeW is the response time minus the service time. To get started, first computethe conditional distribution of W conditioned on the number of jobs in the sys-tem, and later compute the unconditional distribution function. Note that Wis a mixed random variable since its distribution function has a jump equal toP(W = 0) at the origin.

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