Suppose that a customer of the M/M/1 system spends the amount of time x >0 waiting in queue before entering service.

(a) Show that, conditional on the preceding, the number of other customers that were in the system when the customer arrived is distributed as 1+P, where P is a Poisson random variable with mean λ.

(b) Let W

∗

Q denote the amount of time that an M/M/1 customer spends in queue. As a by-product of your analysis in part (a), show that

Transcribed Image Text:

P{Wx}= 1- AWAY if x=0 +(1-e-(-x) if x>0