5.4.4 Customers arrive at a service facility according to a Poisson process of intensity

. The service times Y1;Y2; : : : of the arriving customers are independent random variables having the common probability distribution function G.y/ D PrfYk yg. Assume that there is no limit to the number of customers that can be serviced simultaneously; i.e., there is an infinite number of servers available. LetM.t/ count the number of customers in the system at time t. Argue that M.t/ has a Poisson distribution with mean pt, where

Transcribed Image Text:

p=t[1-G(y)]dy. 0