Question: Consider an M=M=4 queue with no waiting room, for example, four prostitutes hanging out on a street corner. Customers arrive at times of a Poisson

Consider an M=M=4 queue with no waiting room, for example, four prostitutes hanging out on a street corner. Customers arrive at times of a Poisson process with rate 4. Each service takes an exponentially distributed amount of time with mean 1/2. If no server is free, then the customer goes away never to come back.

(a) Find the stationary distribution.

(b) At what rate do customers enter the system?

(c) Use W D L=a to calculate the average time a customer spends in the system.

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