Question: 63. Consider an infinite server queuing system in which customers arrive in accordance with a Poisson process with rate , and where the service distribution

63. Consider an infinite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. LetI mage denote the number of customers in the system at time t. Find

(a) ;

(b) .

Hint: Divide the customers in the system at timeI mage into two groups, one consisting of “old” customers and the other of “new”

customers.

(c) If there is currently a single customer in the system, find the probability that the system becomes empty when that customer departs.

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