Question: 70. For the infinite server queue with Poisson arrivals and general service distribution G, find the probability that (a) the first customer to arrive is

70. For the infinite server queue with Poisson arrivals and general service distribution G, find the probability that

(a) the first customer to arrive is also the first to depart.

Let equal the sum of the remaining service times of all customers in the system at time t.

(b) Argue that is a compound Poisson random variable.

(c) Find .

(d) Find .

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