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

Question:

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

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

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

(c) Find E[S(t)].

(d) Find Var(S(t)).

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