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

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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 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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Introduction To Probability Models

ISBN: 9780080467825

9th Edition

Authors: Sheldon M Ross

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Question Posted: Sep 14, 2024 07:01 AM

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

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Introduction To Probability Models

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