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Math · Statistics And Probability
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Problem 1 (25 points): Consider an M/G/1 system with bulk service. Whenever the server becomes free, he accepts two customers from the queue into service simultaneously, or, if only one is on queue he accepts that one, in either case, the service time for the group (of size 1 or 2) is taken from B(r). Let gn be the number of customers remaining after the nth service instant. Let n be the number of arrivals during the nth service. Define B(s), Q(), and V(z) as transforms associated with the random variables x, q, and u as usual. Let ρ = 2. (a) Using the method of imbedded Markov chains, find E lim n in terms of , ơ , and P[a-0-Ph (b) Find () in terms of B), Po, and p (c) Express pi in terms of Po P1

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