Unformatted text preview: Spring 2009 OR3510/5510 Problem Set 8; due April 6 as usual. Reading: By Wed we will be starting Chapter 7 on renewal theory. Reminder: The 2nd prelim is Thursday April 9, 7:309:30. It will cover material through the end of continuous time Markov chains. There will be no homework assigned April 6. x/y=page x, problem y in Ross. (1) 411/23 (2) 410/17 (3) M/M/1 queue with batch arrivals: As usual, services are iid random variables with exponential distribution and parameter μ . Services are independent of the input. Customers arrive in batches. The batches arrive according to a Poisson process rate λ . So each Poisson arrival event delivers a batch of customers, the batch size being distributed as a random variable N with P [ N = n ] = q n , n ≥ 1 , ∞ X j =1 q n = 1 . Find the generator matrix of the state variable number in the system . (4) In the M/M/s let R ( t ) be the number of busy servers at time t. If ρ < 1 show that a limit distribution exists lim t →∞ P [ R ( t ) = k...
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 Summer '09
 RESNIK
 Probability theory, Exponential distribution, Qn, Poisson process rate, time Markov Chains, Poisson arrival event

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