10SimHw5 - IEOR 4404 Simulation Prof. Mariana...

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IEOR 4404 Assignment #5 Simulation February 24, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #5 – due March 5th, 2010 1. Let Y 1 ,Y 2 ,... be a sequence of iid exponential random variables with parameter λ . Define the random variable N = sup { n : Y 1 + ··· + Y n 1 } Compute the PMF of N . What distribution does N have? 2. Modify the single server queue program given in Lecture 10 to estimate the average time that a customer spends in the system and the average amount of overtime put in by the server, in the case where the arrival process is a Poisson process with rate 10, the service time density is g ( x ) = 20 e - 40 x (40 x ) 2 , x > 0 and T = 9. First try 100 runs and then 1000. 3. Suppose that in the single server queue model from Lecture 10 that we also wanted to obtain information about the amount of idle time a server would experience in a day. Explain how this could be accomplished. 4. Consider a single-server queueing model in which customers arrive according to a nonhomoge-
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