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10SimHw11

# 10SimHw11 - IEOR 4404 Simulation Prof Mariana...

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IEOR 4404 Assignment #11 Simulation April 14, 2010 Prof. Mariana Olvera-Cravioto Page 1 of 1 Assignment #11 – due April 23th, 2010 1. Consider a single server queue where customers arrive according to a Poisson process with rate 2 per minute and the service times are exponentially distributed with mean 1 minute. Let T i denote the amount of time that customer i spends in the system . We are interested in using simulation to estimate θ = E [ T 1 + ··· + T 10 ]. (a) Do a simulation to sestimate the variance of the raw simulation estimator. That is, estimate var( T 1 + ··· + T 10 ). (b) Do a simulation to determine the improvement over the raw estimator obtained by using antithetic variables. (c) Do a simulation to determine the improvement over the raw estimator obtained by using 10 i =1 S i as a control variate, where S i is the i th service time. (d) Do a simulation to determine the improvement over the raw estimator obtained by using 10 i =1 S i - 9 i =1 I i as a control variate, where
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