Consider a single serve queue where customers arrive according to a Poisson process with rate 2 per minute and the servi

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Consider A Single Serve Queue Where Customers Arrive According To A Poisson Process With Rate 2 Per Minute And The Servi 1 (68.64 KiB) Viewed 35 times

Consider a single serve 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 denote the amount of time that customer i spends in the system. We are interested in using simulation to estimate E[T₁+...+ T10]. (a) Do a simulation to estimate the variance of the raw simulation estimator. That is, estimate Var(T₁ + ... + T₁0). (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 S; as a control variate, where S; is the ith service time. (d) Do a simulation to determine the improvement over the raw estimator obtained by using Si-EI; as a control variate, where I; is the time between the ith and (i+1)st arrival. (e) Do a simulation to determine the improvement over the raw estimator obtained by using the estimator E[T;N;], where N₁ is the number in the system when customer i arrives (and so N₁ = 0).