Reliable estimation via simulation

Sharma, Vinod (1995) Reliable estimation via simulation. In: Queueing Systems, 19 (1-2). pp. 169-192.

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Abstract

Let a and s denote the inter arrival times and service times in a GI/GI/1 queue. Let a (n), s (n) be the r.v.s, with distributions as the estimated distributions of a and s from iid samples of a and s of sizes n. Let w be a r.v. with the stationary distribution lr of the waiting times of the queue with input (a, s). We consider the problem of estimating E [w~], tx > 0 and 7r via simulations when (a (n), s (n)) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.

Item Type:	Journal Article
Publication:	Queueing Systems
Publisher:	J.C. Baltzer AG, Science Publishers
Additional Information:	Copyright of this article belongs to J.C. Baltzer AG, Science Publishers.
Keywords:	Continuity;rates of convergence;robust estimation;queueing systems;simulation;regenerative processes.
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	08 Apr 2009 06:35
Last Modified:	19 Sep 2010 05:30
URI:	http://eprints.iisc.ac.in/id/eprint/19768

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