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The Conditional Distribution of Waiting Time Given Queue Length

The Conditional Distribution of Waiting Time Given Queue Length Abstract In this paper we propose a conditional distribution of the waiting time given the queue length. We assume that the number of customers in a queue, that is the queue length, follows a geometric distribution and the waiting time of a newly arrived customer in a queue follows an exponential distribution. We model the conditional distribution of the waiting time given the queue length using Gumbel's bivariate exponential copula. Parameters are estimated using the likelihood approach with a two stage estimation procedure. A simulation study indicates the performance of the estimators. Asymptotic properties of the estimators of the parameters are studied. We apply the model to a real data set to illustrate the dependence between the waiting time and the queue length. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

The Conditional Distribution of Waiting Time Given Queue Length

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
0940-5151
eISSN
1869-6147
DOI
10.1515/eqc-2014-0002
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper we propose a conditional distribution of the waiting time given the queue length. We assume that the number of customers in a queue, that is the queue length, follows a geometric distribution and the waiting time of a newly arrived customer in a queue follows an exponential distribution. We model the conditional distribution of the waiting time given the queue length using Gumbel's bivariate exponential copula. Parameters are estimated using the likelihood approach with a two stage estimation procedure. A simulation study indicates the performance of the estimators. Asymptotic properties of the estimators of the parameters are studied. We apply the model to a real data set to illustrate the dependence between the waiting time and the queue length.

Journal

Economic Quality Controlde Gruyter

Published: Jun 1, 2014

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