Queues with dependency between interarrival and service times using mixtures of bivariates

Iyer, SK and Manjunath, D (2006) Queues with dependency between interarrival and service times using mixtures of bivariates. In: Stochastic Models, 22 (1). 03-20.

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Abstract

We analyze queueing models where the joint density of the interarrival time and the service time is described by a mixture of joint densities. These models occur naturally in multiclass populations serviced by a single server through a single queue. Other motivations for this model are to model the dependency between the interarrival and service times and consider queue control models. Performance models with component heavy tailed distributions that arise in communication networks are difficult to analyze. However, long tailed distributions can be approximated using a finite mixture of exponentials. Thus, the models analyzed here provide a tool for the study of performance models with heavy tailed distributions. The joint density of A and X , the interarrival and service times respectively, f ( a , x ), will be of the form f(a, x) = Sigma(i=1)(M) p(i)f(i)(a,x) where p(i) > 0 and Sigma(i=1)(M) p(i)=1. We derive the Laplace Stieltjes Transform of the waiting time distribution. We also present and discuss some numerical examples to describe the effect of the various parameters of the model.

Item Type:	Journal Article
Publication:	Stochastic Models
Publisher:	Taylor & Francis Group
Additional Information:	Copyrighjt of this article belongs toTaylor & Francis Group.
Keywords:	Bivariate random variables;Correlation;Laplace transform; Queues;Waiting time distribution.
Department/Centre:	Division of Electrical Sciences > Electrical Engineering Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	08 Apr 2009 04:43
Last Modified:	19 Sep 2010 05:02
URI:	http://eprints.iisc.ac.in/id/eprint/18493

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