Analysis of a finite buffer general input queue with Markovianservice process and accessible and non-accessible batch service

Pikkala Vijaya Laxmi; Obsie Mussa Yesuf

doi:10.3934/jimo.2010.6.929

Article Contents

2010, Volume 6, Issue 4: 929-944. Doi: 10.3934/jimo.2010.6.929

This issue Previous Article Analysis of renewal input bulk arrival queue with single working vacation and partial batch rejection Next Article

Analysis of a finite buffer general input queue with Markovian service process and accessible and non-accessible batch service

Pikkala Vijaya Laxmi^1, and
Obsie Mussa Yesuf^2,

1.
Department of Applied Mathematics, Andhra University, Visakhapatnam - 530 003
2.
Department of Mathematics, Andhra University, Visakhapatnam - 530 003

Received: December 31, 2009

Revised: July 31, 2010

Published: September 2010

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Abstract

Queues with Markovian service process ($MSP$) are mainly useful in modeling and performance analysis of telecommunication networks based on asynchronous transfer mode (ATM) environment. This paper analyzes a finite buffer single server batch service ($a, b)$ queue with general input and Markovian service process ($MSP$). The server accesses new arrivals even after service has started on any batch of initial number $a$. This operation continues till the service time of the ongoing batch is completed or the maximum accessible capacity $d ~(a\le d < b)$ of the batch being served is attained whichever occurs first. Using the embedded Markov chain technique and the supplementary variable technique we obtain the steady state queue length distributions at pre-arrival and arbitrary epochs. The primary focus is on the various performance measures of the steady state distribution of the batch service, special cases and also on numerical illustrations.

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Mathematics Subject Classification: Primary: 60K25; Secondary: 90B22, 68M20.

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