Performance analysis of renewal input $(a,c,b)$ policy queue with multiple workingvacations and change over times

Pikkala Vijaya Laxmi; Seleshi Demie

doi:10.3934/jimo.2014.10.839

Article Contents

2014, Volume 10, Issue 3: 839-857. Doi: 10.3934/jimo.2014.10.839

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Performance analysis of renewal input $(a,c,b)$ policy queue with multiple working vacations and change over times

Pikkala Vijaya Laxmi^1, and
Seleshi Demie^1,

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

Received: May 31, 2012

Revised: May 31, 2013

Published: June 2014

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Abstract

This paper analyzes a renewal input multiple working vacations queue with change over times under $(a,c,b)$ policy. The service and vacation times are exponentially distributed. The server begins service if there are at least $c$ units in the queue and the service takes place in batches with a minimum of size $a$ and a maximum of size $b~ (a\leq c \leq b)$. The steady state queue length distributions at arbitrary and pre-arrival epochs are obtained along with some special cases of the model. Performance measures and optimal cost policy is presented with numerical experiences for some particular values of the parameters. The genetic algorithm is employed to search the optimal values of some important parameters of the system.

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

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