Transient Analysis of an M/M/1 queue with Multiple Exponential Vacation and N-Policy

Vijayashree KV, Janani B

Abstract


A single server Markovian queueing model is considered.  The arrivals are allowed to join the queue according to a Poisson distribution and the service takes place according to an exponential distribution.  Whenever the system is empty, the server goes for a vacation and return back to the system after N or more customers are found in the system. If the number of customers in the system is less than ‘’ then the server takes another vacation.  In this paper, we obtain explicit expressions for the time dependent system size probabilities of such a model using Laplace transform and generating function techniques.  Numerical illustrations are added to support the theoretical results obtained.


Keywords


System Size Probabilities, Transient Analysis, Laplace Transform, Generating Function, Multiple Vacation

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DOI: http://dx.doi.org/10.18187/pjsor.v11i4.968

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Copyright (c) 2015 Pakistan Journal of Statistics and Operation Research

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Title

Transient Analysis of an M/M/1 queue with Multiple Exponential Vacation and N-Policy

Keywords

System Size Probabilities, Transient Analysis, Laplace Transform, Generating Function, Multiple Vacation

Description

A single server Markovian queueing model is considered.  The arrivals are allowed to join the queue according to a Poisson distribution and the service takes place according to an exponential distribution.  Whenever the system is empty, the server goes for a vacation and return back to the system after N or more customers are found in the system. If the number of customers in the system is less than ‘’ then the server takes another vacation.  In this paper, we obtain explicit expressions for the time dependent system size probabilities of such a model using Laplace transform and generating function techniques.  Numerical illustrations are added to support the theoretical results obtained.


Date

2015-12-03

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 11 No. 4, 2015



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810