Abstract

In this paper, we discuss a non-Markovian batch arrival general bulk service single-server queueing system with server breakdown and repair, a stand-by server, multiple vacation and re-service. The main server’s regular service time, re-service time, vacation time and stand-by server’s service time are followed by general distributions and breakdown and repair times of the main server with exponential distributions. There is a stand-by server which is employed during the period in which the regular server remains under repair. The probability generating function of the queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.

Highlights

  • Queueing systems with general bulk service and vacations have been studied by many researchers because they deal with effective utilization of the server’s idle time for secondary jobs

  • Senthilnathan and Jeyakumar [13] studied the behavior of the server breakdown without interruption in an M[ X ] /G ( a, b)/1 queueing system with multiple vacations and closedown time

  • The main server may breakdown at any time during regular service with exponential rate α, and in such cases, the main server immediately goes for a repair, which follows an exponential distribution with rate η, while the service to the current batch is interrupted

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Summary

Introduction

Queueing systems with general bulk service and vacations have been studied by many researchers because they deal with effective utilization of the server’s idle time for secondary jobs. Jeyakumar and Senthilnathan [5] analyzed the bulk service queueing system with multiple working vacations and server breakdown. The first work on re-service was done by Madan [6] He consider an M/G /1 queueing model, in which the server performs the first essential service for all arriving customers. Haridass and Arumuganathan [9] analyzed a batch service queueing system with multiple vacations, setup times and server choice of admitting re-service. Senthilnathan and Jeyakumar [13] studied the behavior of the server breakdown without interruption in an M[ X ] /G ( a, b)/1 queueing system with multiple vacations and closedown time.

Literature Survey
Model Description
Queue Size Distribution
Steady State Condition
Computational Aspects
Result 1
Result 2
Particular Case
The Main Server’s Expected Length of Idle Period
Numerical Example
Conclusions
Full Text
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