Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns

Jau-Chuan Ke[1]; Kuo-Hsiung Wang

  • [1] Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.

RAIRO - Operations Research - Recherche Opérationnelle (2003)

  • Volume: 37, Issue: 3, page 157-177
  • ISSN: 0399-0559

Abstract

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In this paper we consider a like-queue production system in which server startup and breakdowns are possible. The server is turned on (i.e. begins startup) when units are accumulated in the system and off when the system is empty. We model this system by an M/M/1 queue with server breakdowns and startup time under the policy. The arrival rate varies according to the server’s status: off, startup, busy, or breakdown. While the server is working, he is subject to breakdowns according to a Poisson process. When the server breaks down, he requires repair at a repair facility, where the repair time follows the negative exponential distribution. We study the steady-state behaviour of the system size distribution at stationary point of time as well as the queue size distribution at departure point of time and obtain some useful results. The total expected cost function per unit time is developed to determine the optimal operating policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.

How to cite

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Ke, Jau-Chuan, and Wang, Kuo-Hsiung. "Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns." RAIRO - Operations Research - Recherche Opérationnelle 37.3 (2003): 157-177. <http://eudml.org/doc/245474>.

@article{Ke2003,
abstract = {In this paper we consider a like-queue production system in which server startup and breakdowns are possible. The server is turned on (i.e. begins startup) when $N$ units are accumulated in the system and off when the system is empty. We model this system by an M$^\{\rm [x]\}$/M/1 queue with server breakdowns and startup time under the $N$ policy. The arrival rate varies according to the server’s status: off, startup, busy, or breakdown. While the server is working, he is subject to breakdowns according to a Poisson process. When the server breaks down, he requires repair at a repair facility, where the repair time follows the negative exponential distribution. We study the steady-state behaviour of the system size distribution at stationary point of time as well as the queue size distribution at departure point of time and obtain some useful results. The total expected cost function per unit time is developed to determine the optimal operating policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.},
affiliation = {Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.},
author = {Ke, Jau-Chuan, Wang, Kuo-Hsiung},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {batch arrivals; breakdowns; control; sensitivity analysis; startup; stochastic decomposition},
language = {eng},
number = {3},
pages = {157-177},
publisher = {EDP-Sciences},
title = {Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns},
url = {http://eudml.org/doc/245474},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Ke, Jau-Chuan
AU - Wang, Kuo-Hsiung
TI - Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 3
SP - 157
EP - 177
AB - In this paper we consider a like-queue production system in which server startup and breakdowns are possible. The server is turned on (i.e. begins startup) when $N$ units are accumulated in the system and off when the system is empty. We model this system by an M$^{\rm [x]}$/M/1 queue with server breakdowns and startup time under the $N$ policy. The arrival rate varies according to the server’s status: off, startup, busy, or breakdown. While the server is working, he is subject to breakdowns according to a Poisson process. When the server breaks down, he requires repair at a repair facility, where the repair time follows the negative exponential distribution. We study the steady-state behaviour of the system size distribution at stationary point of time as well as the queue size distribution at departure point of time and obtain some useful results. The total expected cost function per unit time is developed to determine the optimal operating policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided.
LA - eng
KW - batch arrivals; breakdowns; control; sensitivity analysis; startup; stochastic decomposition
UR - http://eudml.org/doc/245474
ER -

References

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