Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-06-12T06:35:53.541Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of Operating Characteristics for the Heterogeneous Batch Arrival Queue with Server Startup and Breakdowns

Published online by Cambridge University Press:  15 December 2003

Jau-Chuan Ke  and
Kuo-Hsiung Wang
Jau-Chuan Ke
Affiliation:
Department of Statistics, National Taichung Institute of Technology, Taichung, Taiwan 404, R.O.C.; jauchuan@mail.ntit.edu.tw.
Kuo-Hsiung Wang
Affiliation:
Department of Applied Mathematics, National Chung-Hsing University, Taichung, Taiwan 402, R.O.C.
Get access

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[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.

Keywords

Batch arrivalsbreakdownscontrolsensitivity analysisstartupstochastic decomposition.
Type
Research Article
Information
RAIRO - Operations Research , Volume 37 , Issue 3 , July 2003 , pp. 157 - 177
Copyright
© EDP Sciences, 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, K.R., A note on operating policies for the queue M/M/1 with exponential startup. INFOR 11 (1973) 71-72.
A. Borthakur, J. Medhi and R. Gohain, Poisson input queueing systems with startup time and under control operating policy. Comput. Oper. Res. 14 (1987) 33-40 .
M.L. Chaudhry and J.G.C. Templeton, A first course in bulk queues. Wiley, New York (1983).
Choudhury, G., On a Poisson queue with general setup time and vacation period. Indian J. Pure Appl. Math. 27 (1996) 1199-1211.
R.B. Cooper, Introduction to queueing theory. 3rd edn., CEE press Books (1990).
Fuhrmann, S.W. and Cooper, R.B., Stochastic decompositions in the M/G/1 queue with generalized vacation. RAIRO Oper. Res. 33 (1985) 1117-1129. CrossRef
D. Gross and C.M. Harris, Fundamentals of queueing theory. John Wiley and Sons, New York, 2nd edn. (1985).
Hur, S. and Paik, S.J., The effect of different arrival rates on the N-policy of M/G/1 with server setup. Appl. Math. Modelling 23 (1999) 289-299. CrossRef
Lee, H.S. and Srinivasan, M.M., Control policies for the M [x]/G/1 Queueing System. Manag. Sci. 35 (1989) 708-721. CrossRef
Lee, H.W., Lee, S.S. and Chae, K.C., Operating characteristics of the M [x]/G/1 queue with N-policy. Queueing Syst. 15 (1994) 387-399. CrossRef
Lee, H.W., Lee, S.S., Park, J.O. and Chae, K.C., Analysis of the M [x]/G/1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 476-496.
S.S. Lee, H.W. Lee, S.H. Yoon and K.C. Chae, Batch arrival queue with N-policy and single vacation. Comput. Oper. Res. 22 (1995) 173-189 .
H.W. Lee and J.O. Park, Optimal strategy in N-policy production system with early set-up. J. Oper. Res. Soc. 48 (1997) 306-313 .
J. Medhi and J.G.C. Templeton, A Poisson input queue under N-policy and with a general start-up time. Comput. Oper. Res. 19 (1992) 35-41 .
D.L. Minh, Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations. Eur. J. Oper. Res. 36 (1988) 197-201 .
B.D. Sivazlian and L.E. Stanfel, Analysis of systems in operations research. Englewood Cliffs, New Jersey (1975).
H. Takagi, Queueing analysis: A foundation of performance evaluation, vacation and priority systems 1. North Holland, Amsterdam (1991).
Takagi, H., M/G/1/K Queues with N-policy and setup times. Queueing Syst. 14 (1993) 79-98. CrossRef
Wang, K.-H., Infinite source M/M/1 queue with breakdown. J. Chinese Inst. Engrs. 7 (1990) 47-55.
K.-H. Wang, Optimal operation of a Markovian queueing system with a removable and non-reliable server. Microelectron. Reliab. 35 (1995) 1131-1136 .
K.-H. Wang, Optimal control of an M/E k /1 queueing system with removable service station subject to breakdowns. J. Oper. Res. Soc. 48 (1997) 936-942 .
Wang, K.-H., Chang, K.-W. and Sivazlian, B.D., Optimal control of a removable and non-reliable server in an infinite and a finite M/H2/1 queueing system. Appl. Math. Modelling 23 (1999) 651-666. CrossRef
Yadin, M. and Naor, P., Queueing systems with a removable service station. Oper. Res. Quart. 14 (1963) 393-405. CrossRef