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.
@article{RO_2003__37_3_157_0, author = {Ke, Jau-Chuan and Wang, Kuo-Hsiung}, title = {Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {157--177}, publisher = {EDP-Sciences}, volume = {37}, number = {3}, year = {2003}, doi = {10.1051/ro:2003019}, mrnumber = {2034537}, zbl = {1070.90028}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro:2003019/} }
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 SP - 157 EP - 177 VL - 37 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2003019/ DO - 10.1051/ro:2003019 LA - en ID - RO_2003__37_3_157_0 ER -
%0 Journal Article %A Ke, Jau-Chuan %A Wang, Kuo-Hsiung %T Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns %J RAIRO - Operations Research - Recherche Opérationnelle %D 2003 %P 157-177 %V 37 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2003019/ %R 10.1051/ro:2003019 %G en %F RO_2003__37_3_157_0
Ke, Jau-Chuan; Wang, Kuo-Hsiung. Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns. RAIRO - Operations Research - Recherche Opérationnelle, Volume 37 (2003) no. 3, pp. 157-177. doi : 10.1051/ro:2003019. http://archive.numdam.org/articles/10.1051/ro:2003019/
[1] A note on operating policies for the queue M/M/1 with exponential startup. INFOR 11 (1973) 71-72. | MR | Zbl
,[2] Poisson input queueing systems with startup time and under control operating policy. Comput. Oper. Res. 14 (1987) 33-40. | MR | Zbl
, and ,[3] A first course in bulk queues. Wiley, New York (1983). | MR | Zbl
and ,[4] On a Poisson queue with general setup time and vacation period. Indian J. Pure Appl. Math. 27 (1996) 1199-1211. | MR | Zbl
,[5] Introduction to queueing theory. 3rd edn., CEE press Books (1990). | MR | Zbl
,[6] Stochastic decompositions in the M/G/1 queue with generalized vacation. RAIRO Oper. Res. 33 (1985) 1117-1129. | MR | Zbl
and ,[7] Fundamentals of queueing theory. John Wiley and Sons, New York, 2nd edn. (1985). | MR | Zbl
and ,[8] The effect of different arrival rates on the N-policy of M/G/1 with server setup. Appl. Math. Modelling 23 (1999) 289-299. | Zbl
and ,[9] Control policies for the M/G/1 Queueing System. Manag. Sci. 35 (1989) 708-721. | MR | Zbl
and ,[10] Operating characteristics of the M/G/1 queue with N-policy. Queueing Syst. 15 (1994) 387-399. | MR | Zbl
, and ,[11] Analysis of the M/G/1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 476-496. | MR | Zbl
, , and ,[12] Batch arrival queue with N-policy and single vacation. Comput. Oper. Res. 22 (1995) 173-189. | Zbl
, , and ,[13] Optimal strategy in N-policy production system with early set-up. J. Oper. Res. Soc. 48 (1997) 306-313. | Zbl
and ,[14] A Poisson input queue under N-policy and with a general start-up time. Comput. Oper. Res. 19 (1992) 35-41. | Zbl
and ,[15] Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations. Eur. J. Oper. Res. 36 (1988) 197-201. | MR | Zbl
,[16] Analysis of systems in operations research. Englewood Cliffs, New Jersey (1975).
and ,[17] Queueing analysis: A foundation of performance evaluation, vacation and priority systems 1. North Holland, Amsterdam (1991). | MR | Zbl
,[18] M/G/1/K Queues with N-policy and setup times. Queueing Syst. 14 (1993) 79-98. | MR | Zbl
,[19] Infinite source M/M/1 queue with breakdown. J. Chinese Inst. Engrs. 7 (1990) 47-55.
,[20] Optimal operation of a Markovian queueing system with a removable and non-reliable server. Microelectron. Reliab. 35 (1995) 1131-1136.
,[21] Optimal control of an M/E/1 queueing system with removable service station subject to breakdowns. J. Oper. Res. Soc. 48 (1997) 936-942. | Zbl
,[22] Optimal control of a removable and non-reliable server in an infinite and a finite M/H/1 queueing system. Appl. Math. Modelling 23 (1999) 651-666. | Zbl
, and ,[23] Queueing systems with a removable service station. Oper. Res. Quart. 14 (1963) 393-405.
and ,Cited by Sources: