Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns
RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 3, pp. 157-177.

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.

DOI : https://doi.org/10.1051/ro:2003019
Mots clés : batch arrivals, breakdowns, control, sensitivity analysis, startup, stochastic decomposition
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     title = {Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns},
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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, Tome 37 (2003) no. 3, pp. 157-177. doi : 10.1051/ro:2003019. http://www.numdam.org/articles/10.1051/ro:2003019/

[1] K.R. Baker, A note on operating policies for the queue M/M/1 with exponential startup. INFOR 11 (1973) 71-72. | MR 339803 | Zbl 0247.60057

[2] 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. | MR 877412 | Zbl 0654.60091

[3] M.L. Chaudhry and J.G.C. Templeton, A first course in bulk queues. Wiley, New York (1983). | MR 700827 | Zbl 0559.60073

[4] G. Choudhury, On a Poisson queue with general setup time and vacation period. Indian J. Pure Appl. Math. 27 (1996) 1199-1211. | MR 1425807 | Zbl 0862.60082

[5] R.B. Cooper, Introduction to queueing theory. 3rd edn., CEE press Books (1990). | MR 1100757 | Zbl 0486.60002

[6] S.W. Fuhrmann and R.B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacation. RAIRO Oper. Res. 33 (1985) 1117-1129. | MR 806922 | Zbl 0585.90033

[7] D. Gross and C.M. Harris, Fundamentals of queueing theory. John Wiley and Sons, New York, 2nd edn. (1985). | MR 910687 | Zbl 0658.60122

[8] S. Hur and S.J. Paik, 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 0957.90031

[9] H.S. Lee and M.M. Srinivasan, Control policies for the M [x] /G/1 Queueing System. Manag. Sci. 35 (1989) 708-721. | MR 1001484 | Zbl 0671.60099

[10] H.W. Lee, S.S. Lee and K.C. Chae, Operating characteristics of the M [x] /G/1 queue with N-policy. Queueing Syst. 15 (1994) 387-399. | MR 1266802 | Zbl 0789.60081

[11] H.W. Lee, S.S. Lee, J.O. Park and K.C. Chae, Analysis of the M [x] /G/1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 476-496. | MR 1274803 | Zbl 0804.60081

[12] 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. | Zbl 0821.90048

[13] 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. | Zbl 0890.90065

[14] 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. | Zbl 0742.60100

[15] D.L. Minh, Transient solutions for some exhaustive M/G/1 queues with generalized independent vacations. Eur. J. Oper. Res. 36 (1988) 197-201. | MR 953617 | Zbl 0649.60099

[16] B.D. Sivazlian and L.E. Stanfel, Analysis of systems in operations research. Englewood Cliffs, New Jersey (1975).

[17] H. Takagi, Queueing analysis: A foundation of performance evaluation, vacation and priority systems 1. North Holland, Amsterdam (1991). | MR 1149382 | Zbl 0744.60114

[18] H. Takagi, M/G/1/K Queues with N-policy and setup times. Queueing Syst. 14 (1993) 79-98. | MR 1238663 | Zbl 0793.60099

[19] K.-H. Wang, Infinite source M/M/1 queue with breakdown. J. Chinese Inst. Engrs. 7 (1990) 47-55.

[20] K.-H. Wang, Optimal operation of a Markovian queueing system with a removable and non-reliable server. Microelectron. Reliab. 35 (1995) 1131-1136.

[21] 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. | Zbl 0892.90085

[22] K.-H. Wang, K.-W. Chang and B.D. Sivazlian, Optimal control of a removable and non-reliable server in an infinite and a finite M/H 2 /1 queueing system. Appl. Math. Modelling 23 (1999) 651-666. | Zbl 0951.93073

[23] M. Yadin and P. Naor, Queueing systems with a removable service station. Oper. Res. Quart. 14 (1963) 393-405.

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