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標題: 含有故障服務者,啟動時間及第二選擇服務之N-方策M/G/1排隊系統之最佳控制
Optimal Control of the N Policy M/G/1 Queue with Server Breakdowns,Startup and Second Optional Service
作者: 許書維
Hsu, Shu-Wei
關鍵字: first essential service;第一主要服務;second optional service;general repair time;general startup time;optimal policy;sensitivity analysis;第二選擇服務;一般修理時間;一般啟動時間;最佳控制;敏感度分析
出版社: 應用數學系所
引用: 1. Wang, K.-H., Optimal operation of a Markovian queueing system with a removable and non-reliable server, Microelectronics and Reliability, Vol. 35, pp. 1131-1136, 1995. 2. Wang, K.-H., Optimal control of an M/Ek/1 queueing system with removable service station subject to breakdowns, Journal of the Operational Research Society, Vol. 48, pp. 936-942, 1997. 3. 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, Applied Mathematical Modelling, Vol. 23, pp. 651-666, 1999. 4. Wang, K.-H., Kao, H.-T. and Chen, G., Optimal management of a removable and non-reliable Server in an infinite and a finite M/Hk/1 queueing system, Quality Technology & Quantitative Management, Vol. 1, No. 2, pp. 325-339, 2004. 5. Baker, K.R., A note on operating policies for the queue M/M/1 with ezponential startup, INFOR, Vol. 11, pp. 71-72, 1973. 6. Borthakur, A., Medhi, J., and Gohain, R., Poisson input queueing systems with startup time and under control operating policy, Computers and Operations Reseach, Vol. 14, pp. 33-40, 1987. 7. Wang, K.-H., Optimal control of a removable and non-reliable server in an M/M/1 queueing system with exponential startup time, Mathematical Methods of Operations Research, Vol. 58, pp. 29-39, 2003. 8. Medhi, J., and Templeton, J.G.C., A poisson input queue under N-policy and with a general start up time, Computers and Operations Research, Vol. 19, pp. 35-41, 1992. 9. Takagi, H., A M/G/1/K queues with N-policy and setup times, Queueing Systems, Vol. 14, pp. 79-98, 1993. 10. Lee, H.W., and Park, J.O., Optimal strategy in N-policy production system with early set-up, Journal of the Operational Research Society, Vol. 48, pp. 306-313, 1997. 11. Hur, S., and Paik, S.J., The effect of different arrival rates on the N-policy of M/G/1 with server setup, Applied Mathematical Modelling, Vol.23, pp. 289-299, 1999. 12. Wang, K.-H., and Ke, J.-C., Control policies of an M/G/1 queueing system with a removable and non-reliable server, International Transactions in Operations Research, Vol. 9, pp. 195-212, 2002. 13. Wang, K.-H., Wang, T.-Y., and Pearn, W.L., Optimal control of the N polcy M/G/1 queueing system with server breakdowns and general startup times, Applied Mathematical Modelling, in press. 14. Madan, K.C., An M/G/1 queue with second optional service, Queueing Systems, Vol. 34, pp. 37-46, 2000. 15. Medhi, J., A single server Poisson input queue with a second optional channel, Queueing Systems, Vol. 42, pp. 239-242, 2002. 16. Al-Jararha, J., and Madan, K.C., An M/G/1 queue with second optional service with general service time distribution, Information and Management Sciences, Vol. 14, No. 2, pp. 47-56, 2003. 17. Wang, J., An M/G/1 queue with second optional service and server breakdowns, Computers and Mathematics with Applications, Vol. 47, pp. 1713-1723, 2004.
此篇論文分析研究了含有故障服務者, 啟動時間及第二選擇服務之N-方策M/G/1排隊系統. 其中第一主要服務之服務時間假設為一般分配, 而第二選擇服務則假設為其它一般分配. 在完成第一主要服務後, 顧客有(1-θ)的機率離開或者有θ(0<θ<1)的機率立刻進行第二選擇服務. 當排隊長度到達預先決定的值N(N>1)時, 系統需要一個啟動時間後才開始服務顧客直到系統再次變空. 我們分析各種系統性能且正確的導出穩態結果. 發展每單位時間每位顧客的總期望花費在最小花費時決定N之最佳值. 敏感度分析的分析結果也被導出.

This paper studies the N policy M/G/1 queue with server breakdowns, startup and second optional service. The service times of the first essential service are assumed to follow a general distribution and that of second optional service with another general distribution. A customer may leave the system either after the first essential service with probability (1-θ) or at the completion of the first essential service may immediately go for a second optional service with probability θ(0<θ<1). When the queue length reaches to a predetermined value N(N>1), the server requires a startup time before providing service until the system is again empty. We analyze various system performance and steady-state results are derived explicitly. The total expected cost per customer per unit time is developed to determine the optimal value N at a minimum cost. Analytic results for sensitivity analysis are also derived.
其他識別: U0005-2606200713544700
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