Vacation Policies for Machine Interference Problem with an Un-Reliable Server and State-Dependent Service Rate

具不可信任及不齊一服務者之機器修理問題的假期策略

10.29977/JCIIE.200603.0002

柯昭川(Jau-Chuan Ke)

不齊一 ； 機器修理問題 ； 多重假期 ； 單一假期 ； 不可信任服務者 ； machine interference problem ； multiple vacations ； single vacation

工業工程學刊

23卷2期（2006 / 03 / 01）

100 - 114

英文

本篇論文研究含有單一不齊一且不可信任服務者M/M/1機器修理問題的兩種假期策略：一組在線上操作之M台機器，由一個不齊一且不可信任服務者負責維修，當系統中沒有故障機器等待要維修時，服務者立即執行一個指數隨機長度的假期，且可能操作兩種假期策略。(1)多重假期：服務者從假期回來，若發現系統中沒有故障機器等待要維修，則繼續執行一序列隨機長度之假期，直到從假期回來發現至少有一故障機器等待要維修，即展開維修工作。(2)單一假期：服務者從第一個假期回來，若系統有故障機器，立即展開維修工作；若沒有故障機器，服務者則閒置在系統中直到故障機器到達。我們推導這兩個假期機器修理系統的穩態結果，建立其成本模式，作數值實驗，決定線上操作之最佳機器數，在最佳操作條件下實施敏感度分析。

This paper studies the machine interference problem consisting of M operating machines and an un-reliable server who leaves for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the server returns and operates two different vacation policies. In Policy 1, the server doesn't take a vacation again and remain idle until the first arriving failed machine arrives, which starts a busy period in the repair facility. In Policy 2, the server takes vacations repeatedly until they find the repair facility has at least one waiting failed machine in the queue. For both policies, a profit model is developed in order to determine the optimal value of the number of machines. Numerical results are provided in which several system characteristics are evaluated under optimal operating conditions.

1. Benson, F.,D.R. Cox(1951).The productivity of machines requiring attention at random interval.Journal of the Royal Statistical Society B,13,65-82.
2. Doshi, B.T.(1986).Queueing system with vacations - A survey.Queueing Systems,1,29-66.
3. Elsayed, E.A.(1981).An optimum repair policy for the machine Interference problem.Journal of the Operational Research Society,32,793-801.
4. Feller, W.(1967).An Introduction to Probability Theory and Its Applications
5. Gupta, S.M.(1997).Machine interference problem with warm spares, server vacations and exhaustive service.Performance Evaluation,29,195-211.
6. Ke, J.-C.,K.-H. Wang(1999).Cost analysis of the M/M/R machine repair problem with balking, reneg ing, and server breakdowns.Journal of the Operational Research Society,50,275-282.
7. Medhi, J.(1991).Stochastic Processes
8. Osaki, S.(1992).Applied Stochastic System Modeling
9. Sivazlian, B.D.,K.-H. Wang(1989).Economic analysis of the M/M/R machine repair problem with warm standbys.Microelectronics and Reliability,29,25-35.
10. Takagi, H.(1991).Queueing Analysis: A Foundation of Performance Evaluation, Vol. I, vacation and priority systems
11. Toft, F.J.,H. Boothroyd(1959).A queueing model for spare coal faces.Operational Research Quarterly,10,245-251.
12. Wang, K.-H.(1990).Profit analysis of the machine repair problem with a single service station subject to breakdowns.Journal of the Operational Research Society,41,1153-1160.
13. Wang, K.-H.(1994).Profit analysis of the M/M/R machine repair problem with spares and server breakdowns.Journal of the Operational Research Society,45,539-548.
14. Wang, K.-H.,L.-Y Hsu(1995).Cost analysis of the mamachine repair problem with R non-reliable service stations.Microelectronics and Reliability,35,923-934.
15. Wang, K.-H.,M.-Y Kuo(1997).Profit analysis of the M/Ek/1 machine repair problem with a non-reliable service station.Computers and Industrial Engineering,32,587-594.