Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/97330
標題: 具伺服器故障及修復門檻策略之重試機器修理系統最佳化分析
Optimization analysis of retrial machine repair system with server breakdown and threshold recovery policy
作者: 施涵晴
Han-Ching Shih
關鍵字: 等候理論;重試排隊;修復門檻策略;二階段最佳化演算法;queue theory;retrial queue;threshold recovery policy;two-stage optimization method
引用: [1] M. Jain, A. Jain, Working vacations queueing model with multiple types of server breakdowns, Appl. Math. Model. 34 (2010) 1–13. [2] K. Kalidass, R. Kasturi. A queue with working breakdowns, Comput. Ind. Eng. in press (2012). [3] L. Haque, M.J. Armstrong, A survey of the machine interference problem, Eur. J. Opl. Res. 179 (2007) 469-482. [4] M. Jain, G.C. Sharma, R.S. Pundhir, Some perspectives of machine repair problems, Int. J. Eng. 23 (2010) 253-268. [5] K.-H. Wang, Profit analysis of the machine repair problem with a single service station subject to breakdowns, J. Opl. Res. Soc. 41(1990) 1153–1160. [6] K.-H. Wang, M.-Y. Kuo, Profit analysis of the M/Ek/1 machine repair problem with a non-reliable service station, Comput. Ind. Eng. 32 (1997) 587–594. [7] G. Falin, J. Templeton, Retrial queues, Chapman & Hall, 1997. [8] J. Artalejo, A. Corral, Retrial queueing systems, Springer, 2008. [9] T. Yang, J. Templeton, A survey on retrial queues, Que. Syst. 2(1987) 201–233. [10] J. Artalejo, G. Falin, Standard and retrial queueing systems: a comparative analysis, Rev. Mat. Complut. 15 (2002) 101-129. [11] J. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model, 51 (2010) 1071-1081. [12] D. V. Efrosinin, O. V. Semenova, An M/M/1 system with an unreliable device and a threshold recovery policy, J. Commu. Technol. Elec. 55 (2010) 1526-1531. [13] D.-Y. Yang, Y.-C. Chiang, An evolutionary algorithm for optimizing the machine repair problem under a threshold recovery policy, J. Chin. Inst. Ind. Eng. 37 (2014) 224-231. [14] Neuts, M. F. (1984). Matrix-analytic methods in queuing theory. European Journal of Operational Research, 15(1), 2-12. [15] Wright, S., & Nocedal, J. (1999). Numerical optimization. Springer Science, 35(67-68), 7. [16] Shang, S. W. (2010). 具有阻礙, 放棄及服務壓力係數之 M/M/R 暖備機器修理問題. 中興大學統計學研究所學位論文, 1-33. [17] 郭瓊穗. (2012). 以粒子群優化演算法計算具有阻礙, 放棄及服務壓力係數之暖備機器修理問題的最低成本. 中興大學應用數學系所學位論文, 1-28
摘要: 
在需要排隊的時候,若能安排適當的排隊機制可以協助顧客更有效率的獲得服務,怎樣的排隊機制可以營造出老闆省錢、顧客滿意雙贏的局面,就要運用排隊理論了。排隊理論可以用來計算執行時所需的資源以及系統的運作狀況,這對決策很有幫助。然而隨著科技的發達,很多服務從現實生活中轉移到網路的虛擬世界,比如:線上購物,而這些服務的背後都需要仰賴排隊理論。因此排隊理論的應用,從實體排隊擴及到製造系統、可維修系統及通信網路…等。近期雲端運算的發展,使得使用者可以在網頁上直接執行相關程式,而不再像以前需要在用戶端的設備上安裝程式才可以執行,這樣的發展的確讓很多硬體資源不足的使用者省事不少。但在提供服務的雲端平台上,如何保有服務品質又不需太高的成本,便是需要探討的問題。
本論文探討具伺服器故障與修復門檻策略之重試機器修理系統最佳化分析,考慮在系統中備有 台運作中的機器及 台暖備用機器供使用,當運作中的機器故障時,若尚有暖備機器則直接以其取代故障機器,而故障的機器將被送往維修中心。維修中心一次只能修理一台機器,其餘的故障機器便要進入排隊中等待,待一段時間後再重試提出維修請求。某些情況的故障(例如:硬體損壞),為了節省成本,會設定維修門檻値,待故障機器累積到一定數量後,再進貨以降低成本。
我們先繪製狀態轉移率圖,列出穩態方程式,再撰寫Maple程式計算穩態機率以及系統效能測度。參考各系統效能測度,我們定義了成本函數 ,其中 為離散變數且 , 及 為連續變數且為正數。先以直接搜尋法找出 的最佳解,再利用二階段最佳化演算法搜尋全區域中 及 的最佳解,以計算出成本函數的最小值 。

Queue theory, which can analyzes the resources needed to provide a service, is very helpful for operating decisions. With the advances in technology, the application of Queue theory has become more and more extensive, including queuing from reality to virtual. To improve both quality and cost of service, Queue theory is an important analytic method.
Cloud computing has gained lots of popularity in recent years. A Virtual Machine is a software installed in a virtual storage, which provides cloud SaaS service. Virtual Machines shift the deployment of computing infrastructure from end users to the cloud data center. Users can get the service via the Internet, requiring no hardware devices on the client''s side. Cloud computing administrative tools can create, manage, and deploy cloud services, such as CloudStack. We wonder how cloud computing administrative tools could operate with Queue theory.
This paper explores optimization analysis of retrial machine repair system with server breakdown and threshold recovery policy. There are operating machines with warm standby machines, and a repairman in the system. The repairman can repair only one machine at a time. If the repairman is busy, the failed machine will be transmitted to the retrial orbit to wait for check. When the number of failed machines in the system accumulates to the predefined threshold , the system would fix the repairman or failed machines.
At first, we build up the state-transition-rate diagram and steady-state equations. And then, we calculate the steady-state probabilities and system performance measures by Maple software. Consider system performance measures to define the cost function , where is a discrete variable and , and are continuous variables and . We find the optimal value by using the direct search method, then find the minimum value by using two-stage optimization method. is the minimum cost value.
URI: http://hdl.handle.net/11455/97330
Rights: 同意授權瀏覽/列印電子全文服務,2019-07-27起公開。
Appears in Collections:應用數學系所

Files in This Item:
File SizeFormat Existing users please Login
nchu-107-5103053004-1.pdf1.67 MBAdobe PDFThis file is only available in the university internal network    Request a copy
Show full item record
 
TAIR Related Article

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.