M/M/m排隊系統最佳化控制與設計

Abstract

本論文我們將探討M/M/m (m=2)可移式伺服器排隊系統最佳化的問題。論文中我們使用兩種方法以決定伺服器需求數量。在數值方法中，為了評估系統績效我們參考文獻中排隊系統的數學公式以定義成本函數。其中成本函數由客戶排隊成本、伺服器切換成本以及遺失客戶的成本所組成。接下來最佳化(0,Q,N,M)的系統狀態以決定何時打開或關閉伺服器。由於此排隊系統的數學公式為高維度非線性函數，因此模糊理論自然而然成為很好的工具以解決此類問題，根據數值方法經驗，我們選定重要參數成為歸屬函數。然後運用模糊推論得到伺服器變動數量。最後我們使用監督理論讓排隊系統操作於可允許成本區間外。並接受(0,Q,N,M)的系統狀態有多一次切換機會

In this thesis, we study M/M/m (m=2) with removable server and discuss the system states to turn on or off server at a time in two approaches. One is numerical approach, while the other is fuzzy approach. In the numerical approach, one needs to derive the analytical form with triadic policy (0,Q,N,M) for queueing system and then define cost function to evaluate the performance. Due to highly nonlinear characteristics in the analytical form, the fuzzy approach is then to be a nature tool to handle such problems even for (m>3). Some key factors learned from numerical approach are chosen to be the fuzzy set and then apply the fuzzy reasoning to obtain the decision for the variation number of server. We also design a supervisory controller to make sure the queueing system running under the modified triadic policy (0,Q,N,M) so that each Q,N,M has one more chance to switch system states with allowable cost.