以二維度馬可夫鏈的排隊模型研究客戶服務中心之等候機制

Abstract

在這篇論文中，藉由一個二維度的馬可夫鏈，\r\n建立保護VIP線路同時允許重試現象的一般客戶線路的數學模型。\r\n我們提出一個融合階段演算法以處理此二維度的馬可夫鏈，並且提出管理成本函數以研究在客服中心中最適當的服務人員數目\r\n。藉由逼近法，找出一般顧客在重試群裡的平均等候時間和等候時間機率分配函數的上界與下界。\r\n數值結果說明逼近方法對於計算一個很大的系統時可以省下很多計算時間，而且不失準確性。\r\n最後，我們探討逼近法和實際解之間的誤差，數值結果也說明隨著系統容量或顧客到達率的增加，逼近法將更為準確。

In this thesis, we model a call center with guard channel scheme for VIP calls and retrial phenomenon\r\nfor regular calls by a 2-dimensional Markov chain.\r\nWe present a phase merging algorithm to solve the 2-dimensional Markov chain and\r\na managerial cost function corresponding to studying the optimum number of servers in a call center.\r\nAlso we will obtain upper and lower bounds with probability distribution functions of waiting time by using approximation.\r\nNumerical results show the approximation can save computational time without losing precision in the case of a call center with\r\nlarge capacity. Moreover, errors of the approximation are discussed,\r\nand it shows that the approximation is more accurate when the capacity of system or the arrival rate is large.

Abstract\r\n中文摘要\r\nList of Figures\r\nList of Tables\r\n1. Introduction\r\n2. System description\r\n2.1 A queueing model\r\n2.2 Waiting time\r\n2.3 Computation of stationary probability distribution\r\n3. Approximation and its computing procedure\r\n3.1 Approximation of pi-method\r\n3.2 Applications\r\n3.3 Errors between Approximation and pi-method\r\n4. Conclusion\r\nAppendix A\r\nAppendix B\r\nBibliography