臺灣博碩士論文加值系統

在本篇論文裏，我們研究穩態狀況下，在M/M/1有限容量的排隊系統內，針對顧客數的控制，其控制決策為F-方策，包含了服務者故障及啟動服務時間。所謂F-方策的含意是指在系統中，當顧客抵達數超過系統容量時，則系統將不允許顧客再進入，此時，服務者提供服務使顧客數減少，當顧客數減少至F個，或少於F個時，系統又會開始接受顧客進入，並提供服務。
由於無法推導出穩態機率解，因而利用電腦軟體（MATLAB）針對不同的系統參數值，求出穩態機率的數值解，因而獲得多種系統效能測度。
最後，我們定義單位時間之穩態期望成本函數，藉由此成本函數決定控制參數F的最佳解F*，使成本函數達到最小。同時，我們也研究了敏感度分析。

In this thesis, we study the controlling arrivals in an M/M/1 queueing system with server breakdowns and startup time operating under the F policy. Customers arrive following a Poisson process. The service times of the customers according to an exponential distribution. Two different types of a single server which are subject to breakdowns. One type is that the server can break down only when there is at least one customer in the system. The other type is that the server can break down even if there are no customers in the system. When the server breaks down, it is immediately repaired at a repair facility. Breakdown times and repair times are both assumed to be exponentially distributed. Numerical results of system performance measures can be evaluated for various values of system parameters. Finally, we construct a cost model to determine the optimal operating F policy at minimum cost. Sensitivity analysis is also investigated.

Chapter 1：Introduction…………………………………………..1
1.1 Problem Statement………………………….………………...2
1.2 Literature Review…………………………………………….3
1.3 The Scope of the Study……………………………………….4
Chapter 2：Steady-State Results……………………..……………6
2.1 Assumptions………………………………………………….7
2.2 Steady-State Solutions………………………………………..7
2.3 System Performance Measures……...…………………….11
Chapter 3：Optimal F Policy…………….……………….……...14
3.1 Cost Model…………………………...…………………….…14
3.2 Sensitivity Analysis and Numerical Studies…………………..16
Chapter 4：Conclusions and Future Research………….............21
4.1 Conclusions…………………………………………….…….21
4.2 Future Research…………………………………………22
Reference…………………………………………………………….23

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