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研究生:高宏艇
研究生(外文):H.-T, KAO
論文名稱:N方策單一服務者會故障之M/Hk/1排隊系統
論文名稱(外文):A single removable and non-reliable server in the N-policy M/Hk/1 queueing system
指導教授:王國雄王國雄引用關係
指導教授(外文):K.-H, WANG
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
中文關鍵詞:N方策
外文關鍵詞:N-policyhyper-exponential distribution
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在本篇論文,我們研究N方策單一服務者會故障之 排隊系統,顧客到達是服從卜瓦松過程而服務者的服務時間則是服從k階多重指數分配,所謂N方策是指當系統顧客數到達某一數目N時,則服務者開始服務,直到系統中沒有顧客時,服務者就停止服務。服務者的故障和修復時間會服從負指數分配。我們首先求出穩態解,再利用此穩態解求出系統特性如:在系統之平均顧客數與在系統之顧客平均等待時間。我們再導出其穩態的條件。其次,我們可以證明本文之排隊系統比標準 排隊系統、標準 排隊系統服務者會故障、N方策 排隊系統與N方策 排隊系統服務者會故障更一般化。最後,我們建立一個總成本函數,來決定最佳N值使總成本最小。

In this thesis, we study a single removable and non-reliable server in an infinite queueing system with Poisson arrivals and k-type hyper-exponential distribution for the service times. The so-called N-policy is that turns the server on when the number of customers reaches N and turns the server off when there are no customers in the system. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. We develop the steady-state results and present some system characteristics such as the expected number of customers in the system and the expected waiting time in the system. We provide the conditions for a stable queueing system. We also show that this system generalizes the ordinary queueing system with a reliable sever, the ordinary queueing system with a non-reliable server, the N-policy queueing system with a reliable server, and the N-policy queueing system with a non-reliable server. Finally, the total expected cost function is developed to determine the optimal value of the control parameter N.

Abstract
1. Introduction
1.1 Problem Statement
1.2 Literature Review 2
1.3 The Scope of the Study 3
2. Steady-State Results 4
2.1 Assumptions 4
2.2 Steady-State Equations 5
2.3 Probability Generating Functions 6
2.4 Stability Conditions 9
2.5 Special Cases 10
2.6 Computation of 10
3. Optimal N-policy 12
3.1 Computation for , , and 13
3.2 Total Expected Cost Function 13
3.3 Determining the Optimal Operating Policy 15
4. Conclusions and Future Research 16
4.1 Conclusions 16
4.2 Future Research 16
References 17

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[2] A.O. Allen, ”Probability, Statistics, and Queueing Theory with Computer Science Applications”, 2nd ed., Academic Press, Now York, (1990).
[3] K.-H. Wang, H.-M. Huang, “Optimal control of an queueing system with a removable service station”, Journal of the Operational Research Society, Vol. 46, 1014-1022, (1995).
[4] K.-H. Wang, H.-M. Huang, “Optimal control of a removable server in an queueing system with finite capacity”, Microelectronics and Reliability, Vol. 35, 1023-1030, (1995).
[5] K.-H.Wang, K.-L. Yen, “Optimal control of a removable server in an queueing system”, Thesis, (2000).
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[13] K.-H. Wang, “Optimal operation of a Markovian queueing system with a removable and non-reliable server”, Microelectronics and Reliability, Vol. 35, 1131-1136, (1995).
[14] K.-H. Wang, “Optimal control of an queueing system with removable service station subject to breakdowns”, Journal of the Operational Research Society, Vol. 48, 936-942, (1997).
[15] K.-H. Wang and J.C. Ke “A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity”, Applied Mathematical Modelling, Vol.24, 899-914, (2000).
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[17] K.-H. Wang and J.C.Ke “Control policies of an M/G/1 queueing system with a removable and non-reliable server”, International Transactions in Operational Research, Vol. 9, 195-212, (2002).

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