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標題: 含有會調整工作效率之 M/M/R 排隊系統之成本分析
Cost Analysis of M/M/R Queue with Multiple Working Vacations
作者: 巫佳煌
Wu, Chia-Huang
關鍵字: cost
rate matrix
sensitivity analysis
working vacations
出版社: 應用數學系所
引用: [1] Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters 33 (2005) 201-209. [2] A.D. Banik, U.C. Gupta, S.S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation, Applied Mathematical Modelling (2006), in press. [3] U. Chatterjee, S.P. Mukherjee, GI/M/1 queue with server vacations, Journal of the Operational Research Society 41 (1990) 83-87. [4] B.T. Doshi, Queueing systems with vacations- a survey, Queueing Systems 1 (1986) 29-66. [5] S.W. Fuhrmann, R.B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacations, Operations Research 33 (1985) 1117-1129. [6] F. Karaesmen, S.M. Gupta, The finite capacity GI/M/1 queue with server vacations, Journal of the Operational Research Society 47 (1996) 817-828. [7] T. Lee, The M/G/1/N queue with vacation and exhaustive service discipline, Operations Research 32 (1984) 774-784. [8] M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models, Johns Hopkins University Press, Baltimore, 1981. [9] L.D. Servi, S.G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Perform. Evaluation 50 (2002) 41-52. [10] H. Takagi, Queueing Analysis - A Foundation of Performance Evaluation Vacation and Priority Systems, vol. 1, North-Holland, New York, 1991. [11] N.S. Tian, The GI/M/1 queueing system with a single exponential vacation, J. Syst. Sci. Math. Sci. 13 (1993) 1-9. [12] N.S. Tian, The GI/M/1 queue with phase-type vacations, Acta Mathematicae Applicatae Sinica 16 (1993) 452-461. [13] N. Tian, D. Zhang, C. Cao, The GI/M/1 queue with exponential vacations, Queueing Systems 5 (1989) 331-344. [14] J.A. White, J.W. Schmidt, G.K. Bennett, Analysis of Queueing Systems, Academic Press, New York, 1975. [15] D.A. Wu, H. Takagi, M/G/1 queue with multiple working vacations, Performance Evaluation 63 (2006) 654-681.
摘要: 此篇論文分析研究了M/M/R排隊含多個服務者會調整工作效率之成本分析情形。其中顧客到達為一卜瓦松過程,服務者的休假時間長度與服務時間的分配假設為指數分配。我們假設當系統中沒有等待服務的顧客時,服務者會調降工作效率。矩陣幾何法在此篇論文的用處主要是去簡化繁雜的穩態方程式以及推導出穩態機率解與系統效能測度。我們把導出的結果與之前學者所完成的M/M/1/WV排隊系統做比較確認,可以發現我們的結果是正確的。矩陣幾何法在實際應用上是十分有效率的。同時我們做了數值模擬與敏感度分析。在成本函數與單位成本確定之後我們也完成了成本分析並找到了服務者與另一服務效率的聯合最佳解。
This thesis analyzes an M/M/R queue with multiple working vacations which the server works with different service rates rather than completely terminates service during the vacation period. We assume that the server begins a working vacation when the system is empty. We show that this is a generalization of an M/M/1 queue with working vacations considered in the literature. Service times during vacation period, service times during service period and vacation times are all exponentially distributed. We obtain the useful formula for the rate matrix through matrix-geometric method. We further develop the explicit formulae for system performance measures. A cost model is derived to determine the optimal values of the number of servers and the working vacation rate simultaneously at the minimal total expected cost per unit time. Under the optimal operating conditions, numerical results are provided in which several system performance measures are calculated based on assumed numerical values of the system parameters. Sensitivity investigation is also presented.
其他識別: U0005-2706200716200700
Appears in Collections:應用數學系所



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