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標題: 有限容量M/M/R排隊系統含有第二選擇服務之成本分析
Cost analysis of a finite capacity M/M/R queueing system with second optional service
作者: 郭育廷
Kuo, Yu-Ting
關鍵字: 成本
first essential service (FES) channel
second optional service (SOS) channel
matrix-geometric method
sensitivity analysis
出版社: 應用數學系所
引用: References [1] Al-Jararha, J. and Madan, K.C. (2003) An M/G/1 queue with second optional service with general service time distribution. Information and Management Sciences 14, 47-56. [2] Arumuganathan, R. and Jeyakumar, S. (2005) Steady state analysis of a bulk queue with multiple vacations, setup times with N-policy with closedown times. Applied Mathematical Modelling 29 (10), 972-986. [3] Choudhury, G. and Paul, M. (2006) A batch arrival queue with a second optional service channel under N-policy. Stochastic Analysis and Applications 24, 1-21. [4] Hilliard, J.E., (1976) An approach to cost analysis of maintenance float systems. AIIE Transaction 8, 128-133. [5] Ke, J.-C., (2007) An M[x]/G/1 system with startup server and J additional options for service. Applied Mathematical Modelling, (in press) [6] Madan K.C., (2000) An M/G/1 queue with second optional service. Queueing Systems 34, 37-46. [7] Medhi, J., (2002) A single server Poisson input queue with a second optional channel. Queueing Systems 42, 239-242. [8] Neuts, M.F., (1981) Matrix Geometric Solutions in Stochastic Models: an Algorithmic Approach. The John Hopkins University Press: Baltimore. [9] Wang, J., (2004) An M/G/1 queue with second optional service and server breakdowns. Computers and Mathematics with Applications 47, 1713-1723.
摘要: 在本篇論文中,我們研究有限容量M/M/R排隊系統,服務者可提供 主要與選擇之兩種服務模式。顧客的到達時間呈指數分配,服務 者的第一主要服務與第二選擇服務兩者皆服從指數分配。每一位 顧客到達系統時均需先接受主要服務,並在完成主要服務後有 theta (0<=theta<=1) 的機率會繼續使用第二選擇 服務,或有(1−theta) 的機率會選擇離開系統。我們使用 矩陣-幾何法求得穩態機率值,並進而定義多種系統效能測度。 接著建立一個成本模型,且同時找出最佳的服務者個數與最佳的 系統顧客容量數。在給定的系統參數值之下,我們計算了在最佳 控制時的一些系統特性之數值結果。同時,我們亦進行了敏感度 分析的研究。
In this thesis, we have studied a finite capacity M/M/R queueing system with second optional service (SOS) channel. The interarrival times of arriving customers follow an exponential distribution. The service times of the first essential service (FES) channel and the second optional service channel are assumed to follow an exponential distribution. A customer may leave the system either after the first essential service channel with probability (1−theta) or at the completion of the first essential service channel may immediately go for a second optional service channel with probability theta (0<=theta<=1). Using matrix-geometric method, we obtain the steady-state probabilities and various system performance measures. Cost model is developed to determine the optimal number of channels and the optimal system capacity, simultaneously. The minimum expected cost, the optimal number of channels, the optimal system capacity, and system performance measures are evaluated for some specified system parameters' values. Sensitivity investigation for the expected cost with respect to specified parameters is also performed.
其他識別: U0005-2306200717420100
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