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標題: 自我阻礙型排隊系統的效能分析
Measures of self-blocking queueing system
作者: 蔡裕立
Tsai, Yu-Li
關鍵字: Self-blocking
Series queue
Poisson arrival process
Quasi-birth-and-death process
Matrix-geometric method
出版社: 應用數學系所
引用: References [1] G.C. Hunt, Sequential arrays of waiting lines. Operations Research 4 (1956) 674-683. [2] B. Avi-Itzhak, A sequence of service stations with arbitrary input and regular service times. Management Science 11 (1965) 565-571. [3] B. Avi-Itzhak, H. Levy, A sequence of servers with arbitrary input and regular service times revisited. Management Science 41 (1995) 1039-1047. [4] B. Avi-Itzhak, M. Yadin, A sequence of two servers with no intermediate queue. Management Science 11 (1965) 553-564. [5] M.F. Neuts, Two queues in series with a finite, intermediate waiting room. Journal of Applied Probability 5 (1968) 123-142. [6] C. Langaris, B. Conolly, On the waiting time of a two stage queueing system with blocking. Journal of Applied Probability 21 (1984) 628-638. [7] T. Altiok, Approximate analysis of queues in series with phase-type service times and blocking. Operations Research 37 (1989) 601-610. [8] A. Brandwajn, Y.L.L. Jow, An approximation method for tandem queues with blocking. Operations Research 36 (1988) 73-83. [9] R.O. Onvural, Survey of closed queueing networks with blocking. ACM Computing Surveys 22 (1990) 83-121. [10] B. Avi-Itzhak, S. Halfin, Servers in tandem with communication and manufacturing blocking. Journal of Applied Probability 30 (1993) 429-437. [11] C.-M. Liu, C.-L. Lin, An efficient two-phase approximation method for exponential tandem queueing systems with blocking. Computers & Operations Research 22 (1995) 745-762. [12] A.Gomez-Corral, A tandem queue with blocking and Markovian arrival process. Queueing Systems 41 (2002) 343-370. [13] M. Vuuren, I. Adan, S.A.E.Resing-Sassen, Performance analysis of multi-server tandem queues with finite buffers and blocking. OR Spectrum 27 (2005) 315-338. [14] A. Gomez-Corral, M.E. Martos, Performance of two-stage tandem queues with blocking: The impact of several flows of signals. Performance Evaluation 63 (2006) 910-938. [15] G. Latouche, M.F. Neuts, Efficient algorithmic solutions to exponential tandem queues with blocking. SIAM. Journal on Algebraic and Discrete Methods 1 (1980) 93-106. [16] M.F. Neuts, Matrix-geometric solutions in stochastic models: An algorithmic approach. revised ed., Dover publications (1995) [17] T.J. Lee and G. de Veciana, Model and performance evaluation for multiservice network link supporting ABR and CBR services. IEEE Communications Letters, 4 (2000) 375-377. [18] R. Nelson, A performance evaluation of a general parallel processing model. ACM SIGMETRICS Performance Evaluation Review, 18 (1990) 13-26. [19] Y.Y. Kim and S.Q. Li, Performance evaluation of packet data services over cellular voice networks. Wireless Networks, 5 (1999) 211-219 [20] U.R. Krieger and V. Naumov, Analysis of a delay-loss system with a superimposed Markovian arrival process and state-dependent service times. In W.S. et al., editor, Numerical Solution of Markov Chains (NSMC99), Zaragoaz, Spain, Prensas Universitaris de Zaragoza (1999) 261-279. [21] M.S. Do, Y. Park, and J.Y. Lee, Channel assignment with QoS guarantees for a multiclass multicode CDMA System. IEEE Transactions on Vehicular Technology, 51 (2002) 935-948. [22] G. Bloch, S. Greiner, Meer, K.S. Trivedi, Queueing networks and Markov Chains: Modeling and performance evaluation with computer science applications. 2nd ed., Wiley-Interscience (2006) 127-140.
摘要: 我們研究考慮一種會產生自我阻礙現象的序列型排隊系統。我們假設顧客到達情形為Poisson過程,而服務站的服務時間遵循指數分配。我們推導出具備無限容量排隊系統的結構生成矩陣,並且運用矩陣幾何法來解出此系統的穩定狀態機率。我們也推導出系統穩定條件的解析式。關於無限容量系統的效能分析包含了:平均在系統的顧客人數、平均在系統的等候時間、系統的自我阻礙機率以及系統的平均生產量。對於個別服務站在設定不同的服務率下,配置次序對效能的影響也是本研究關注的重點。
In this thesis, we study a queueing system with self-blocking phenomenon. Poisson arrivals and exponential service times are assumed. We develop the structured generator matrix to compute steady-state probabilities of the self-blocking system with infinite space by matrix-geometric method. The stability condition of the system is obtained in closed-form. We also present some performance measures including mean number of customers in the system, mean waiting time in the system, blocking probability and mean throughput of the system, etc. The characteristics of the system with different service orders are discussed as well.
其他識別: U0005-0506201212183700
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