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Title: 以矩陣分解法計算特別階段形機率分配並有多人服務之排隊模型
A phase-type queueing model with multiple servers by matrix decomposition approaches
Authors: 顏源亨
Yen, Yuan Heng
Contributors: 陸行
Luh, Hsing
Yen, Yuan Heng
Keywords: 階段形機率分配
Phase-type distribution
multiple servers
stationary probability
Date: 2010
Issue Date: 2011-10-05 14:39:41 (UTC+8)
Abstract: 穩定狀態機率是讓我們了解各種排隊網路性能的基礎。在擬生死過程(Quasi-Birth-and-Death) Phase-type 分配中求得穩定狀態機率,通常是依賴排隊網路的結構。在這篇論文中,我們提出了一種計算方法-LU分解,可以求得在排隊網路中有多台服務器的穩定狀態機率。此計算方法提供了一種通用的方法,使得複雜的大矩陣變成小矩陣,並減低計算的複雜性。當需要計算一個複雜的大矩陣,這個成果變得更加重要。文末,我們提到了離開時間間隔,並用兩種方法 (Matlab 和 Promodel) 去計算期望值和變異數,我們發現兩種方法算出的數據相近,接著計算離開顧客的時間間隔相關係數。最後,我們提供數值實驗以計算不同服務器個數產生的離去過程和相關係數,用來說明我們的方法。
Stationary probabilities are fundamental in response to various measures of performance in queueing networks. Solving stationary probabilities in Quasi-Birth-and-Death(QBD) with phase-type distribution normally are dependent on the structure of the queueing network. In this thesis, a new computing scheme is developed for attaining stationary probabilities in queueing networks with multiple servers. This scheme provides a general approach of consindering the
complexity of computing algorithm. The result becomes more
significant when a large matrix is involved in computation. After determining the stationary probability, we study the departure process and the moments of inter-departure times. We can obtain the moment of inter-departure times. We compute the moments of inter-departure times and the variance by applying two numerical methods (Matlab and Promodel). The lag-k correlation of inter-departure times is also introduced in the thesis. The proposed approach is proved theoretically and verifieded with illustrative examples.
Reference: 1.Bitran, G.R., Dasu, S., Analysis of the Ph/Ph/1 queue.
Operations Research, Vol. 42, No. 1, pp.158--174, 1994.
2.Bodrog, L., Horvath, A., Telek, M.,Moment
characterization of matrix exponential and Markovian
arrival processes. Annals of operations Reseach, to
appear, 2008.
3.Chuan, Y.W., Luh, H., Solving a two-node closed queueing
network by a new approach, International Journal of
Information and Management Sciences, Vol. 16, No. 4, pp.
49--62, 2004.
4.Curry, G.L., Gautam, N., Characterizing the departure
process from a two server Markovian queue: A non-renewal
approach, Proceedings of the 2008 Winter Simulation
Conference, pp. 2075--2082, 2008.
5.El-Rayes, A., Kwiatkowska, M., Norman, G., Solving
infinite stochastic process algebra model through martix-
geometric methods, Proceedings of 7th Process Algebras
and Performance Modelling Workshop (PAPM99), J. Hillston
and M. Silva (Eds.), pp. 41--62, University of Zaragoza,
6.Gene H. Golub, Charles F. Van Loan, Matrix Computations,
3rd Edition, The Johns Hopkins University Press, 1996.
7.Latouche, G., Ramaswami, V., Introduction to Matrix
Analytic Methods in Stochastic Modeling, ASA-SIAM Series
on Statistics and Applied Probability (SIAM), Society for
Industrial Mathematics, Philadelphia, PA, 2000.
8.Neuts, M.F., Matrix-Geometric Solutions in Stochastic
Models, The John Hopkins University Press, 1981.
9.Roger, A.H., Charles, R.J., Matrix analysis, 4th
Edition,The Press Syndicate of the University of
Cambrige, 1990.
10.Sikdar, K., Gupta, U.C., The queue length distributions
in the finite buffer bulk-service $MAP/G/1$ queue with
multple vacations, Sociedad de Estadistica e
Investigacion Operativa, Vol. 13, No.1, pp. 75--103, 2005.
11.Telek, M., Horvath, G., A minimal representation of
Markov arrival processes and a moments matching method.
Performance Evaluation, Vol. 64, pp. 1153--1168, 2007.
12.Whitt, W. The queueing network analyzer, The Bell system
Technical Journal, Vol. 62, No. 9, pp. 2779--2814, 1983.
13.The MathWorks Company,
MATLAB The Language of Technical Computing: Using
MALTAB, Version 6, 2002.
14.Promodel Corp., Promodel User Guide, Promodel Corp.,
Description: 碩士
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Data Type: thesis
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