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研究生:莊依文
論文名稱:封閉式等候網路機率分配之估計與分析
論文名稱(外文):Estimation of probability distributions on closed queueing networks
指導教授:陸行陸行引用關係
學位類別:碩士
校院名稱:國立政治大學
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:2001
畢業學年度:89
語文別:英文
論文頁數:32
中文關鍵詞:封閉式等候線網路穩定機率
外文關鍵詞:Phase typeclosedproduct-formsstationary probabilities
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在這一篇論文裡,我們討論兩個階段的封閉式等候線網路,其中服務時間的機率分配都是Phasetype 分配。
我們猜測服務時間的機率分配和離開時間間隔的機率分配滿足一組聯立方程組。然後, 我們推導出非邊界狀態的穩定機率可以被表示成 product-form 的線性組合, 而每個 product-form 可以用聯立方程組的根來構成。
利用非邊界狀態的穩定機率, 我們可以求出邊界狀態的機率。
最後我們建立一個求穩定機率的演算過程。 利用這個演算方法,
可以簡化求穩定機率的複雜度。

In this thesis, we are concerned with the
property of a two-stage closed system in which the service times
are identically of phase type. We first conjecture that the
Laplace-Stieltjes Transforms (LST) of service time distributions
may satisfy a system of equations. Then we present that the
stationary probabilities on the unboundary states can be written
as a linear combination of product-forms. Each component of these
products can be expressed in terms of roots of the system of
equations. Finally, we establish an algorithm to obtain all the
stationary probabilities. The algorithm is expected to work well
for relatively large customers in the system.



1.Bellman R., Introduction to Matrix Analysis
(MacGraw-Hill, London) (1960).
2.Bertsimas D., An exact FCFS waiting time analysis for a class of G/G/s queueing systems. QUESTA, 3,(1988) 305-320.
3.Bertsimas D., An analytic approach to a general class of G/G/s queueing systems. Operations Research, 38 (1990) 139-155.
4.Buzen, J.P., Computational algorithms for the
closed queueing networks with exponential servers. Commun.
ACM, 16, 9(Sept.), (1973) 527-531.
5.Conway, A.E., and Georganas, N.D., RECAL--A new
efficient algorithm for the exact analysis of multiple-chain
closed queuing networks ,Journal-of-the-Association-for-Computer-Machinery , 33, 4(Oct.), (1986) 768-791.
6. Conway, A.E., and Georganas, N.D., Docomposition and arregation by class in closed queueing networks. IEEE Trans. Softw. Eng., 12, 1025-1040, (1986).
7. Ganesh, A., and Anantharam, V., Stationary tail in probabilities in exponential server tandem queues with renewal arrivals. in Frank P.\ Kelly and Ruth J. Williams (eds.), Stochastic Networks, The IMA Volumes in Mathematics
and Its Applications, 71, (Springer-Verlag, 1995), 367-385.
8.Fujimoto, K., and Takahashi, Y., Tail behavior of the stationary distributions in two-stage tandem queues---numerical experiment and conjecture. Journal of the Operations Research Society of Japan, 39-4, (1996) 525-540.
9. Fujimoto, K., Takahashi, Y., and Makimoto, N., Asymptotic Properties of Stationary Distributions in Two-Stage Tandem Queueing Systems. Journal of the Operations Research Society of Japan, 41-1, (1998) 118-141.
10. Gordon, W.J., and Newell, G.F., Matrix-Geometric Solutions in Stochastic Models (The John Hopkins University Press, 1981).
11. Golub, G.H., and Van Loan, C.F.,
Matrix--Computations (The John Hopkins University Press, 1989).
12. Chao, X., A Queueing Network Model with Catastrophe and Product Form Solution, Operations Research Letters, 18, (1995)
75-79.
13. Chao, X., Pinedo, M. and Shaw, D., An Assembly Network of Queues with Product Form Solution, Journal of Applied Probability, 33, (1996) 858-869.
14. Chao, X., Miyazawa, M., Serfozo, R., and
Takada. H., Necessary and sufficient conditions for product form
queueing networks, Queueing Systems, 28, (1998),377-401.
15. Chao, X., and Miyazawa. M., On quasi-reversibility and partial balance: An alternative approach to product form results, Operations Research, 46, (1998) 927-933.
16. Neuts, M.F., Matrix-Geometric Solutions in
Stochastic Models (The John Hopkins University Press, 1981).
17. Neuts, M.F., and Takahashi, Y.\, Asymptotic
behavior of the stationary distributions in the $GI/PH/c$ queue with heterogeneous servers, Z. Wahrscheinlichkeitstheorie verw.\ Gebiete, 57 (1988) 441-452.
18. Le Boudec, J.Y., Steady-state probabilities of the PH/PH/1
queue. Queueing Systems, 3 (1988) 73-88.
19. Luh, H., Matrix product-form solutions of stationary probabilities in tandem queues. Journal of the Operations Research, 42-4 (1999) 436-656.
20. Reiser, M., and Kobayashi, H., Queueing networks
with multiple closed chains, theory and computational algorithms. IBM J. Res. Dev. , 19,(1975) 283-294.
21. Reiser, M., and Lavenberg, S. S., Mean value
analysis of closed multichain queueing networks.
Journal-of-the-Association-for-Computer-Machinery , 27,
(1980) 313-322.
22. Seneta, E., Non-negative Matrices and Markov Chains
(Springer-Verlag, 1980).
23. Takahashi, Y., Asymptotic exponentiality of the tail of the waiting-time distribution in a PH/PH/c queue. Advanced Applied Probability, 13 (1981) 619-630.

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