Loading...
|
Please use this identifier to cite or link to this item:
https://nccur.lib.nccu.edu.tw/handle/140.119/32568
|
| Title: | Invariant Subspace of Solving Ck/Cm/1
計算 Ck/Cm/1 的機率分配之不變子空間 |
| Authors: | 劉心怡
Liu,Hsin-Yi |
| Contributors: | 陸行
劉心怡
Liu,Hsin-Yi |
| Keywords: | 不變子空間
矩陣多項式
飽和機率
invariant subspace
matrix polynomial
Kronecker products |
| Date: | 2003 |
| Issue Date: | 2009-09-17 13:45:59 (UTC+8) |
| Abstract: | 在這一篇論文中，我們討論 Ck/Cm/1 的等候系統。 我們利用矩陣多項式的奇異點及向量造 C_k/C_m/1 的機率分配的解空間。而矩陣多項式的非零奇異點和一個由抵達間隔時間與服務時間所形成的方程式有密切的關係。我們證明了在 E_k/E_m/1 的等候系統中，方程式的所有根都是相異的。但是當方程式有重根時，我們必須解一組相當複雜的方程式才能得到構成解空間的向量。此外，我們建立了一個描述飽和機率為 Kronecker products 線性組合的演算方法。
In this thesis, we analyze the single server queueing system
Ck/Cm/1. We construct a general solution space of the vector for stationary probability and describe the solution space in terms of singularities and vectors of the fundamental matrix polynomial Q(w). There is a relation between the singularities of Q(w) and the roots of the characteristic polynomial
involving the Laplace transforms of the interarrival and service
times distributions. In the Ek/Em/1 queueing system, it is proved that the roots of the characteristic polynomial are
distinct if the arrival and service rates are real. When
multiple roots occur, one needs to solve a set of equations of matrix polynomials. As a result, we establish a procedure for describing those vectors used in the expression of saturated probability as linear combination of Kronecker products. |
| Reference: | [1] Bellman R. Introduction to Matrix Analysis, MacGraw-
Hill, London, (1960).
[2] Bertsimas D., An analytic approach to a general class of
G/G/s queueing systems. Operations Research 38,139-155,
(1990).
[3] Bertsimas D., An exact FCFS waiting time analysis for a
general class of G/G/s queueing systems. Queueing systems
3, 305-320, (1988).
[4] Le Boudec, J. Y., Steady-state probabilities of the
PH/PH/1 queue. Queueing systems 3, 73-88, (1988).
[5] Evans, R. V. Geometric distribution in some two-
dimensional queueing systems. Operations Research 15, 830-
846, (1967).
[6] Gail, H. R., Hantler, S. L. and Taylor, B., A Spectral
analysis of M/G/1 and G/M/1 Type Markov chaons. Adv.
Appl. Prob. 28, 114-165, (1996).
[7] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrix
polynomials. Academic Press, New York (1982).
[8] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrix Topics
in Matrix (1991).
[9] Neuts, M. F. Matrix-Geomatric Solutions in Stochastic
Models. The John Hopkins University Press, (1981).
[10] Wang, H. S. A new Approach to Analyze Stationary
Probabilities Distributions of a PH/PH/1/N Queue, Master
thesis National Chengchi University, (2002).
[11] Wallace, V. The solution of quasi birth and death
processes arising from multiple access computer systems,
Ph. D. diss. Systems Engineering Laboratory, University
of Michigan, Tech. Report N 07742-6-T, (1969). |
| Description: | 碩士
國立政治大學
應用數學研究所
91751006
92 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0091751006 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
|
All items in 政大典藏 are protected by copyright, with all rights reserved.
|
