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題名 Invariant Subspace of Solving Ck/Cm/1
計算 Ck/Cm/1 的機率分配之不變子空間
作者 劉心怡
Liu,Hsin-Yi
貢獻者 陸行
劉心怡
Liu,Hsin-Yi
關鍵詞 不變子空間
矩陣多項式
飽和機率
invariant subspace
matrix polynomial
Kronecker products
日期 2003
上傳時間 17-Sep-2009 13:45:59 (UTC+8)
摘要 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.
參考文獻 [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).
描述 碩士
國立政治大學
應用數學研究所
91751006
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091751006
資料類型 thesis
dc.contributor.advisor 陸行zh_TW
dc.contributor.author (Authors) 劉心怡zh_TW
dc.contributor.author (Authors) Liu,Hsin-Yien_US
dc.creator (作者) 劉心怡zh_TW
dc.creator (作者) Liu,Hsin-Yien_US
dc.date (日期) 2003en_US
dc.date.accessioned 17-Sep-2009 13:45:59 (UTC+8)-
dc.date.available 17-Sep-2009 13:45:59 (UTC+8)-
dc.date.issued (上傳時間) 17-Sep-2009 13:45:59 (UTC+8)-
dc.identifier (Other Identifiers) G0091751006en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32568-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 91751006zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.abstract (摘要) 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.		en_US
dc.description.tableofcontents Chapter 1. Introduction......................................1
Chapter 2. Analysis of Ck/Cm/1...............................4
Chapter 3. Solution Spaces...................................9
Chapter 4. Singularities of Q(w) in the Open Unit Disk.......21
Chapter 5. A Method of Constructing Solution Spaces..........28
Chapter 6. Conclusion........................................43
Bibliography.................................................44
Appendix ....................................................46		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091751006en_US
dc.subject (關鍵詞) 不變子空間zh_TW
dc.subject (關鍵詞) 矩陣多項式zh_TW
dc.subject (關鍵詞) 飽和機率zh_TW
dc.subject (關鍵詞) invariant subspaceen_US
dc.subject (關鍵詞) matrix polynomialen_US
dc.subject (關鍵詞) Kronecker productsen_US
dc.title (題名) Invariant Subspace of Solving Ck/Cm/1zh_TW
dc.title (題名) 計算 Ck/Cm/1 的機率分配之不變子空間zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] Bellman R. Introduction to Matrix Analysis, MacGraw-zh_TW
dc.relation.reference (參考文獻) Hill, London, (1960).zh_TW
dc.relation.reference (參考文獻) [2] Bertsimas D., An analytic approach to a general class ofzh_TW
dc.relation.reference (參考文獻) G/G/s queueing systems. Operations Research 38,139-155,zh_TW
dc.relation.reference (參考文獻) (1990).zh_TW
dc.relation.reference (參考文獻) [3] Bertsimas D., An exact FCFS waiting time analysis for azh_TW
dc.relation.reference (參考文獻) general class of G/G/s queueing systems. Queueing systemszh_TW
dc.relation.reference (參考文獻) 3, 305-320, (1988).zh_TW
dc.relation.reference (參考文獻) [4] Le Boudec, J. Y., Steady-state probabilities of thezh_TW
dc.relation.reference (參考文獻) PH/PH/1 queue. Queueing systems 3, 73-88, (1988).zh_TW
dc.relation.reference (參考文獻) [5] Evans, R. V. Geometric distribution in some two-zh_TW
dc.relation.reference (參考文獻) dimensional queueing systems. Operations Research 15, 830-zh_TW
dc.relation.reference (參考文獻) 846, (1967).zh_TW
dc.relation.reference (參考文獻) [6] Gail, H. R., Hantler, S. L. and Taylor, B., A Spectralzh_TW
dc.relation.reference (參考文獻) analysis of M/G/1 and G/M/1 Type Markov chaons. Adv.zh_TW
dc.relation.reference (參考文獻) Appl. Prob. 28, 114-165, (1996).zh_TW
dc.relation.reference (參考文獻) [7] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrixzh_TW
dc.relation.reference (參考文獻) polynomials. Academic Press, New York (1982).zh_TW
dc.relation.reference (參考文獻) [8] Gohberg, I. C., Lancaster, P. and Rodman, L. Matrix Topicszh_TW
dc.relation.reference (參考文獻) in Matrix (1991).zh_TW
dc.relation.reference (參考文獻) [9] Neuts, M. F. Matrix-Geomatric Solutions in Stochasticzh_TW
dc.relation.reference (參考文獻) Models. The John Hopkins University Press, (1981).zh_TW
dc.relation.reference (參考文獻) [10] Wang, H. S. A new Approach to Analyze Stationaryzh_TW
dc.relation.reference (參考文獻) Probabilities Distributions of a PH/PH/1/N Queue, Masterzh_TW
dc.relation.reference (參考文獻) thesis National Chengchi University, (2002).zh_TW
dc.relation.reference (參考文獻) [11] Wallace, V. The solution of quasi birth and deathzh_TW
dc.relation.reference (參考文獻) processes arising from multiple access computer systems,zh_TW
dc.relation.reference (參考文獻) Ph. D. diss. Systems Engineering Laboratory, Universityzh_TW
dc.relation.reference (參考文獻) of Michigan, Tech. Report N 07742-6-T, (1969).zh_TW