計算 Ck/Cm/1 的機率分配之不變子空間

• Main Authors: Liu,Hsin-Yi, 劉心怡
• Other Authors: Hsing， Luh
• Format: Others
• Language: en_US
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/35059445181813127363

碩士 === 國立政治大學 === 應用數學研究所 === 92 === 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.