BMAP的轨道分析和Q过程的伴随MAP

本文用轨道分析方法研究批量Markov到达过程(BMAP),有别于研究BMAP常用的矩阵解析方法.通过BMAP的表现(D_k,k=0,1,2,…),得到BMAP的跳跃概率,证明了BMAP的相过程是时间齐次Markov链,求出了相过程的转移概率和密度矩阵.此外,给定一个带有限状态空间的Q过程J,其跳跃点的计数过程记为N,证明了Q过程J的伴随过程X*=(N,J)是一个MAP,求出了该MAP的转移概率和表现(D_0,D_1),它们是通过密度矩阵Q来表述的.

Path Analysis of BMAP and Adjoint MAP of a Q Process

This article researches the batch Markov arrival process (BMAP) by using path-analysis method which is different from using conventional matrix analysis method. We are capable of calculating its jumping probability through the representation (D_k, k=0, 1, 2,...) of BMAP, demonstrating the fact that BMAP's phase process is time-homogeneous Markov chain, figuring out the transition probabilities and density matrix of the phase process. Moreover, if we give a Q process J with a finite state space and define the counting process of its jumping points as N, we can demonstrate that adjoint process X^*=(N, J) of Q process J is a MAP. The MAP's transition probabilities and representation (D₀, D₁) are exactly worked out, which are expressed by density matrix Q.