APPROXIMATIONS FOR MARKOV CHAINS WITH UPPER HESSENBERG TRANSITION MATRICES

スポンサーリンク

概要

• 論文の詳細を見る

• We present an approximation for the stationary distribution πof a countably infinite-state Markov chain with transition probability matrix P=(p_<ij>) of upper Hessenberg form. Our approximation makes use of an associated upper Hessenberg matrix which is spatially homogeneous one P^<(N)> except for a finite number of rows obtained by letting p_<ij>=P_<j-i+1>, i>__-N+1, for some distribution p={p_j} with mean ρ<1, where p_<-j>=0 for j>__-1. We prove that there exists an optimal ρ, say ρ^<*(N)> with which our method provides exact probabilities up to the level N. However, in general to find this optimal ρ^<*(N)> is practically impossible unless one has the exact distribution π. Therefore, we propose a number of approximations to ρ^<*(N)> and prove that a better approximation than that given by finite truncation methods can be obtained in the sense of smaller l_1-distance between exact distribution of its approximation. Numerical experiments are implemented for the M/M/1 retrial queue.

• 社団法人日本オペレーションズ・リサーチ学会の論文

著者

• Shin Y

  Department Of Statistics Changwon National University

• Shin Yang

  Department of Statistics, Changwon National University

• Shin Yang

  Department Of Electronic Engineering Faculty Of Engineering Graduate School Of Osaka University

関連論文

• APPROXIMATIONS FOR MARKOV CHAINS WITH UPPER HESSENBERG TRANSITION MATRICES
• CW Laser Oscillation in Z-Cut Nd-Diffused Ti:MgO:LiNbO_3 Waveguides

スポンサーリンク