Study of level-dependent structured Markov chains and queues

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K00034
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical informatics
• Research Institution: Kyoto University
• Principal Investigator: Masuyama Hiroyuki 京都大学, 情報学研究科, 准教授 (60378833)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: マルコフ連鎖 / 待ち行列理論 / 漸近解析 / 切断近似 / 誤差評価 / 数値計算

Outline of Final Research Achievements

We first studied the subexponentially asymptotic analysis of upper block Hessenberg Markov chains with asymptotic level independence. Next, we derived computable upper bounds for the last-column-block-augmented truncation approximation to the stationary distribution in block-monotone Markov chains. Associated with this result, we also studied the convergence speed of the last-column-block-augmented truncation approximation of M/G/1-type Markov chains. Then, for general level-dependent structured Markov chains, we presented computable upper bounds for the last-column-block-augmented truncation approximation to the stationary distribution and a limit formula for the normalized fundamental matrix of the northwest-corner truncation. In addition, we derived computable upper bounds for the quasi-birth-and-death approximation to the stationary distribution in a special two-dimensional reflecting random walk.

Free Research Field

マルコフ連鎖と待ち行列理論の研究