Explicit Convergence Rates of the Embedded M/G/1 Queue

作     者：Yuan Yuan LIU Zhen Ting HOU 

作者机构：School of MathematicsCentral South University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2007年第23卷第7期

页      面：1289-1296页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(No.10171009) 

主　　题：convergence rate Markov chains queues polynomial ergodicity geometric ergodicity 

摘      要：This paper investigates the explicit convergence rates to the stationary distribution π of the embedded M/G/1 queue; specifically, for suitable rate functions r（n） which may be polynomial with r（n） = n^l, l 〉 0 or geometric with r（n） = α^n, a 〉 1 and ＂moments＂ f ≥ 1, we find the conditions under which Σ∞n=0 r（n）｜｜P^n（i,·） - π（·）｜｜f ≤ M（i） for all i ∈ E. For the polynomial case, the explicit bounds on M（i） are given in terms of both ＂drift functions＂ and behavior of the first hitting time on the state O; and for the geometric case, the largest geometric convergence rate α＊ is obtained.