The Spectral Gap for Quasi-birth and Death Processes  

作　　者：Yong Hua MAO Liang Hui XIA 

机构地区：[1]School of Mathematical Sciences,LMCS,Ministry of Education,Beijing Normal University [2]Department of Mathematics,Ji'nan University

出　　处：《Acta Mathematica Sinica,English Series》2012年第5期1075-1090,共16页数学学报（英文版）

基　　金：Supported in part by Program for New Century Excellent Talents in University (NCET);973 Project (Grant No. 2011CB808000);NSFC (Grant No. 10721091)

摘　　要：For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.

关 键 词：Quasi-birth and death process spectral gap birth-death process M/M/1 in random environment MIMIc with synchronous vacation 

分 类 号：O211.6[理学—概率论与数理统计]