We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we g...We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization procedure.The upper bound of the spectral gap is also presented.展开更多
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 an...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.展开更多
基金Supported in part by 985 Project973 Project(Grant No.2011CB808000)+2 种基金NSFC(Grant No.11131003)SRFDP(Grant No.20100003110005)the Fundamental Research Funds for the Central Universities
文摘We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization procedure.The upper bound of the spectral gap is also presented.
基金Supported in part by Program for New Century Excellent Talents in University (NCET)973 Project (Grant No. 2011CB808000)NSFC (Grant No. 10721091)
文摘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.
