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
The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctu...The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. In the overloaded （OL） case, the asymptotic variability is studied for five performance measures： queue length, workload, busy time, idle time and number of departures. The proof is based on strong approximations, which approximate discrete performance processes with （reflected） Brownian motions. We conduct numerical examples to provide insights on these LIL results.展开更多
Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic p...Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.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 by the National Natural Science Foundation of China(No.11471053)
文摘The asymptotic variability analysis is studied for multi-server generalized Jackson network. It is characterized by law of the iterated logarithm （LIL）, which quantifies the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. In the overloaded （OL） case, the asymptotic variability is studied for five performance measures： queue length, workload, busy time, idle time and number of departures. The proof is based on strong approximations, which approximate discrete performance processes with （reflected） Brownian motions. We conduct numerical examples to provide insights on these LIL results.
文摘Using a bounding technique, we prove that the fluid model of generalized Jackson network （GJN） with vacations is the same as a GJN without vacations, which means that vacation mechanism does not affect the dynamic performance of GJN under fluid approximation. Furthermore, in order to present the impact of vacation on the performance of GJN, we show that exponential rate of convergence for fluid approximation only holds for large N, which is different from a GJN without vacations. The results on fluid approximation and convergence fate are embodied by the queue length, workload, and busy time processes.
