Objective:To study several types of ergodicity of the queue length of M/M/c queue with synchronous vacation. Methods: A matrix analytical method is applied to deal with it. Result: It is shown that {L ( t ), J (t) } i...Objective:To study several types of ergodicity of the queue length of M/M/c queue with synchronous vacation. Methods: A matrix analytical method is applied to deal with it. Result: It is shown that {L ( t ), J (t) } is geometrically ergodic if and only if it is ergodic. Conclusion:The criteria for the other types of ergodicity are obtained.展开更多
Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of...Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of P. In this paper, we study the relationship between gap（P） and the convergence rate of P^n. When P is transient, the convergence rate of pn is equal to 1 - gap（P）. When P is ergodic, we give the explicit upper and lower bounds for the convergence rate of pn in terms of gap（P）. These results are extended to L^∞ （π）-space.展开更多
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 ...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.展开更多
基金This work was partially supported by NNSF of China(No.10171009)"211 Project"+1 种基金"985 Project" Research Fund for Ph. D Programs of MOE of China(No.20010533001)
文摘Objective:To study several types of ergodicity of the queue length of M/M/c queue with synchronous vacation. Methods: A matrix analytical method is applied to deal with it. Result: It is shown that {L ( t ), J (t) } is geometrically ergodic if and only if it is ergodic. Conclusion:The criteria for the other types of ergodicity are obtained.
基金Supported in part by 985 Project,973 Project(Grant No.2011CB808000)National Natural Science Foundation of China(Grant No.11131003)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20100003110005)the Fundamental Research Funds for the Central Universities
文摘Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of P. In this paper, we study the relationship between gap（P） and the convergence rate of P^n. When P is transient, the convergence rate of pn is equal to 1 - gap（P）. When P is ergodic, we give the explicit upper and lower bounds for the convergence rate of pn in terms of gap（P）. These results are extended to L^∞ （π）-space.
基金Supported by National Natural Science Foundation of China(No.10171009)
文摘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.
