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.
In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of a GI/G/N queueing system and the transient distribution of the length of queueing networks are obtained.
Zhen-ting HouSchool of Mathematical Sciences and Computing Technology, Central South University. Changsha 410075, China
In the present paper we first obtain the comparison principle for the nonlinear stochastic differentialdelay equations with Markovian switching. Later, using this comparison principle, we obtain some stabilitycriteria, including stability in probability, asymptotic stability in probability, stability in the pth mean, asymptoticstability in the pth mean and the pth moment exponential stability of such equations. Finally, an example isgiven to illustrate the effectiveness of our results.
The stability of stochastic delayed cellular neural networks(DCNNs) is investigated in this paper. Under the help of Lyapunov functional and the semimartingale convergence theorem, some sufficient criteria were obtained to check the almost sure exponential stability of the DCNNs.
