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Asymptotic Expansions of backward equations for Two-time-scale Markov Chains in Continuous Time

Acta Mathematicae Applicatae Sinica 2009年第3期25卷 457-476页

作者： Dung Tien Nguyen Department of Mathematics Wayne State University

This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained.

关键词： Markov chain backward equation two-time scale asymptotic expansion

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MARKOV SKELETON PROCESS IN PERT NETWORKS

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Acta Mathematica Scientia 2010年第5期30卷 1440-1448页

作者：孔祥星张玄候振挺 School of Mathematics Central South University

In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network （only consisting of all the related activities） is equal to the completion time of this path. We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process, the state space is related to the subnetwork structure. Then use the backward equation to compute the distribution of the sub-network＇s completion time, which is an important rule in project management and scheduling.

关键词： PERT networks Markov skeleton process backward equation

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Markov Skeleton Processes and Applications to Queueing Systems

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 537-552页

作者： Zhen-ting HouSchool of Mathematical Sciences and Computing Technology, Central South University. Changsha 410075, China School of Mathematical Sciences and Computing Technology Central South University Changsha China

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 ... 详细信息

关键词： Markov skeleton process (MSP) queueing system (H,Q)-pair backward equation

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