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Two-time-scale markov chains and applications to quasi-birth-death queues (2005)
| Content Provider | CiteSeerX |
|---|---|
| Author | Yin, G. Zhang, Hanqin |
| Abstract | Abstract. Aiming at reduction of complexity, this work is concerned with two-time-scale Markov chains and applications to quasi-birth-death queues. Asymptotic expansions of probability vectors are constructed and justified. Lumping all states of the Markov chain in each subspace into a single state, an aggregated process is shown to converge to a continuous-time Markov chain whose generator is an average with respect to the stationary measures. Then a suitably scaled sequence is shown to converge to a switching diffusion process. Extensions of the results are presented together with examples of quasi-birth-death queues. Key words. Markov chain, singular perturbation, countable state space, asymptotic expansion, occupation measure, aggregation, switching diffusion, quasi-birth-death queue |
| File Format | |
| Volume Number | 65 |
| Journal | SIAM journal on applied mathematics |
| Language | English |
| Publisher Date | 2005-01-01 |
| Access Restriction | Open |
| Subject Keyword | Quasi-birth-death Queue Two-time-scale Markov Chain Asymptotic Expansion Markov Chain Singular Perturbation Aggregated Process Stationary Measure Diffusion Process Key Word Continuous-time Markov Chain Countable State Space Occupation Measure Probability Vector Single State |
| Content Type | Text |
| Resource Type | Article |
