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Abstract Block-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In… Click to show full abstract
Abstract Block-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In this paper we will present transient properties for two specific types of block-structured Markov chains, including M/G/1 type and GI/M/1 type. Necessary and sufficient conditions in terms of system parameters are obtained for geometric transience and algebraic transience. Possible extensions of the results to continuous-time Markov chains are also included.
Journal Title: Journal of Applied Probability
Year Published: 2020
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