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.

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关于块结构马尔可夫链的几何和代数瞬态

块结构马尔可夫链模拟了各种各样的排队问题，并在各个领域有许多重要的应用。已经对这些马尔可夫链的稳定性特性进行了很好的研究。在本文中，我们将介绍两种特定类型的块结构马尔可夫链的瞬态特性，包括 M/G/1 类型和 GI/M/1 类型。得到了几何瞬态和代数瞬态的系统参数的充要条件。还包括将结果可能扩展到连续时间马尔可夫链。