Geometric Ergodicity for Skip-Free Markov Processes and Its Applications to Queueing Models

关于马氏过程几何遍历性的研究已有较多成果，但是对于一般状态空间中的马氏过程，关于几何遍历性的判定条件及收敛速率依然具有研究的意义。本文考虑一般状态空间自由跳马氏过程的几何遍历判定条件以及遍历速度，并将结果应用于M/G/1嵌入排队过程，给出了嵌入排队过程几何遍历性的判定条件和遍历速度，并提供了相应的数值验证。Numerous studies have been conducted on the geometric ergodicity of Markov processes. However, for Markov processes in general state spaces, there still remains significant value in determining the criteria for geometric ergodicity and convergence rates. This paper investigates the geometric ergodicity criteria and convergence rates for skip-free Markov processes in general state spaces. Our results are applied to the embedded M/G/1 process, establishing criterion for geometric ergodicity and explicit convergence rates for this process. Corresponding numerical examples are also presented.