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arXiv · 2404.18044

Decay property of a class of d-dimensional Markov processes

Yanyun Li
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Abstract

In this paper, we consider the decay property of a special class of $d$-dimensional Markov processes, which can be viewed as a stopped network with the external customer being blocked to empty nodes. The exact value of the decay parameter $\lambda_{\mathcal{C}}$ is obtained by using a new method. It is proved that the process is $\lambda_{\mathcal{C}}$-transient. The corresponding $\lambda_{\mathcal{C}}$-invariant measures and quasi-distributions are also presented. Finally, an example on auto quick repair service network is presented to illustrate the results obtained in this paper.

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Yanyun Li. 2024-04-28. Decay property of a class of d-dimensional Markov processes. https://arxiv.org/abs/2404.18044

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