First passage times for Markov renewal processes and applications

First passage times for Markov renewal processes and applications

This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be eff...

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Veröffentlicht in:Science China. Mathematics 2000-12, Vol.43 (12), p.1238-1249
Hauptverfasser: Xu, Guanghui, Yuan, Xueming, Li, Quanlin
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Algorithms
Convergence
Queuing theory
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Yuan, Xueming
Li, Quanlin
description This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.
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subjects Algorithms
Convergence
Queuing theory
title First passage times for Markov renewal processes and applications
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