Abstract
In this paper, we study the superposition of finitely many Markov renewal processes with countable state spaces. We define the S-Markov renewal equations associated with the superposed process. The solutions of the S-Markov renewal equations are derived and the asymptotic behaviors of these solutions are studied. These results are applied to calculate various characteristics of queueing systems with superposition semi-Markovian arrivals, queueing networks with bulk service, system availability, and continuous superposition remaining and current life processes.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Reference34 articles.
1. Jacod J. (1971) Théorème de renouvellement et classification pour les chaînes semi-Markoviennes. Ann. Inst. H. Poincaré, B 7, 83–129.
2. Cherry W. P. and Disney R. L. (1983) The superposition of two independent Markov renewal processes. Zastos Mat. XVII, 567–602.
3. The Existence and Uniqueness of Stationary Measures for Markov Renewal Processes
4. On the Equilibrium Distribution of a Class of Finite-State Generalized Semi-Markov Processes
5. Corrections et compléments à l'article: Théorème de renouvellement et classification pour les chaînes semi-Markoviennes;Jacod;Ann. Inst. H. Poincaré,1974
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献