Comparison Results for Markov-Modulated Recursive Models
- 1 April 1997
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 11 (2), 203-217
- https://doi.org/10.1017/s0269964800004769
Abstract
We consider a general discrete-time stochastic recursive model that is influenced by an external Markov chain. Our aim is to investigate the effect that the transition matrix of the external process has on the system states of the model. To answer this question, we use new stochastic ordering concepts. Especially interesting are the results for infinite-stage Markov-modulated models. We illustrate our main results by three applications: an inventory model, a consumption model, and a queueing model for a time division multiplexing system.Keywords
This publication has 14 references indexed in Scilit:
- Stochastic Ordering and Dependence in Applied ProbabilityPublished by Springer Science and Business Media LLC ,1995
- MR/GI/1 queues by positively correlated arrival streamJournal of Applied Probability, 1994
- Monotonicity results for queues with doubly stochastic Poisson arrivals: Ross's conjectureAdvances in Applied Probability, 1991
- Stochastic convexity for multidimensional processes and its applicationsIEEE Transactions on Automatic Control, 1991
- Queues with nonstationary inputsQueueing Systems, 1989
- Risk theory in a Markovian environmentScandinavian Actuarial Journal, 1989
- Performance Trade-Offs in an integrated voice/data services TDM systemPerformance Evaluation, 1988
- On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian EnvironmentASTIN Bulletin, 1984
- Inequalities for Distributions with Given MarginalsThe Annals of Probability, 1980
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962