The input-output map of a monotone discrete-time quasireversible node (queueing theory)
- 1 March 1993
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 39 (2) , 543-552
- https://doi.org/10.1109/18.212284
Abstract
A class of discrete-time quasi-reversible nodes called monotone, which includes discrete-time analogs of the ./M/∞ and ./M/1 nodes, is considered. For stationary ergodic nonnegative integer valued arrival processes, the existence and uniqueness of stationary regimes are proven when a natural rate condition is met. Coupling is used to prove the contractiveness of the input-output map relative to a natural distance on the space of stationary arrival processes that is analogous to Ornstein's d¯ distance. A consequence is that the only stationary ergodic fixed points of the input-output map are the processes of independent and identically distributed Poisson random variables meeting the rate conditionKeywords
This publication has 10 references indexed in Scilit:
- Departures from Many Queues in SeriesThe Annals of Applied Probability, 1991
- An invariant distribution for the G/G/1 queueing operatorAdvances in Applied Probability, 1990
- Probability, Random Processes, and Ergodic PropertiesPublished by Springer Nature ,1988
- A discrete-time queueing networkJournal of Applied Probability, 1983
- A probabilistic look at networks of quasi-reversible queuesIEEE Transactions on Information Theory, 1983
- A Generalization of Ornstein's $\bar d$ Distance with Applications to Information TheoryThe Annals of Probability, 1975
- An Application of Ergodic Theory to Probability TheoryThe Annals of Probability, 1973
- Some Applications of Probability Generating Functionals to the Study of Input-Output StreamsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1968
- PROBABILITY MEASURES IN A METRIC SPACEPublished by Elsevier ,1967
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962