Dependencies in Markovian networks
- 1 March 1995
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 27 (1) , 226-254
- https://doi.org/10.2307/1428105
Abstract
Monotonicity and correlation results for queueing network processes, generalized birth–death processes and generalized migration processes are obtained with respect to various orderings of the state space. We prove positive (e.g. association) and negative (e.g. negative association) correlations in space and positive correlations in time for different situations, in steady state as well as in the transient phase of the system. This yields exact bounds for joint probabilities in terms of their independent versions.Keywords
This publication has 21 references indexed in Scilit:
- Lagged queue-length correlations in two-node networksQueueing Systems, 1991
- Comments on "A state-space interpretation of simultaneous stabilizationIEEE Transactions on Automatic Control, 1991
- Monotonicity of the throughput of a closed exponential queueing network in the number of jobsOR Spectrum, 1989
- Poisson functionals of Markov processes and queueing networksAdvances in Applied Probability, 1989
- Positive correlations in a three-node Jackson queueing networkAdvances in Applied Probability, 1989
- Association of probability measures on partially ordered spacesJournal of Multivariate Analysis, 1988
- Lower bounds for the probability of overload in certain queueing networksJournal of Applied Probability, 1985
- Interacting Particle SystemsPublished by Springer Nature ,1985
- Comparing counting processes and queuesAdvances in Applied Probability, 1981
- Point Processes and QueuesPublished by Springer Nature ,1981