Networks of queues
- 1 June 1976
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 8 (2) , 416-432
- https://doi.org/10.2307/1425912
Abstract
The behaviour in equilibrium of networks of queues is studied. Equilibrium distributions are obtained and in certain cases it is shown that the state of an individual queue is independent of the state of the rest of the network. The processes considered in this paper are irreversible; however, the method used to establish equilibrium distributions is one which has previously only been used when dealing with reversible processes. Results are obtained for models of communication networks, machine interference and birth-illness-death processes.Keywords
This publication has 21 references indexed in Scilit:
- The continuity of queuesAdvances in Applied Probability, 1974
- Interaction of Markov processesAdvances in Mathematics, 1970
- Jobshop-Like Queueing SystemsManagement Science, 1963
- Letter to the Editor—The Output of an M/G/∞ Queuing System is PoissonOperations Research, 1963
- Cyclic QueuesJournal of the Operational Research Society, 1958
- Waiting Times When Queues are in TandemThe Annals of Mathematical Statistics, 1957
- An Ergodic Theorem for Markov Processes and Its Application to Telephone Systems with RefusalsTheory of Probability and Its Applications, 1957
- Random Queueing Processes with Phase-Type ServiceJournal of the Royal Statistical Society Series B: Statistical Methodology, 1956
- An Application of the Birth and Death Process to the Provision of Spare MachinesJournal of the Operational Research Society, 1954
- Queueing Systems with Phase Type ServiceJournal of the Operational Research Society, 1954