On stability of state-dependent queues and acyclic queueing networks
- 1 September 1989
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 21 (3) , 681-701
- https://doi.org/10.2307/1427642
Abstract
We consider a single server first-come-first-served queue with a stationary and ergodic input. The service rate is a general function of the workload in the queue. We provide the necessary and sufficient conditions for the stability of the system and the asymptotic convergence of the workload process to a finite stationary process at large times. Then, we consider acyclic networks of queues in which the service rate of any queue is a function of the workloads of this and of all the preceding queues. The stability problem is again studied. The results are then extended to analogous systems with periodic inputs.Keywords
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