On stability of state-dependent queues and acyclic queueing networks

The authors 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. The authors 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, they 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.