On stability of state-dependent queues and acyclic queueing networks

Nicholas Bambos C · Jean C. Walrand

15 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Age of Information Optimization

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.

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References

1987Limit Theorems for Stochastic Processes 1962The stability of a queue with non-independent inter-arrival and service times 1987Introduction to Queueing Networks 1990An Introduction to Queueing Networks 1985Queues and Point Processes.1983Queues and Point Processes 1987Palm Probabilities and Stationary Queues 1967Queues with State-Dependent Stochastic Service Rates

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