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On stability of state-dependent queues and acyclic queueing networks

Published online by Cambridge University Press:  01 July 2016

Nicholas Bambos  and
Jean Walrand
Nicholas Bambos
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗Department of Electrical Engineering and Computer Sciences and Electronic Research Laboratory, University of California, Berkeley CA 94720, USA.
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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

STATE-DEPENDENT ACYCLIC QUEUEING NETWORKSRANDOM MARKED POINT PROCESSESERGODICITYSTOCHASTIC DIFFERENTIAL EQUATIONSASYMPTOTIC BEHAVIOR
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 681 - 701
Copyright
Copyright © Applied Probability Trust 1989 

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