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On queues with periodic inputs

Published online by Cambridge University Press:  14 July 2016

Nicholas Bambos  and
Jean Walrand
Nicholas Bambos
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗ Postal address for both authors: Department of Electrical Engineering and Computer Sciences, and Electronics Research Laboratory, University of California, Berkeley, CA 94720, USA.
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Abstract

We consider a single-server queue with a periodic and ergodic input. It is shown that if the traffic intensity is less than 1, then the waiting time process is asymptotically periodic. Limit theorems associated with the asymptotic behavior of the queue are also proven. The results are then extended to acyclic networks of queues with periodic inputs. Particular cases of these results had been previously obtained for a single queue with periodic Poisson arrival input process and with independent and identically distributed service times.

Keywords

PERIODIC RANDOM MARKED POINT PROCESSESERGODICITYSTABILITYASYMPTOTIC PERIODICITYLIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 381 - 389
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Research supported in part by NSF Grant No. ECS-8421128.

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