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On closed ring queueing networks

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Nicholas Bambos
Nicholas Bambos*
Affiliation:
University of California, Los Angeles
*
∗ Postal address: Electrical Engineering Department, School of Engineering and Applied Science, 405 Hilgard Avenue, Los Angeles, CA 90024–1594, USA.
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Abstract

In this paper we first study ring structured closed queueing networks with distinguishable jobs. Under assumptions of periodicity and ergodicity of the service times, essentially the most general, it is shown that the limits defining the average flows of the jobs exist almost surely, and methods for their estimation by simulation are given. However, it turns out that the values of the flows depend on the initial positions of the jobs, due to the emergence of distinct persistent blocking modes. The effect of these modes on the behavior of general networks with queueing loops is examined.

For independent and identically distributed service times, conditions are specified for the network to asymptotically approach a steady state at large times.

Finally, we study the special case of ring networks with indistinguishable items and stationary and ergodic service times. It is shown that as the number of jobs in the network increases towards infinity, the average circulation time converges to the maximum of the expectations of the service times.

Keywords

STATIONARY RING NETWORKSFLOW ERGODICITYSUBADDITIVE STOCHASTIC PROCESSESRESONANT BLOCKING MODESFLOW ASYMPTOTICS

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 4 , December 1992 , pp. 979 - 995
Copyright
Copyright © Applied Probability Trust 1992 

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