[Tccc] Jackson Network and Queueing Theory
Prof. Victor Li
vli
Thu Nov 10 02:18:51 EST 2011
Dear colleagues,
Nearly a decade ago we initiated a discussion about Jackson networks of queues
on this mailing list. Since then some colleagues have enquired about our follow-up
research regarding this issue. A recent paper by us is now available
as a technical report at the website below:
http://www.eee.hku.hk/research/doc/tr/TR2011003_Queueing_Theory_Revisited.pdf
In this paper we consider the stability of queues. We find that
the condition given in the literature, i.e., the traffic intensity is less
than 1, is only necessary but not sufficient for a general single-server queue to be
stable. This shows again that product-form solutions of Jackson networks
are incorrect for such networks are actually unstable.
In the paper we also give necessary and sufficient conditions for a G/G/1 queue to
be stable, and discuss the implications of our results.
Queueing theory has been widely used in performance analysis of computer and
communication systems. Colleagues who are teaching courses on performance
analysis or doing research in this area, and students who are learning how to apply
queueing theory to performance analysis, might be interested in our results.
Comments on our paper are very much appreciated and can be sent to us by
e-mail. Thank you very much for your attention.
Best regards,
Guang-Liang Li and Victor O.K. Li
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