[Tccc] Jackson Network and Queueing Theory
Lachlan Andrew
lachlan.andrew
Thu Nov 10 05:32:36 EST 2011
Greetings Victor and Guang-Liang,
In general, it is wise to be very careful about claiming that an
entire field is wrong. A theorem that says "All M/M/1 queues are
unstable" should generally be regarded as suspect.
I believe Theorem 1 of this paper is flawed. The proof of Theorem 1
seems to assume that
(("for all queues, P(S)=1 implies P(B)=0" is false) and (for all
queues, P(B)=0 or P(B)=1))
implies
("for all queues, P(S)=1 implies P(B)=1" is true).
That is not the case. It simply implies
(there exists a queue such that either P(B)=1 or P(S)\neq 1)
A D/D/1 queue is such a queue. I don't think that tells us anything
about the stability of other queues in {\mathcal G}.
Please correct me if I am wrong.
As an aside, this is a good example of the benefit of peer review over
the "open review" that is being discussed on another thread. It is
more efficient to have three reviewers point out this flaw (if it is
one) than have all readers of the TCCC list spend time reading the
technical report.
Cheers,
Lachlan
On 10 November 2011 18:18, Prof. Victor Li <vli at eee.hku.hk> wrote:
> 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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>
--
Lachlan Andrew? Centre for Advanced Internet Architectures (CAIA)
Swinburne University of Technology, Melbourne, Australia
<http://caia.swin.edu.au/cv/landrew>
Ph +61 3 9214 4837
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