[Tccc] Jackson Network and Queueing Theory
nfonseca@ic.unicamp.br
nfonseca
Thu Nov 10 05:46:41 EST 2011
Is there any separated thread to discuss this and related problems?
nelson
> 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
>> _______________________________________________
>> IEEE Communications Society Tech. Committee on Computer Communications
>> (TCCC) - for discussions on computer networking and communication.
>> Tccc at lists.cs.columbia.edu
>> https://lists.cs.columbia.edu/cucslists/listinfo/tccc
>>
>
>
>
> --
> 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
>
> _______________________________________________
> IEEE Communications Society Tech. Committee on Computer Communications
> (TCCC) - for discussions on computer networking and communication.
> Tccc at lists.cs.columbia.edu
> https://lists.cs.columbia.edu/cucslists/listinfo/tccc
>
More information about the TCCC
mailing list