[Tccc] Jackson Network and Queueing Theory

Flaminio Borgonovo borgonov
Fri Nov 11 18:41:13 EST 2011


   Hi Victor and Guang-Liang,
   I think  the  contrapositive argument in  Theorem 1 of  your paper is
   misused,  as Lachlan suspects.
   The proof of Theorem 1 shows that  statement <<P(B)=1 implies P(S)=0>>
   is false. Therefore we must assume:

    P(B)=1 implies P(S)=1  (bounded waiting times ---->  stable
   queue).
   Its contrapositive statement, still true, should be
   P(S)=0 implies P(B)=0,  (unstable queue ----> unbounded waiting times)
   and not, as sustained in the paper,
    P(S)=1 implies P(B)=1,  (stable queue ----> bounded waiting times).
   Therefore P(B)=1 for stable queues is not proved. And classic theory,
   where it can be also P(S=1) and P(B)=0 (stable queue  and unbounded
   waiting times), is not invalidated.
   This seems to invalidate Theorem 1 and the whole paper.
   Regards,
   Flaminio

   Prof. Flaminio Borgonovo
   Dip. di Elettronica e Informazione
   Politecnico di Milano
   P.zza L. Da Vinci 32
   20133 Milano, Italy
   tel. 39-02-2399-3637
   fax. 39-02-2399-3413
   e-mail: borgonov at elet.polimi.it
   URL [1]http://home.dei.polimi.it/borgonov/index.html
   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:
   >
   >
   [2]http://www.eee.hku.hk/research/doc/tr/TR2011003_Queueing_Theory_Rev
   isited.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
   > [3]https://lists.cs.columbia.edu/cucslists/listinfo/tccc
   >

References

   1. http://home.dei.polimi.it/borgonov/index.html
   2. http://www.eee.hku.hk/research/doc/tr/TR2011003_Queueing_Theory_Revisited.pdf
   3. https://lists.cs.columbia.edu/cucslists/listinfo/tccc



More information about the TCCC mailing list