Dear Lachlan and Flaminio, Thanks for your comments. Let V(X, Y) stand for "X implies Y", a logical implication statement in general. Write (X, Y) = (T, F) to mean "the value of X is T (true) and the value of Y is F (false)". Let V(T, F) = F represent "the value of V(X, Y) is F when (X, Y) = (T, F)". Smilarly, V(F, F) = V(F, T) = V(T, T) = T. In fact, V(T, F) = F and V(F, F) = V(F, T) = V(T, T) = T correspond to the truth table values of the implication, and V(T, F) = F is completely determined by (X, Y) = (T, F) regardless of what X or Y means. Any other assumption is unnecessary for V(T, F) = F. Unless one is reasoning with a different logic, V(T, F) = F is just fine both in general and in particular when X and Y represent P(B) = 1 and P(S) = 0, respectively. If one lets the value of "P(B) = 1" be "true", then one must let the value of "P(S) = 0" be "false" because a queue with a.s. bounded waiting time is not unstable.
Best regards, Guang-Liang and Victor -----Original Message----- From: Flaminio Borgonovo Sent: Saturday, November 12, 2011 7:41 AM To: Prof. Victor Li Cc: [email protected] ; [email protected] Subject: Re: [Tccc] Jackson Network and Queueing Theory 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: [email protected] URL [1]http://home.dei.polimi.it/borgonov/index.html On 10 November 2011 18:18, Prof. Victor Li <[email protected]> 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. > [email protected] > [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 _______________________________________________ IEEE Communications Society Tech. Committee on Computer Communications (TCCC) - for discussions on computer networking and communication. [email protected] https://lists.cs.columbia.edu/cucslists/listinfo/tccc _______________________________________________ IEEE Communications Society Tech. Committee on Computer Communications (TCCC) - for discussions on computer networking and communication. [email protected] https://lists.cs.columbia.edu/cucslists/listinfo/tccc
