Dear Victor and Guang-Liang, following our messages on your paper, I, and the collegue that signs below, have discussed it thouroughly, and we have agreed that, besides logical issues in Theorem 1, there are other primary objections to your proof, originated by (5). a) Theorem 1 derives from relation (5), that we have interpreted as (roughly speaking): - if waiting times are unbounded the queue is unstable Since a variable can be unbounded even if finite, as it is for the negative exponential, (5) implies that queues with waiting times with such distributions cannot be stable. In our view, the thesis of Theorem 1 is already here: unbounded W_n implies unstable queue. Therefore (contrapositive) stable queue implies bounded W_n. Therefore we must clarify the origin of (5). b) We have looked at Loynes'article, that you cite as [3], and we have not found assertion (5), that you refer to [3]. The only result that resembles (5) is, in Loynes' article, Theorem 1, which asserts that "a queue is stable iff lim_n sup sum U_k < infty", which is completely different from your (5). The condition above, in fact, is not contradicted by negative exponential service and interarrival times with E[U_k]<0. In this case, in fact, E[sum U_k]=-infty. Can you explain these objections? Regards Flaminio and Luca Barletta
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 visit [2]http://www.como.polimi.it/Patria/ References 1. http://home.dei.polimi.it/borgonov/index.html 2. http://www.como.polimi.it/Patria/ _______________________________________________ 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
