On Q(H log H) Scaling of Network Delays
Burchard, A.; Liebeherr, J.; Ciucu, F.
INFOCOM 2007. 26th IEEE International Conference on Computer Communications. IEEE
Volume , Issue , 6-12 May 2007 Page(s):1866 - 1874
Digital Object Identifier   10.1109/INFCOM.2007.217
Summary:A recent result in network calculus theory provided statistical delay bounds for exponentially bounded traffic that grow as O(H log H) with the number of nodes on the network path. In this paper we establish the corresponding lower bound which shows that for such such types of traffic, typical end-to-end delays can indeed grow as Theta (H log H). The lower bound is obtained by analyzing the end-to-end delay in a tandem network where each packet maintains the same service time at each traversed node. The results of this paper provide conclusive evidence that, in general, delays have a qualitatively different scaling behavior than is suggested by a worst-case analysis or by an analysis that assumes independent service times at network nodes.

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