On Q(H log H) Scaling of Network Delays

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.