Universal packet routing with arbitrary bandwidths and transit times

Abstract

We prove bounds for the length of optimal schedules for store-and-forward packet routing in the setting of arbitrary bandwidths and transit times. The problem is commonly studied only in the setting of unit bandwidths and unit transit times. Our results generalize the existing work to a much broader class of instances and also improve the known bounds significantly. For the case of unit transit times and bandwidths we improve the best known bound of 39(C + D) to 23.4(C + D), where C and D denote the trivial lower bounds congestion and dilation. If every link in the network has a certain minimum transit time or capacity our bounds improve even further up to 4.32(C + D). Key to our results is a framework which employs tight bounds for instances where each packet travels along only a small number of edges. Further insights for such instances would reduce our constants even more. This is the first improvement of the bounds for this very fundamental problem in more than 10 years. © 2011 Springer-Verlag.