The necessity of timekeeping in adversarial queueing

Abstract

We study queueing strategies in the adversarial queueing model. Rather than discussing individual prominent queueing strategies we tackle the issue on a general level and analyze classes of queueing strategies. We introduce the class of queueing strategies that base their preferences on knowledge of the entire graph, the path of the packet and its progress. This restriction only rules out time keeping information like a packet's age or its current waiting time. We show that all strategies without time stamping have exponential queue sizes, suggesting that time keeping is necessary to obtain subexponential performance bounds. We further introduce a new method to prove stability for strategies without time stamping and show how it can be used to completely characterize a large class of strategies as to their 1-stability and universal stability. © Springer-Verlag Berlin Heidelberg 2005.