Adversarial queueing theory

We introduce a new approach to the study of dynamic (or continuous) packet routing, where packets are being continuously injected into a network. Our objective is to study what happens to packet routing under continuous injection as a function of network load, for various queueing policies. Our approach is based on the adversarial generation of packets, so that the results are more robust in that they do not hinge upon particular probabilistic assumptions. In suggesting a new approach to studying a classical phenomenon, it is important to give careful consideration to all the relevant previous work in packet routing, queueing theory and probabilistic analysis. We give a more detailed account of previous work in Appendix A, to permit comparison with our work. Here we summarize the salient features of prior work in order to motivate our model. Most prior work on packet routing has been in the static model in which there is a fixed initial set of packet routing requests; when these packets are delivered, the problem is considered solved and the analysis stops there. Static packet routing is a basic problem in the context of parallel computation models, but for the setting of communications networks it is essential to study the case of continuous injection of packets. While it is possible to try modelling such continuous problems statically, by delaying the entry of packets using synchronization barriers, a much more natural approach is to analyze standard (local–control) routing algorithms in this fully dynamic setting. Nearly all previous work in this regard has used probabilistic models for the generation (and sometimes, delivery) of packets. Such work can broadly be classified into: ∗Department of Computer Science, University of Toronto, Toronto, Canada M5S 1A4. Part of this work was performed while visiting the IBM T.J. Watson Research Center. †Laboratory for Computer Science, MIT, Cambridge, MA 02139. Supported by an ONR Graduate Fellowship. Part of this work was performed while visiting the IBM T.J. Watson Research Center. ‡IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120. §IBM T.J. Watson Research Center, Box 218, Yorktown Heights, NY 10598. 1. Queueing-theoretic approaches, where packets are generated by a Poisson injection process; frequently, each packet is assumed to have a random destination. A common assumption in queueing theory is that the time for a packet to pass through a server (i.e., an edge) is exponentially distributed whereas for packet routing this time is a constant. This apparently slight difference poses a world of subtle difficulties in adapting queueing theory to continuous packet routing.

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