Effective routing and scheduling in adversarial queueing networks

In an adversarial queueing network, the incoming traffic is decided by an adversary, who operates under a reasonable rate restriction. This model provides a valuable, complementary point of view to that of the traditional queueing network model in which arrivals are modeled by stochastic processes. As a result, the adversarial queueing network model has attracted much attention in recent years, especially as a way of modeling packet injections into a communication network. Our main result is a simple, effective packet routing and scheduling algorithm with a provably good performance. Specifically, our algorithm keeps the system stable (bounded number of packets in the system), with the bound on the number of packets in the system that is O((1 - r)(-1)), where r can be interpreted as the arrival rate of the packets into the communication network. This improves upon the work of Gamarnik [12], who designed an algorithm for which the number of packets in the system is O((1 - r)(-2)); moreover, our result matches the traditional queueing-theoretic number-in-system bound.