Minimizing Queue Length Regret Under Adversarial Network Models

Abstract

Stochastic models have been dominant in network optimization theory for over two decades, due totheir analytical tractability. However, these models fail to capture non-stationary or even adversarialnetwork dynamics which are of increasing importance for modeling the behavior of networksunder malicious attacks or characterizing short-term transient behavior. In this paper, we focuson minimizing queue length regret under adversarial network models, which measures the finite-time queue length difference between a causal policy and an “oracle” that knows the future. Twoadversarial network models are developed to characterize the adversary’s behavior. We provide lowerbounds on queue length regret under these adversary models and analyze the performance of twocontrol policies (i.e., the MaxWeight policy and the Tracking Algorithm). We further characterizethe stability region under adversarial network models, and show that both the MaxWeight policyand the Tracking Algorithm are throughput-optimal even in adversarial settings.