Minimizing Queue Length Regret Under Adversarial Network Models

Stochastic models have been dominant in network optimization theory for over two decades, due to their analytical tractability. However, these models fail to capture non-stationary or even adversarial network dynamics which are of increasing importance for modeling the behavior of networks under malicious attacks or characterizing short-term transient behavior. In this paper, we focus on 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. Two adversarial network models are developed to characterize the adversary's behavior. We provide lower bounds on queue length regret under these adversary models and analyze the performance of two control policies (i.e., the MaxWeight policy and the Tracking Algorithm). We further characterize the stability region under adversarial network models, and show that both the MaxWeight policy and the Tracking Algorithm are throughput-optimal even in adversarial settings.