Adversarial Models for Priority-Based Networks

We propose several variations of the adversarial queueing model to cope with packets that can have different priorities, the priority and variable priority models, and link failures, the failure and reliable models. We address stability issues in the proposed adversarial models. We show that the set of universally stable networks in the adversarial model remains the same in the four introduced models. From the point of view of queueing policies we show that several queueing policies that are universally stable in the adversarial model remain so in the priority, failure and reliable models. However, we show that lis, a universally stable queueing policy in the adversarial model, is not universally stable in any of the other models, and that no greedy queueing policy is universally stable in the variable priority model. Finally we analyze the problem of deciding stability of a given network under a fixed protocol. We provide a characterization of the networks that are stable under fifo and lis in the failure model. This characterization allows us to show that deciding network stability under fifo and lis in the proposed models can be solved in polynomial time.