Adversarial models for priority-based networks

In this article, we propose several variations of the adversarial queueing model and address stability issues of networks and protocols in those proposed models. The first such variation is the priority model, which is directed at static network topologies and takes into account the case in which packets can have different priorities. Those priorities are assigned by an adversary at injection time. A second variation, the variable priority model, is an extension of the priority model in which the adversary may dynamically change the priority of packets at each time step. Two more variations, namely the failure model and the reliable model, are proposed to cope with dynamic networks. In the failure and reliable models the adversary controls, under different constraints, the failures that the links of the topology might suffer. Concerning stability of networks in the proposed adversarial models, we show that the set of universally stable networks in the adversarial model remains the same in the priority, variable priority, failure, and reliable models. From the point of view of protocols (or queueing policies), we show that several protocols that are universally stable in the adversarial queueing model remain so in the priority, failure, and reliable models. However, we show that the longest-in-system (LIS) protocol, which is universally stable in the adversarial queueing model, is not universally stable in any of the other models we propose. Moreover, we show that no 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 first-in-first-out (FIFO) and LIS in the failure model (and therefore in the reliable and priority models). This characterization allows us to show that the stability problem under FIFO and LIS in the failure model can be solved in polynomial time. (C) 2004 Wiley Periodicals, Inc.