Adversarial models for priority‐based networks

Abstract

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 firstin-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.

Stability of Adversarial Routing with Feedback

“…Next, we demonstrate that any scheduling policy universally stable in the 2-priority model remains stable in the adversarial model that we propose. This extends our understanding of universal stability in adversarial queuing with prioritized packets, as obtained byÀlvarez et al [1]. Finally, we show a possible extension of the proposed adversarial model to capture permanent link faults.…”

Stability of adversarial routing with feedback

“…Next, we demonstrate that any scheduling policy universally stable in the 2‐priority model remains stable in the adversarial model that we propose. This extends our understanding of universal stability in adversarial queuing with prioritized packets, as obtained by Àlvarez et al . Finally, we show a possible extension of the proposed adversarial model to capture permanent link faults.…”

“…In this section, we show that some scheduling policies are stable in the adversarial‐queuing model . We will use an auxiliary model, known as the priority model , which was introduced in . We refer to the model as a c‐priority model when there are c priorities.…”

“…Àlvarez et al showed that the scheduling policies Farthest‐To‐Go (FTG), Nearest‐From‐Source (NFS), and Shortest‐In‐System (SIS) are universally stable for the 2‐priority model. By this and Theorem , we obtain the following corollary.…”

“…Álvarez et al proposed a model that allows transient disruptions of the connectivity of the system. That model was extended by Álvarez et al to incorporate node failures.…”