Throughput in Asynchronous Networks

Abstract: We introduce a new, "worst-case" model for an asynchronous communication network and investigate the simplest (yet central) task in this model, namely the feasibility of end-to-end routing. Motivated by the question of how successful a protocol can hope to perform in a network whose reliability is guaranteed by as few assumptions as possible, we combine the main "unreliability" features encountered in network models in the literature, allowing our model to exhibit all of these characteristics simultaneously. In particular, our model captures networks that exhibit the following properties: 1) On-line; 2) Dynamic Topology; 3)Distributed/Local Control 4) Asynchronous Communication; 5) (Polynomially) Bounded Memory; 6) No Minimal Connectivity Assumptions. In the confines of this network, we evaluate throughput performance and prove matching upper and lower bounds. In particular, using competitive analysis (perhaps somewhat surprisingly) we prove that the optimal competitive ratio of any on-line protocol is 1/n (where n is the number of nodes in the network), and then we describe a specific protocol and prove that it is n-competitive. The model we describe in the paper and for which we achieve the above matching upper and lower bounds for throughput represents the "worst-case" network, in that it makes no reliability assumptions. In many practical applications, the optimal competitive ratio of 1/n may be unacceptable, and consequently stronger assumptions must be imposed on the network to improve performance. However, we believe that a fundamental starting point to understanding which assumptions are necessary to impose on a network model, given some desired throughput performance, is to understand what is achievable in the worst case for the simplest task (namely end-to-end routing).