Time and Energy Efficient Contention Resolution in Asynchronous Shared Channels

Abstract

A shared channel (also called a multiple access channel), introduced nearly 50 years ago, is among the most popular and widely studied models of communication and distributed computing. In a nutshell, a number of stations, independently activated over time, is able to communicate by transmitting and listening to a shared channel in discrete time slots, and a message is successfully delivered to all stations if and only if its source station is the only transmitter at a time. Despite a vast amount of work in the last decades, many fundamental questions remain open in the realistic situation where stations do not start synchronously but are awaken in arbitrary times (called dynamic or asynchronous scenario). What is the impact of an asynchronous start on channel utilization? How important is the knowledge/estimate of the number of contenders? Could non-adaptive protocols be asymptotically as efficient as adaptive ones? In this work we present a broad picture of results answering the abovementioned questions for the fundamental problem of Contention resolution, in which each of the contending stations needs to broadcast successfully its message.We show that adaptive algorithms or algorithms with the knowledge of the contention size k achieve a linear O(k) message latency even if the channel feedback is restricted to simple acknowledgements in case of successful transmissions and in the absence of synchronization. This asymptotically optimal performance cannot be extended to other settings: we prove that there is no non-adaptive algorithm without the knowledge of contention size k admitting latency o(k log k/(log log k) 2 ). This means, in particular, that coding (even random) with acknowledgements is not very efficient on a shared channel without synchronization or an estimate of the contention size. We also present a non-adaptive algorithm with no knowledge of contention size that almost matches the lower bound on latency.Finally, despite the absence of a collision detection mechanism, we show that our algorithms are also efficient in terms of energy, understood as the total number of transmissions performed by the stations during the execution.Key words-shared channel, multiple-access channel, contention resolution, distributed algorithms, randomized algorithms, lower bound, dynamic communication, adaptive and oblivious adversaries two classes: those allowing asymptotically optimal channel utilization and those which incur a substantial overhead.The formal model considered in this paper is the one commonly taken as the basis for theoretical studies on multiple access channels (cf. the surveys by Gallager [18] and Chlebus [14]). In what follows we overview it, paying special attention to the particular settings of this paper.Stations. A set of k stations are connected to the same multi-point transmission medium. The stations are anonymous, that is, they have no identification label (ID) to uniquely distinguish them. There is no central control: every station acts autonomously by means of a distributed algorithm. A...