Contention Resolution Without Collision Detection: Constant Throughput And Logarithmic Energy

Abstract

A shared channel, also called a multiple access channel, is among the most popular and widely studied models of communication in distributed computing. An unknown number of stations (potentially unbounded) is connected to the channel and can communicate by transmitting and listening. A message is successfully transmitted on the channel if and only if there is a unique transmitter at that time; otherwise the message collides with some other transmission and nothing is sensed by the participating stations. We consider the general framework without collision detection and in which any participating station can join the channel at any moment. The contention resolution task is to let each of the contending stations to broadcast successfully its message on the channel. In this setting we present the first algorithm which exhibits asymptotically optimal Θ(1) throughput and only an O (log k ) energy cost, understood as the maximum number of transmissions performed by a single station (where k is the number of participating stations, initially unknown). We also show that such efficiency cannot be reproduced by non-adaptive algorithms, i.e. , whose behavior does not depend on the channel history (for example, classic backoff protocols). Namely, we show that non-adaptive algorithms cannot simultaneously achieve throughput Ω (cid:16) k ) (cid:17) and energy O (cid:16) log 2 k (loglog k ) 2 (cid:17) .