Broadcasting in Ad Hoc Multiple Access Channels

TL;DR

This paper investigates the capabilities of deterministic broadcast algorithms in dynamic adversarial multi-access channels, establishing bounds on injection rates for bounded latency and demonstrating the limits of such algorithms.

Contribution

It introduces new algorithms with increasing injection rate thresholds and proves the impossibility of bounded latency at higher rates.

Findings

Algorithms achieve bounded latency at injection rates up to 1/2

Injection rate 3/4 cannot be handled with bounded latency

Progression of algorithms corresponds to increasing injection rate thresholds

Abstract

We study broadcast in multiple access channels in dynamic adversarial settings. There is an unbounded supply of anonymous stations attached to a synchronous channel. There is an adversary who injects packets into stations to be broadcast on the channel. The adversary is restricted by injection rate, burstiness, and by how many passive stations can be simultaneously activated by providing them with packets. We consider deterministic distributed broadcast algorithms, which are further categorized by their properties. We investigate for which injection rates can algorithms attain bounded packet latency, when adversaries are restricted to be able to activate at most one station per round. The rates of algorithms we present make the increasing sequence consisting of $\frac{1}{3}$, $\frac{3}{8}$ and $\frac{1}{2}$, reflecting the additional features of algorithms. We show that injection rate $\frac{3}{4}$ cannot be handled with bounded packet latency.