Self-stabilizing TDMA Algorithms for Wireless Ad-hoc Networks without External Reference

TL;DR

This paper investigates the design of collision-free, self-stabilizing TDMA algorithms for wireless ad-hoc networks without external references, establishing fundamental limits and demonstrating the existence of solutions with constant frame size through simulations.

Contribution

It introduces the first study of self-stabilizing TDMA algorithms without external references, providing lower bounds and proving the existence of solutions with constant frame size.

Findings

No solution exists for frame size less than max{2δ, χ₂}.

Existence of collision-free self-stabilizing TDMA algorithms with constant frame size is proven.

Simulations show convergence despite computation time uncertainties.

Abstract

Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, $\xi$, and then combine them into frames of uniform size, $\tau$. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, $\delta$, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no solution when the frame size is $\tau < \max\{2\delta,\chi_2\}$, where $\chi_2$ is the chromatic number for distance-$2$ vertex coloring. As a complement to this lower bound, we focus on proving the existence of collision-free self-stabilizing TDMA algorithms that use constant frame size of $\tau$. We consider basic settings (no hardware support for collision detection and no prior clock synchronization), and the collision of concurrent transmissions from transmitters that are at most two hops apart. In the context of self-stabilizing systems that have no external reference, we are the first to study this problem (to the best of our knowledge), and use simulations to show convergence even with computation time uncertainties.