Analysis of d-ary Tree Algorithms with Successive Interference Cancellation

TL;DR

This paper analyzes the performance of d-ary tree algorithms with successive interference cancellation, providing new results on throughput, collisions, successes, and idle slots, and challenging previous assumptions about binary trees.

Contribution

It introduces a novel analytical method applicable to various observables and disproves the claim that only binary trees maximize throughput.

Findings

Calculated mean throughput, collisions, successes, and idle slots for random tree algorithms.

Disproved the claim that only binary trees maximize throughput.

Provided new analytical results for non-binary tree algorithms.

Abstract

In this article, we calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximises throughput. Our method works with many observables and can be used as a blueprint for further analysis.