# On the stability of two-chunk file-sharing systems

## TL;DR

This paper analyzes the stability of various two-chunk peer-to-peer file sharing algorithms, identifying conditions for stability and proposing a system with provably desirable performance under certain assumptions.

## Contribution

It provides a rigorous stability analysis of multiple chunk selection algorithms, highlighting which are stable and proposing a stable system design.

## Key findings

- Many algorithms are unstable or oscillate under certain conditions.
- Most results are based on deterministic large system limits.
- Proofs for stochastic systems are provided in simple cases.

## Abstract

We consider five different peer-to-peer file sharing systems with two chunks, with the aim of finding chunk selection algorithms that have provably stable performance with any input rate and assuming non-altruistic peers who leave the system immediately after downloading the second chunk. We show that many algorithms that first looked promising lead to unstable or oscillating behavior. However, we end up with a system with desirable properties. Most of our rigorous results concern the corresponding deterministic large system limits, but in two simplest cases we provide proofs for the stochastic systems also.