Mean Field Models of Message Throughput in Dynamic Peer-to-Peer Systems

TL;DR

This paper develops mean field models to analyze how peer churn rates and buffer sizes limit message throughput in dynamic peer-to-peer networks, providing a framework for system tuning and future analysis.

Contribution

It introduces an Instantaneous Message Exchange (IME) model for peer-to-peer systems, accurately describing system behavior under churn and buffer constraints, and offers a basis for analyzing more complex scenarios.

Findings

Coverage rate is limited by churn rate and buffer size.

The IME model provides accurate equations for system dynamics.

Models can be used to tune peer-to-peer system parameters.

Abstract

The churn rate of a peer-to-peer system places direct limitations on the rate at which messages can be effectively communicated to a group of peers. These limitations are independent of the topology and message transmission latency. In this paper we consider a peer-to-peer network, based on the Engset model, where peers arrive and depart independently at random. We show how the arrival and departure rates directly limit the capacity for message streams to be broadcast to all other peers, by deriving mean field models that accurately describe the system behavior. Our models cover the unit and more general k buffer cases, i.e. where a peer can buffer at most k messages at any one time, and we give results for both single and multi-source message streams. We define coverage rate as peer-messages per unit time, i.e. the rate at which a number of peers receive messages, and show that the coverage rate is limited by the churn rate and buffer size. Our theory introduces an Instantaneous Message Exchange (IME) model and provides a template for further analysis of more complicated systems. Using the IME model, and assuming random processes, we have obtained very accurate equations of the system dynamics in a variety of interesting cases, that allow us to tune a peer-to-peer system. It remains to be seen if we can maintain this accuracy for general processes and when applying a non-instantaneous model.