The averaging principle

TL;DR

This paper introduces an averaging principle stating that outcomes of heterogeneous models are approximately equivalent to their homogeneous counterparts within an error of order , under certain conditions, with applications across queueing, game theory, and social networks.

Contribution

It establishes a general averaging principle for heterogeneous models satisfying differentiability and interchangeability, providing a new theoretical tool for analyzing complex systems.

Findings

Outcomes are $O(\u03b5^2)$ close to homogeneous models under specified conditions.

The principle applies to queueing, auction, and social network models.

New analytical results are derived using the averaging principle.

Abstract

Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced with its average value. In this study we show that any outcome of a heterogeneous model that satisfies the two properties of \emph{differentiability} and \emph{interchangibility}, is $O(\epsilon^2)$ equivalent to the outcome of the corresponding homogeneous model, where $\epsilon$ is the level of heterogeneity. We then use this \emph{averaging principle} to obtain new results in queueing theory, game theory (auctions), and social networks (marketing).