Hydrodynamic limit of move-to-front rules and search cost probabilities

TL;DR

This paper investigates the large-scale behavior of move-to-front algorithms by deriving a hydrodynamic limit, which helps in understanding search cost distributions for large systems with various jump rate distributions.

Contribution

It introduces a hydrodynamic limit framework for move-to-front rules and derives asymptotic formulas for search cost probabilities applicable to general jump rate distributions.

Findings

Derived a hydrodynamic limit for move-to-front rules.

Provided asymptotic formulas for search cost distributions.

Applicable to general jump rate distributions.

Abstract

We study a hydrodynamic limit approach to move-to-front rules, namely, a scaling limit as the number of items tends to infinity, of the joint distribution of jump rate and position of items. As an application of the limit formula, we present asymptotic formulas on search cost probability distributions, applicable for general jump rate distributions.