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.
['Kumiko Hattori', 'Tetsuya Hattori']
Hydrodynamic limit of move-to-front rules and search cost probabilities