On the on-line maintenance scheduling problem

A machine instantly serves requests but needs to undergo maintenance after serving a maximum of L requests. We want to maximize the number of requests served. In the on-line version, we prove that serving L requests before placing a maintenance is 0.5-competitive and is best possible for deterministic algorithms. We describe a 0.585-competitive randomized algorithm and show an upper bound of 2L/(3L-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2L/(3L-1)$$\end{document}. We also analyze the empirical performance of various on-line algorithms on specific arrival distributions.