Average-Case Competitive Analyses for Ski-Rental Problems
Let $s$ be the ratio of the cost for purchasing skis over the cost for renting them. Then the famous result for the ski-rental problem shows that skiers should buy their skis after renting them $(s-1)$ times, which gives us an optimal competitive ratio of $2-\frac{1}{s}$. In practice, however, it appears that many skiers buy their skis before this optimal point of time and also many skiers keep renting them forever. In this paper we show that these behaviors of skiers are quite reasonable by using an {\em average-case competitive ratio}. For an exponential input distribution $f(t) = \lambda e^{-\lambda t}$, optimal strategies are (i) if $\frac{1}{\lambda} \leq s$, then skiers should rent their skis forever and (ii) otherwise should purchase them after renting approximately $s^2\lambda \;\;(
online algorithm
competitive analysis
1-3
Regular Paper
Hiroshi
Fujiwara
Hiroshi Fujiwara
Kazuo
Iwama
Kazuo Iwama
10.4230/DagSemProc.05031.8
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode