Average-case Analysis for Special Cases of Online Bahncard Problem

The special Bahncard problem is a generalization of the Ski-Rental problem. In this paper, average-case competitive analysis which integrates probability distribution into pure competitive analysis is employed to restudy this problem. Theoretical and numerical results show that the performance measure of competitive analysis can be dramatically improved. Moreover, we study the special Bahncard problem with interest rate which should be considered in any reasonable financial model. The optimal deterministic competitive ratio is obtained and the competitive ratio C(k) decreases with the interest rate i. 1