Abstract
We introduce the compound interest rate into the continuous version of the online leasing problem and discuss the generalized model by competitive analysis. On the one hand, the optimal deterministic strategy and its competitive ratio are obtained; on the other hand, a nearly optimal randomized strategy is constructed and a lower bound for the randomized competitive ratios is proved by Yao′s principle. With the help of numerical examples, the theoretical results show that the interest rate puts off the purchase date and diminishes the uncertainty involved in the decision making.
Highlights
In this paper, we consider the continuous version of the online leasing problem in a market with compound interest rate
For the online leasing problem in a market without interest rate, the optimal deterministic competitive strategy is S k and its competitive ratio is 2, which coincides with the previous results 2
We pursuit the lower bound for the randomized competitive ratios by Yao’s principle see, e.g., 11
Summary
We consider the continuous version of the online leasing problem in a market with compound interest rate. In the context of competitive analysis, an online algorithm, which has no knowledge of the future events, is measured by the ratio of its performance to the performance of an optimal offline. An oblivious adversary knows the probability distribution of the randomized algorithm but does not know which action the online player will adopt exactly, and he must predetermine the input before the game begins and pays for it optimally. The competitive ratio for randomized algorithm A with respect to an oblivious adversary is defined the same as 1.1 with Coston I; A replaced by E Coston I; A , which is the expected value of A’s cost on input I.
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