To Rent or to Buy in the Presence of Statistical Information: The Constrained Ski-Rental Problem

Abstract

Cloud service providers enable tenants to elastically scale resources to meet their demands. While running cloud applications, a tenant aiming to minimize cost is often challenged with crucial tradeoffs. For instance, upon each arrival of a query, a Web application can either choose to pay for CPU to compute the response fresh, or pay for cache storage to store the response to reduce future compute costs. The Ski-Rental problem abstracts such scenarios where a tenant is faced with a to-rent-or-to-buy tradeoff; in its basic form, a skier should choose between renting or buying a set of skis without knowing the number of days she will be skiing. In the multislope version of the Ski-Rental problem, the skier can choose among multiple services that differ in their buying and renting prices. In this paper, we introduce a variant of the classical Ski-Rental problem in which we assume that the skier knows the first (or second) moment of the distribution of the number of ski days in a season. We also extend the classical multislope Ski-Rental problem, where the skier can choose among multiple services, to this setting. We demonstrate that utilizing this information leads to achieving the best worst-case expected competitive ratio performance. Our method yields a new class of randomized algorithms that provide arrivals-distribution-free performance guarantees. Simulations illustrate that our scheme exhibits robust average-cost performance that combines the best of the well-known deterministic and randomized schemes previously proposed to tackle the Ski-Rental problem.

Competitive Analysis of the Online Leasing Problem for Scarce Resources

“…In addition, variants of lease options in the online leasing problem are also investigated in [12,31,32]. Khanafer et al [33] further factored in the availability of statistical data on the usage time of the resource to perform smarter decision making. For other classic variations of the online leasing problem, we refer readers to the replacement problem [34], the capital investment problem [35], and the Bahncard problem [36].…”