The constrained Ski-Rental problem and its application to online cloud cost optimization

Abstract

Cloud service providers (CSPs) enable tenants to elastically scale their resources to meet their demands. In fact, there are various types of resources offered at various price points. While running applications on the cloud, a tenant aiming to minimize cost is often faced with crucial trade-off considerations. 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 so as to reduce the compute costs of future requests. The Ski-Rental problem abstracts such scenarios where a tenant is faced with a to-rent-or-to-buy trade-off; 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 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 demonstrate that utilizing this information leads to achieving the best worst-case expected competitive ratio (CR) performance. Our method yields a new class of randomized algorithms that provide arrivals-distribution-free performance guarantees. Further, we apply our solution to a cloud file system and demonstrate the cost savings obtained in comparison to other competing schemes. 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. • Recompute the query from scratch. This involves the CPU and I/O costs, if any, for using the disk.

Robust resource reservation in virtual wireless networks

“…As could be noticed, COST DU P (B, α, β, µ) is similar to (13) except for the addition of the term αµ and the change of ρ to β. Therefore, we can use the results of section III to obtain optimal policies for reservation with DUP model.…”

“…The problem is shown to be a generalization of the well-studied ski-rental problem [15] which it admits to constant-factor approximation. The effect of various statistical information on the optimal solution to the ski-rental problem is investigated in [13], [14]. In contrast to the above works that allow the decision maker to buy the ski (reserve the required resources) at any point during the time frame of the operation, we allow the MVNO to reserve virtual resources only at the beginning of the time frame.…”

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

“…Let denote the cost incurred by an optimal offline algorithm. With these definitions, we can now write the CR as 1 The renting price used here is adopted for notational simplicity, and it can be scaled without changing the results we present here. Let us first determine the possible values for .…”

A Cost Efficient Online Algorithm for Automotive Idling Reduction

“…We use the same technique as in [13] to convert (24) into a linear programming problem. The observation is that for arbitrary distribution q(y) of stop length, there is a corresponding decision distribution P (x) which can offset the variation from q(y).…”

“…The LP problem (28) can be solved with similar steps as in [13]. First, to find p(x), (28b) is differentiated twice to derive the following ordinary differential equation (ODE):…”