Competitive Strategies for Online Cloud Resource Allocation with Discounts: The 2-Dimensional Parking Permit Problem

Cloud computing heralded an era where resources can be scaled up and down elastically and in an online manner. This paper initiates the study of cost-effective cloud resource allocation algorithms under price discounts, using a competitive analysis approach. We show that for a single resource, the online resource renting problem can be seen as a 2-dimensional variant of the classic online parking permit problem, and we formally introduce the PPP² problem accordingly. Our main contribution is an online algorithm for PPP² which achieves a deterministic competitive ratio of k (under a certain set of assumptions), where k is the number of resource bundles. This is almost optimal, as we also prove a lower bound of k/3 for any deterministic online algorithm. Our online algorithm makes use of an optimal offline algorithm, which may be of independent interest since it is the first optimal offline algorithm for the 1D and 2D versions of the parking permit problem. Finally, we show that our algorithms and results also generalize to multiple resources (i.e., Multi-dimensional parking permit problems).