Online Auctions in IaaS Clouds: Welfare and Profit Maximization with Server Costs

Auction design has recently been studied for dynamic resource bundling and VM provisioning in IaaS clouds, but is mostly restricted to the one-shot or offline setting. This work targets a more realistic case of online VM auction design, where: (i) cloud users bid for resources into the future to assemble customized VMs with desired occupation durations; (ii) the cloud provider dynamically packs multiple types of resources on heterogeneous physical machines (servers) into the requested VMs; (iii) the operational costs of servers are considered in resource allocation; (iv) both social welfare and the cloud provider's net profit are to be maximized over the system running span. We design truthful, polynomial time auctions to achieve social welfare maximization and/or the provider's profit maximization with good competitive ratios. Our mechanisms consist of two main modules: (1) an online primal-dual optimization framework for VM allocation to maximize the social welfare with server costs, and for revealing the payments through the dual variables to guarantee truthfulness; and (2) a randomized reduction algorithm to convert the social welfare maximizing auctions to ones that provide a maximal expected profit for the provider, with competitive ratios comparable to those for social welfare. We adopt a new application of Fenchel duality in our primal-dual framework, which provides richer structures for convex programs than the commonly used Lagrangian duality, and our optimization framework is general and expressive enough to handle various convex server cost functions. The efficacy of the online auctions is validated through careful theoretical analysis and trace-driven simulation studies.