Strategyproof allocation of discrete jobs on multiple machines

We present a model for fair strategyproof allocations in a realistic model of cloud computing centers. This model has the standard Leontief preferences but also captures a key property of virtualization, the use of containers to isolate jobs. We first present several impossibility results for deterministic mechanisms in this setting. We then construct an extension of the well known dominant resource fairness mechanism (DRF), which somewhat surprisingly does not involve the notion of a dominant resource. Our mechanism relies on the connection between the DRF mechanism and the Kalai-Smorodinsky bargaining solution; by computing a weighted max-min over the convex hull of the feasible region we can obtain an ex-ante fair, efficient and strategyproof randomized allocation. This randomized mechanism can be used to construct other mechanisms which do not rely on users' being expected (ex-ante) utility maximizers, in several ways. First, for the case of $m$ identical machines one can use the convex structure of the mechanism to get a simple mechanism which is approximately ex-post fair, efficient and strategyproof. Second, we present a more subtle construction for an arbitrary set of machines, using the Shapley-Folkman-Starr theorem to show the existence of an allocation which is approximately ex-post fair, efficient and strategyproof. This paper provides both a rigorous foundation for developing protocols that explicitly utilize the detailed structure of the modern cloud computing hardware and software, and a general method for extending the dominant resource fairness mechanism to more complex settings.