We propose a novel approach for sharing cluster resources among competing jobs. The key advantage of our approach over current solutions is that it increases cluster utilization while optimizing a user-centric metric that captures both notions of performance and fairness. We motivate and formalize the corresponding resource allocation problem, determine its complexity, and propose several algorithms to solve it in the case of a static workload that consists of sequential jobs. Via extensive simulation experiments we identify an algorithm that runs quickly, that is always on par with or better than its competitors, and that produces resource allocations that are close to optimal. We find that the extension of our approach to parallel jobs leads to similarly good results. Finally, we explain how to extend our work to dynamic workloads.