We propose a novel approach, called Dynamic Fractional Resource Scheduling (DFRS), to share homogeneous cluster computing platforms among competing jobs. DFRS leverages virtual machine technology to share node resources in a precise and controlled manner. A key feature of this approach is that it defines and optimizes a usercentric metric of performance and fairness. We explain the principles behind DFRS and its advantages over the current state of the art, develop a model of resource sharing, and summarize results from two different simulation experiments: one comparing various heuristics in an off-line setting and another comparing our heuristics to current technology in an on-line setting. Finally, we summarize our conclusions and describe our plans for future research.