This report describes a necessary condition for feasibility of scheduling a set of sporadic hard-deadline tasks on identical multiprocessor platforms, which is also a sufficient condition if there is only a single processor. The key contribution is the characterization of the maximum, over all time intervals of a given length, of the amount of computation that must be completed to meet all deadlines, and a method of computing this function efficiently to any desired degree of accuracy. Empirical data are provided to verify that the new infeasibility test can be computed efficiently and is an improvement over previously known checks for infeasibility.