We consider a model of reactive real-time systems in which tasks are enabled in reaction to external events or executions of other tasks, and enabled tasks are scheduled according to a fixed priority policy. For such a model, we propose a schedule validation method. The method is applicable to a class of priority assignments that require less total processor time than assignments that could be validated by previous methods. The method is safe in the sense that if it validates a system, then it is guaranteed that no timing violations occur. However, it is conservative, in the sense that it may not be able to validate some correct systems. Based on this method, we also propose a priority assignment algorithm. The algorithm is optimal in the sense that if an assignment that satisfies the proposed schedule validation method exists, the algorithm will find it.