While utilization bound based schedulability test is simple and effective, it is often difficult to derive the utilization bound. For its analytical complexity, utilization bound results are usually obtained on a case-by-case basis. In this paper, we develop a general framework that allows one to effectively derive schedulability bounds of different workload patterns and schedulers. We introduce an analytical model that is capable of describing a wide range of tasks and schedulers’ behaviors. We propose a new definition of utilization, called workload rate. While similar to utilization, workload rate enables flexible representation of different scheduling and workload scenarios and leads to uniform proof of schedulability bounds. We derive a parameterized schedulability bound for static priority schedulers with arbitrary priority assignment. Existing utilization bounds for different priority assignments and task releasing patterns can be derived from the closed-form formula by simple assignments of proper parameters.