Schedulability Bound of Weighted Round Robin Schedulers for Hard Real-Time Systems

We derive a parameterized, closed-formed schedulability bound for weighted round robin schedulers in hard real-time computing systems. The schedulability bound uses several parameters to represent important system behaviors: (1) Number of tasks; (2) Normalized deadline that measures the tightness of task deadlines; (3) Tasks set workload burst-ness; (4) Overhead ratio, which measures the portion of overhead time consumed in round robin operations; (5) Normalized token rotation frequency, that measures the number of token rotations in a time interval of the shortest relative deadline. Our work follows the network calculus representation framework and is based on a generalized workload and service approximation models. We derive a closed form expression of the utilization bound, so that one can analyze the impact of particular system parameters on the schedulability bound and schedulability bounds for specific system configurations can be easily obtained by simply plugging in proper parameters.