RateMmonotonic

RateMmonotonic, often written Rate-Monotonic Scheduling (RMS), is a fixed-priority preemptive scheduling algorithm used for coordinating periodic tasks in real-time systems. Each task i is characterized by its worst-case execution time C_i, its period T_i, and its relative deadline D_i (typically D_i = T_i). The scheduler assigns static priorities based on periods: shorter periods receive higher priorities.

In operation, the scheduler always runs the highest-priority ready task. A higher-priority task can preempt a lower-priority one, and preemption is determined by the task set’s timing parameters rather than dynamic conditions. Tasks are assumed to be independent, with a known, bounded execution time, and deadlines equal to their periods in the basic model.

Theoretical guarantees for RMS are well studied. A classic sufficient condition for schedulability when deadlines equal periods is the Liu–Liu bound: the total utilization U = sum_i (C_i / T_i) must satisfy U <= n(2^(1/n) − 1), where n is the number of tasks. As n grows, this bound approaches ln(2) ≈ 0.693. For exact analysis, one can perform a response-time analysis: compute R_i = C_i + sum_{j: T_j ≤ R_i} ceil(R_i / T_j) * C_j and iterate until convergence; if R_i ≤ D_i for all tasks, the set is schedulable.

Advantages of RMS include simplicity and strong guarantees for hard real-time periodic workloads. Limitations include conservatism of the utilization bound, reduced efficiency with large task sets, and limited suitability for aperiodic tasks or tasks with deadlines shorter than their periods without augmentations. RMS remains a foundational scheduling approach in many real-time and embedded systems.