WCRT

Worst-case response time (WCRT) is the maximum time interval from when a task is released to when its result is completed, under a given scheduling policy and system conditions. It is a central metric in real-time systems for guaranteeing timing constraints, such as deadlines. WCRT depends on task characteristics—worst-case execution time (C_i), period (T_i), and deadline (D_i)—as well as the chosen scheduling algorithm and the potential interference from other tasks.

In fixed-priority preemptive scheduling, the WCRT of a task i is computed by a forward recurrence: R_i^0 = C_i; R_i^{k+1} = C_i + sum_{j in hp(i)} ceil(R_i^k / T_j) * C_j, where hp(i) is the set of higher-priority tasks. The task is schedulable if R_i ≤ D_i. This method assumes independent tasks with known WCETs. It can be extended to include blocking time B_i caused by non-preemptive sections or shared resources: R_i^0 = C_i + B_i; R_i^{k+1} = C_i + B_i + sum_{j in hp(i)} ceil(R_i^k / T_j) * C_j.

Under other scheduling policies, such as earliest deadline first (EDF), or in multiprocessor contexts, WCRT analysis uses different interference terms and may require additional modeling for synchronization and resource sharing. In systems with shared resources, blocking bounds and protocols (e.g., priority inheritance, priority ceiling) affect the WCRT and must be incorporated.

Limitations include conservatism and reliance on worst-case assumptions. WCRT calculations require accurate WCET estimates and task independence; real hardware and OS effects (caches, memory latency, interrupts) can yield pessimistic results. Nevertheless, WCRT is a fundamental tool in safety-critical domains like avionics, automotive, and industrial control to verify that timing requirements are met.