How the calculator works
The tool models a set of independent periodic tasks running on a single processor. Each task τi is described by its worst-case execution time C, period T and relative deadline D (by default D = T). All calculations run locally in your browser — nothing is sent to a server.
Utilization tests
- Total utilization
U = Σ Ci / Ti. IfU > 1no scheduler can meet all deadlines on one processor. - Liu & Layland bound (RM): a task set with implicit deadlines is schedulable under rate-monotonic priorities if
U ≤ n(2^(1/n) − 1). The test is sufficient, not necessary. - Hyperbolic bound (RM):
Π (Ui + 1) ≤ 2— a tighter sufficient test by Bini, Buttazzo and Buttazzo. - EDF: with implicit deadlines, EDF is optimal and the test
U ≤ 1is exact. For constrained deadlines the calculator uses the density testΣ Ci / min(Di, Ti) ≤ 1(sufficient) and the processor-demand criterion in the simulation.
Response-time analysis (fixed priority)
For RM and DM the exact test computes the worst-case response time of every task with the recurrence R = C + B + Σ ⌈R / Tj⌉ Cj over all higher-priority tasks j, iterating until it converges or exceeds the deadline. The optional blocking term B models critical sections protected by the priority ceiling protocol. Read the full derivation in our worked example.
Gantt chart
The timeline simulates the schedule from a synchronous release (the critical instant) over the hyperperiod (capped for readability). Deadline misses are marked in red. Use the presets to explore classic examples, such as a task set that EDF can schedule but RM cannot — explained in Rate Monotonic vs EDF.
Educational tool. Results assume ideal conditions (zero context-switch overhead, independent tasks except for the blocking term, exact WCETs). They are not a substitute for a formal timing verification of a safety-critical product — see our Schedulability Audit service.