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Consider the problem of scheduling a taskset on a multiprocessor to meet all deadlines. Assume constrained-deadline sporadic tasks and stage-parallelism (i.e., a task comprises one or more stages with a stage comprising one or more segments so that segments in the same stage are allowed to execute in parallel and a segment is allowed to execute only if all segments of the previous stage have finished). Also assume a two-type heterogeneous multiprocessor platform (i.e., there are processors of two types, type-1 and type-2, and for each task, there is a specification of its execution speed on a type-1 processor and on a type-2 processor) and intra-type migration (i.e., a job can migrate between processors of the same type but for a task, all jobs of this task must execute on the same processor type). We present an algorithm for this problem; it assigns each task to a processor type and then schedules tasks on processors of each type with global-Earliest-Deadline-First. It has pseudo-polynomial time complexity and speedup bound at most 5. We also present a variant of this algorithm; it has the same time complexity and same speedup bound but has better average-case performance. We evaluate both algorithms on randomly-generated systems with up to 256 tasks and 256 processors and find that for most systems the algorithms took at most 1 second and they never took more than 42 seconds to finish. Also, for almost 100% of the systems, the latter algorithm succeeds if given processors twice faster than the speed needed to satisfy a necessary feasibility test (hence the algorithm behaves almost as if the speedup bound is two). This is the first work on scheduling parallel real-time tasks on a heterogeneous multiprocessor with provably good performance.

Scheduling Constrained-Deadline Parallel Tasks on Two-type Heterogeneous Multiprocessors