Robust Scheduling of Task Graphs under Execution Time Uncertainty

Abstract

Abstract-Effective multicore computing requires to make efficient usage of the computational resources on a chip. Offline mapping and scheduling can be applied to improve the performance, but classical approaches require considerable a-priori knowledge of the target application. In a practical setting, precise information is often unavailable; one can then resort to approximate time and resource usage figures, but this usually requires to make conservative assumptions. The issue is further stressed if real-time guarantees must be provided. We tackle predictable and efficient non-preemptive scheduling of multi-task applications in the presence of duration uncertainty. Hard real-time guarantees are provided with limited idle time insertion, by exploiting a hybrid off-line/on-line technique known as Precedence Constraint Posting (PCP). Our approach does not require probability distributions to be specified, relying instead on simple and cheaper-toobtain information (bounds, average values). The method has been tested on synthetic applications/platforms and compared with an off-line optimized Fixed Priority Scheduling (FPS) approach and a pure on-line FIFO scheduler; the results are very promising, as the PCP schedules exhibit good stability and improved average execution time (14% on average, up to 30% versus FPS and up to 40% versus the FIFO scheduler).

Disregarding Duration Uncertainty in Partial Order Schedules? Yes, We Can!

“…They have been obtained via two methods: 1) the constructive approach from [12] and 2) the application of a chaining step inspired by [13] to solutions obtained via ILOG CP Optimizer. For each considered instance, we kept all the solutions found by both solvers in the optimization process.…”

“…A POS is an augmentation of the original Project Graph, where a number of precedence constraints has been added to prevent the occurrence of resource conflicts, whatever the activity durations are. A POS can be obtained through a variety of methods (the reader may refer for details to [8,5,6,[11][12][13][14]). A POS can be designed to optimize some probabilistic performance metric, such as the expected makespan (a frequent pick) or the n-th quantile (see [3]).…”

Optimized Waterspace Management and Scheduling Using Mixed-Integer Linear Programming

“…In a similar manner, Bertsimas and Sim create a method to adjust the conservatism of robust MILP solutions in [23] while keeping the robust problem linear. Other work on robust scheduling and integer programming problems in the general sense may be found in [24,25,26]. However, to our knowledge there is no work explicitly incorporating Bayes risk to schedule slips nor for the application of MCM scheduling.…”

Real-Time Workload Allocation on a Uni-Processor

“…Scheduling algorithms in [17], [3] address the problem of task allocation over Grid; The algorithms in [2], [13], [20], [22], [23], [24] address the problem of task allocation over a cluster; The algorithms in [10], [11], [16], [6], [[18], [20] address the problem of allocating tasks over the processors of multiprocessor and multicore systems; while the algorithms in [5], [14], [15], [8], [9], [4] have been proposed to ensure an efficient and predictable scheduling of real-time independent tasks over a uni-processor.…”