Allocation and scheduling of Conditional Task Graphs

We propose an original, complete and efficient approach to the allocation and scheduling of Conditional Task Graphs (CTGs). In CTGs, nodes represent activities, some of them are branches and are labeled with a condition, arcs rooted in branch nodes are labeled with condition outcomes and a corresponding probability. A task is executed at run time if the condition outcomes that label the arcs in the path to the task hold at schedule execution time; this can be captured off-line by adopting a stochastic model. Tasks need for their execution either unary or cumulative resources and some tasks can be executed on alternative resources. The solution to the problem is a single assignment of a resource and of a start time to each task so that the allocation and schedule is feasible in each scenario and the expected value of a given objective function is optimized. For this problem we need to extend traditional constraint-based scheduling techniques in two directions: (i) compute the probability of sets of scenarios in polynomial time, in order to get the expected value of the objective function; (ii) define conditional constraints that ensure feasibility in all scenarios. We show the application of this framework on problems with objective functions depending either on the allocation of resources to tasks or on the scheduling part. Also, we present the conditional extension to the timetable global constraint. Experimental results show the effectiveness of the approach on a set of benchmarks taken from the field of embedded system design. Comparing our solver with a scenario based solver proposed in the literature, we show the advantages of our approach both in terms of execution time and solution quality.