Scheduling Conditional Task Graphs

Michele Lombardi, Michela Milano

Abstract: This paper describes a complete and efficient solution to the scheduling of conditional task graphs whose nodes are activities and whose arcs can be labelled with a probability distribution. Tasks are executed if a set of conditions hold at scheduling execution time. The model is therefore stochastic. The minimization of the expected makespan implies an exponential-sized description of the objective function. We propose an analytic formulation of the stochastic objective function based on the task graph analysis, and a conditional constraint that handles it efficiently. Experimental results show the effectiveness of our approach in comparison with (1) an approach using a deterministic objective function and (2) scenario based constraint programming taking into account all scenarios or only a part of them.