Estimating the execution time distribution for a task graph in a heterogeneous computing system

The problem of statically estimating the execution time distribution for a task graph consisting of a collection of subtasks to be executed in a heterogeneous computing (HC) system is considered. Execution time distributions for the individual subtasks are assumed to be known. A mathematical model for the communication network: that interconnects the machines of the HC system is introduced and a probabilistic approach is developed to estimate the overall execution time distribution of the task graph. It is shown that, for a given matching and scheduling, computing the exact distribution of the overall execution time of a task graph is very difficult, and thus impractical. The proposed approach approximates the exact distribution and requires a relatively small amount of calculation time. The accuracy of the proposed approach is demonstrated mathematically through the derivation of bounds that quantify the difference between the exact distribution and that provided by the proposed approach. Numerical studies are also included to further validate the utility of the proposed methodology.