Before revision:  Using the results from majorization theory, we show thatif the service time of workersis a stochastically (decreasing and) convex random variable , a balanced assignment of non-overlapping batches of tasks minimizes the average job compute time.
After revision:  Using the results from majorization theory, show that, for a general class of workers' service time distributions , a balanced assignment of non-overlapping batches of tasks minimizes the average job compute time.