A Tighter Analysis of Work Stealing

Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel platforms. However, with the increasing number of processors, the cost for managing a single centralized list becomes prohibitive. The objective of this work is to study the extra cost that must be paid when the list is distributed among the processors. We present a general methodology for computing the expected makespan based on the analysis of an adequate potential function which represents the load unbalance between the local lists. A bound on the deviation from the mean is also derived. Then, we apply this technique to show that the expected makespan for scheduling W unit independent tasks on m processors is equal to W/m with an additional term in 3.65log_2 W. Moreover, simulations show that our bound is very close to the exact value, approximately 50% off. This new analysis also enables to study the influence of the initial repartition of tasks and the reduction of the number of steals when several thieves can simultaneously steal work in the same processor's list.