A convergence study of the discrete FGDLS algorithm

The Feedback-Guided Dynamic Loop Scheduling (FGDLS) algorithm [1] is a recent dynamic approach to the scheduling of a parallel loop within a sequential outer loop. Earlier papers have analysed convergence under the assumption that the workload is a positive, continuous, function of a continuous argument (the iteration number). However, this assumption is unrealistic since it is known that the iteration number is a discrete variable. In this paper we extend the proof of convergence of the algorithm to the case where the iteration number is treated as a discrete variable. We are able to establish convergence of the FGDLS algorithm for the case when the workload is monotonically decreasing.