Feedback guided dynamic loop scheduling: Convergence of the continuous case

In this article we present some theoretical results concerning the convergence of Feedback Guided Dynamic Loop Scheduling (FGDLS). This method was proposed by Bull (Proceedings of Euro-Par'98, Springer-Verlag, 1998) and further developed by Bull, Ford, Freeman and Hancock (Proceedings of Ninth SIAM Conference on Parallel Processing for Scientific Computing, SIAM Press, 1999). Based on several synthetic examples it has been shown that the method performs well when the workload associated with the parallel loop changes relatively slowly (see Bull et al., 1999). However the question of convergence of the FGDLS method has remained an open question. In this paper we establish sufficient conditions for the convergence of the method.