A mean field model of work stealing in large-scale systems

Abstract

In this paper, we consider a generic model of computational grids, seen as several clusters of homogeneous processors. In such systems, a key issue when designing efficient job allocation policies is to balance the workload over the different resources. We present a Markovian model for performance evaluation of such a policy, namely work stealing (idle processors steal work from others) in large-scale heterogeneous systems. Using mean field theory, we show that when the size of the system grows, it converges to a system of deterministic ordinary differential equations that allows one to compute the expectation of performance functions (such as average response times) as well as the distributions of these functions.