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

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 evalua-tion 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. We first study the case where all resources are homo-geneous, showing in particular that work stealing is very efficient, even when the latency of steals is large. We also consider the case where distance plays a role: the system is made of several clusters, and stealing within one cluster is faster than stealing between clusters. We compare different work stealing policies, based on stealing probabilities and we show that the main factor for deciding where to steal from is the load rather than the stealing latency