This paper analyzes the way sequential jobs are distributed and the system behaves in a heterogeneous computational grid environment where the brokering is done in such a way that each Computing Element has a probability to be chosen proportional to its number of CPUs and, (new from the previous paper) its relative speed. We give the asymptotic behavior for several metrics (queue sizes, slowdown...) in several cases, or, in some case, an approximation of this behavior. We study those metrics in several workload specifications: for various loads (saturated or non saturated), with several distributions,...We compare our probabilistic analysis to simulation we performed, in order to validate our results.