In this paper, we study the impact of tasks reallocation onto a grid platform. More precisely, we target a multi-cluster environment where clusters can be homogeneous or heterogeneous, and use different policies for their local resources management. In this context, we propose a reallocation mechanism that migrates jobs in waiting state from one cluster to another one. We perform simulations using real traces of jobs to study the benefit of reallocation. We compare two different algorithms providing the reallocation mechanism, each with several heuristics to schedule jobs. Results show that in some cases it is possible to obtain a substantial gain on the average job response time (almost up to a factor of four). In the other cases, the reallocation mechanism is beneficial most of the time for the jobs of the users. It is thus interesting to implement a reallocation mechanism in a Grid framework.