Connected world-widely distributed computers and data systems establish a global source of processing power and data, called, a grid. Key properties of a grid are the fact that computers providing processing power may connect and disconnect at any time, and that demands for processing power may highly fluctuate over time. This has raised the need for the development of applications that are robust against changing circumstances. In (A. M. Dobber et al., 2004) the impact of fluctuations in processing speeds on running times has been investigated, and it was found that dynamic load balancing methods provide a promising means to deal with the ever-changing environment in the grid. In this paper we demonstrate with extensive experiments in a real grid environment, Planetlab, that dynamic load balancing based on predictions via exponential smoothing indeed lead to significant reductions in running times of parallel applications in a randomly changing grid environment.