Given a set of positive-weighted points and a query rectangle r (specified by a client) of given extents, the goal of a maximizing range sum (MaxRS) query is to find the optimal location of r such that the total weights of all points covered by r is maximized. In this paper, we address the problem of processing MaxRS queries over road network databases and propose two new external memory methods. Through a set of simulations, we evaluate the performance of the proposed methods.