The state of the resources at a destination in Grid computing over OBS architecture (GoOBS) may change between a task's selection of a destination and its arrival at the destination. These changes in the availability of the resources requested at the destination may lead to blocking of tasks, and thus increase the resource blocking rate. In this paper, we investigate the resource scheduling problem in GoOBS. Our objective is to minimize the resource blocking rate by containing the impact of the changes in the availability of the resources at a destination. We propose a non-selfish destination selection paradigm to minimize the resource blocking rate. The selection of a destination by a request is called non-selfish, if the selected destination has sufficient resources available to simultaneously process one or more additional requests. Extensive simulations were performed to validate the effectiveness of the heuristics based on the non-selfish destination selection paradigm. Among the proposed heuristics, the NFFD heuristic is most effective in minimizing the resource blocking rate. Compared to the best existing approach, the NFFD heuristic reduces the resource blocking rate by 21% to 73% in our experiments.