—Data-intensive Grid applications require huge data transferring between multiple geographically separated computing nodes where computing tasks are executed. For a future WDM network to efficiently support this type of emerging applications, traditional approaches to establishing lightpaths between given source destination pairs are not sufficient because a computing task may be executed on any one of several computing nodes having the necessary resources. Therefore, lightpath establishment has to be considered jointly with task scheduling to achieve best performance. In this paper, we study the optimization problems of jointly scheduling both computing resources and network resources. We first present the formulation of two optimization problems with the objectives being the minimization of the completion time of a job and minimization of the resource usage/cost to satisfy a job with a deadline. When the objective is to minimize the completion time, we devise an optimal algorith...