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, neither the traditional approaches to establishing lightpaths between given source destination pairs are sufficient, nor are those existing application level approaches that consider computing resources but ignore the optical layer connectivity. Instead, 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 algorithm for a special type of applications. Furthermore, we propose efficient heuristics to deal with general applications with either optimization objective and demonstrate their good performances in simulation.
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