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Grid computing aims to realize a high-performance computing environment, while increasing the usage efficiency of installed resources. This puts considerable constraints on the network technology, and ultimately has led to the development of Grids over optical networks. In this paper, we investigate the fundamental question of how to optimize the performance of such Grid networks. We start with an analysis of different architectural approaches (and their respective technological choices) to integrate Grid computing with optical networks. This results in models and algorithms to design optical Grid networks, and we show the importance to combine both dimensioning (offline) and scheduling (online) in the design phase of such systems. Finally, the concept of anycast routing is introduced and motivated. Both exact and heuristic algorithms are proposed, and their performance in terms of blocking probability and latency is presented.