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This paper investigates an optical burst switching (OBS) based Grid architecture, where Grid traffic is assumed to co-exist with IP/10GE traffic. In Grid networks, the address of the handling resource is of less significance as different resources can process the job. Therefore anycast routing is implemented to route the Grid job bursts. This implies that Grid jobs are assembled in separate bursts from those of the IP/10GE traffic. The performance of both Grid job and IP/10GE bursts is examined through simulation. Two performance metrics are presented, the average burst dropping probability and burst hop count. The influence of varying the Grid job size and the computational resources load on the architecture are examined.