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This paper studies TCP performance with different offset times which arise when hybrid multi-granular technology is employed in OBS core nodes. Multi-granular switches are promising devices to match dynamic application needs while optimizing switch costs and feasibility. They foster optical burst switching in multi-service contexts where switching matrices are designed and optimized in application awareness. OBS base offset time is strictly dependent on switching matrix set up time which, in presence of hybrid technology, is different from path to path. These differences impact on end-to-end performance and in particular on TCP throughput. This work studies end-to-end performance for two basic classes of connections, namely slow and fast connections. Simulations results based on a careful set up of ns-2 simulations according to test bed configurations described in literature are provided to show the effects of the employment of different optical technologies on the TCP throughput.