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This paper addresses end-to-end connectivity planning and call admission control for a high capacity multi-beam satellite network with on-board cross-connectivity. On board satellite switching is a technology designed to offer multimedia services, especially in demographically dispersed areas. Nevertheless, full on-board switching techniques are far from maturity. Their implementations have been proven expensive and difficult. There are also high risks involved in launching satellites for the stationary orbit surrounding the earth. As a substitute, a satellite network with on-board cross-connect is devised in this paper. Connectivity planning and call admission control mechanisms associated with such a network are also presented. Simulation studies are conducted to show the effectiveness of the proposed mechanisms.