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With their tremendous success in broadcasting entertainment services, digital satellite systems are rapidly being viewed as viable service delivery vehicles. In parallel, both the demand for Internet and multimedia services and the subsequent end-user demand for higher bandwidth are forcing network operators to search for mechanisms that can cost effectively provide high speed access to end-users. Network operators are seriously considering satellite based networks to offer broadband and multimedia services to supplement and enhance their existing terrestrial networks. One solution is based on a geosynchronous (GEO) satellite system equipped with on-board processing and switching. Allowing for a maximum number of simultaneous users is an important element of this system, hence requiring effective connection admission control (CAC) and bandwidth on demand (BOD) algorithms. A CAC scheme is studied for the uplink segment of a broadband GEO satellite network with an on-board ATM-like switch. A MF-TDMA scheme is used for the uplink access. The CAC algorithm investigated is ATM-based with heterogeneous traffic traversing the satellite network. Performance evaluations of the CAC algorithm are done by detailed simulations. Connection blocking performance results are given for each type of traffic in the system.