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The problem of call admission control (CAC) is considered for leaky bucket constrained sessions with deterministic service guarantees (zero loss and finite delay bound) served by a generalized processor sharing scheduler at a single node in the presence of best effort traffic. Based on an optimization process, a CAC algorithm capable of determining the (unique) optimal solution is derived. The derived algorithm is also applicable, under a slight modification, in a system where the best effort traffic is absent and is capable of guaranteeing that if it does not find a solution to the CAC problem, then a solution does not exist. The numerical results indicate that the CAC algorithm can achieve a significant improvement on bandwidth utilization as compared to a (deterministic) effective bandwidth-based CAC scheme.