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This paper addresses the issue of call admission control with the necessary quality-of-service (QoS) guarantee for an integrated service mobile cellular network. Specifically, we extend the limited fractional guarded channel (LFGC) scheme to incorporate the multiple traffic types, and derive the set of parameters that leads to the optimal call admission control. The key challenges are the state-dependent nature of the admission control, and the increasing complexity of the state space in a multi-services environment. We propose a novel control mechanism that only uses a few parameters (2-5) to characterize the optimal control planes, and use the simulated annealing technique to obtain the optimal control parameters.