It is well known that in stochastic service systems such as telecommunications networks, selective denial of service based on system state can enhance performance. For example, in a cellular mobile network, preference might be given to hando calls over new calls when the system is more heavily loaded. When the service center can be modeled as a markov process, there exist means to calculate the optimal call admission policy (Markov Decision Processes, MDP). However, for systems with a large number of states MDP is impractical since it requires solving large systems of linear equations. Therefore we seek methods of calculating good policies when calculating the optimal policy is computationally prohibitive. To this end we consider application of Genetic Algorithms to the call admission problem in 1-dimensional cellular networks. We test our methods on smaller systems and then o er evidence that the approach is extensible to substantially larger systems.