This dissertation proposes amodular Artificial Neural Network (ANN) based buffer allocation and routing control model for ATM switching networks. The proposed model considers limited buffer capacity which can adversely impact the switching performance of ATM switching networks. The proposed ANN based approach takes advantage of the favorable control characteristics of neural networks such as high adaptability and high speed collective computing power for effective buffer utilization. The proposed model uses complete sharing buffer allocation strategy and enhances its performance for high traffic loads by regulating the buffer allocation process dynamically via a neural network based controller. In this study, we considered the buffer allocation problem in the context of routing optimization in ATM networks. The modular structure of the proposed model separates the buffer allocation from the actual routing of ATM cells through the switching fabric and allows adaptation of the neural control for routing to different switching structures. The influence of limited buffer capacity, routing conflicts, statistical correlation between arriving ATM cells and cell burst length on ATM switching performance are analyzed and illustrated through computer simulation.