We develop an algorithm based on Infinitesimal Perturbation Analysis for online optimization of a multi-product service facility composed of a network of multi-server machines, modeled using multi-class M/M/m queues. starting from the Robbins-Monro stochastic approximation method, we first develop an online, local optimization algorithm for a single multi-server machine. for the special case of Poisson arrivals and exponentially distributed service time in a multi-machine network, local optimization at individual machines leads to global optimization of the overall network. Simulation results for a single machine are compared to the exact analytical results. Application of the methodology for the optimization of a simple flexible manufacturing system is also presented.