This paper describes a dynamic programming formulation of the airport surface traffic management problem. Movement of aircraft is modeled as the flow of traffic on a network, with stochastic link travel times. This is followed by an algorithm for controlling entry of aircraft into the taxiway system at an airport. Finally, two realistic variations of the formulation are presented -variation of parameters and finite buffer capacity. Optimal control policies for all cases are calculated using policy iteration, with delay mitigation and aircraft fuel burn reduction as explicit objectives.