A complete optimal formulation of a network traffic control scheme in the form of arc flows in a time-expanded network is presented. The platoon dispersion model used in the proposed optimal control formulation forms linear constraints. The integer-linear network programming formulation is solved by using a modified network simplex and branch-and-bound scheme. The formulation does not assume fixed cycle lengths or phase sequences. It assumes full information on external inputs, but it can be incorporated into a sensor-based environment, as well as into a feedback control framework. The integer-linear program formulation may not be efficiently solved by standard simplex and branch-and-bound techniques. Network programming formulations that can be used to handle the linear equations and the integer constraints at the intersections are discussed. A special-purpose network simplex algorithm for fast solution is also mentioned. The optimization model takes the form of mixed integer-linear programming. The control strategies generated by these optimization models were compared with those derived from conventional signal timing models by using the TRAF-NETSIM microscopic simulation model. The proposed optimization models consistently out-performed the conventional signal control methods with respect to the system delay objective. It was found that the optimization models successfully produced optimal signal timing plans for the various signalized intersections, including simulated and real-world networks.