The existing network traffic signal optimization formulations usually do not include traffic flow models, except for control schemes such as SCOOT that use simulation for heuristic optimization. Other conventional models normally use isolated intersection optimization with traffic arrival prediction using detector information, or optimization schemes based on green bandwidth. A complete formulation of the problem is presented, including explicit constraints to model the movement of traffic along the streets between the intersections in a time-expanded network, as well as constraints to capture the permitted movements from modern signal controllers, The platoom dispersion model used is the well-known Robertson's model, which forms linear constraints. Thus, it is a rare example of a traffic simulation being analytically embedded in an optimization formulation. The formulation is an integer-linear program and does not assume fixed cycle lengths or phase sequences. It assumes full information on external inputs but can be incorporated in a sensor-based environment as well as in a feedback control framework. The formulation is an integer-linear program that may not be efficiently solved with standard simplex and branch and bound techniques. Network programming formulations to handle the linear platoon dispersion equations and the integer constraints at the intersections are discussed. A special-purpose network simplex algorithm for fast solutions is also mentioned.
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