Transportation Research Record: Journal of the Transportation Research Board, No. 1978, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 102–112. C. Beard, Crawford Bunte Brammeier, 1830 Craig Park Court, Suite 209, St. Louis, MO 63146. A. Ziliaskopoulos, Systems Optimization Laboratory, Depart- ment of Mechanical and Industrial Engineering, University of Thessaly, 38222 Volos, Greece. 102 A mixed-integer linear programming formulation is proposed to solve the combined system optimal dynamic traffic assignment and signal opti- mization problem. Traffic conditions are modeled with the cell transmis- sion model, a convergent numerical approximation to the hydrodynamic model of traffic flow. The formulation is suited to respond to oversaturated traffic conditions. It also can be adapted to account for turning move- ments, protected and permissive phases (gap acceptance), and multiple signal controller types: dynamic (traffic adaptive) and pretimed. Trials with a test network validated the formulation and achieved promising results. Specifically, dynamic signal control proved to be substantially more effective than pretimed control for incident conditions. In addition, potential benefits of rerouting vehicles in both directions of a roadway were revealed even when only one direction is closed. The past decade has brought many new developments in the field of intelligent transportation systems, including advanced traffic management systems (ATMS) and advanced traveler information systems (ATIS). ATMS include enhanced vehicle detection and traffic control systems, one such application being real-time traffic adaptive (dynamic) signal timing. ATIS comprise communication technologies that distribute traffic information via dynamic mes- sage boards and, more recently, dynamic route guidance systems. These systems are highly interdependent; they simultaneously influ- ence traveler decisions, including departure time and route choice. Notwithstanding, most research and, to some degree, implementa- tion practices have not strongly connected the two systems. Gen- erally, ATMS provide traffic control under the assumption that travel patterns (demand) are not influenced by control settings, whereas ATIS provide travel information (potentially altering the spatiotemporal demand) under the assumption that traffic control systems are fixed. Perhaps the diverse computational tools used in support of each system are responsible for this disconnection. For example, traffic control as part of ATMS uses optimization meth- ods, whereas traveler information as part of ATIS uses assignment models. This paper proposes combining these tools (optimization methods and assignment models) for applications such as dynamic route guidance systems and dynamic signal timing. Combining signal optimization and traffic assignment has long been suggested, and a substantial amount of research has been done pertaining to this problem; however most of this work applies to static user equilibrium (UE) models and is not applicable for real-time traffic management and vehicle routing. This paper examines recent work in networkwide optimization of signal control systems and in combined signal control and dynamic traffic assignment. A mixed-integer linear program formulation for the combined signal optimization and traffic assignment problem is proposed. The formulation uses system optimal (SO) assignment and is referred to as system optimal signal optimization (SOSO). Input to the model includes time-dependent origin–destination demand; the model then optimally assigns demand to the network and optimizes the signals. SIGNAL OPTIMIZATION METHODS Some of the earliest work in signal control is attributed to Webster (1), who introduced a formula for determining signal settings at an iso- lated intersection on the basis of average vehicle delay. Later, com- puter optimization methods were introduced: TRANSYT developed by Robertson (2) and MAXBAND developed by Little et al. (3) were two of the more common programs used. TRANSYT used an opti- mization procedure that minimized a combination of delay and the number of stops, whereas MAXBAND maximized the progression bandwidth of through vehicles. Traffic adaptive signal systems with online optimization were introduced by Hunt et al. (4), who devel- oped SCOOT (split, cycle, and offset optimization technique), and by Lowrie (5), who developed SCATS (Sydney coordinated adap- tive traffic system). For a more thorough history of signal control and optimization refer to Wood (6). More recently researchers have focused on signalization with queue management for oversaturated conditions. Formulations by Park et al. (7 ), Lieberman et al. (8), and Girianna and Benekohal (9) serve as examples. Recently, interest in analytical networkwide signal optimization methods has grown considerably. Most of the research during this time can be attributed to Wey and Jayakrishnan (10–12) and Lo et al. (13–16). Wey and Jayakrishnan formulated the network signal opti- mization problem as a mixed-integer linear program and developed a special purpose network simplex algorithm to solve the problem. The weaknesses of this formulation are an inability to determine fixed timing plans and vehicle propagation based on an empirical queuing model that fails to consider the fundamental relationship between traffic flow and density. Michalopoulos et al. (17 ) and Lo (14) argue that without the fundamental relationship, a model can- not infer accurate information on queue dynamics. Alternatively, Lo (13) and Lo et al. (15) formulated the network signal optimization problem as a mixed-integer linear program using the cell transmis- sion model (CTM), a traffic flow model that incorporates the fun- damental relationship between flow and density. Lo’s formulation also permits the optimization of signals with fixed timing plans. System Optimal Signal Optimization Formulation Christopher Beard and Athanasios Ziliaskopoulos