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We consider a traffic network subject to known time-varying demands between its origins and destinations. We model the network as a discrete-time dynamical system driven by these demands. The state of the system at each time epoch is defined in a way that avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no path enumeration. The control variables correspond to the assignment or routing of the platoons on downstream links at the nodes of the network. Impedance functions combined with link outflow functions are used to model link travel times in the state transition function. This modeling approach allows for the study of the problem of dynamic traffic assignment in networks in the framework of the optimal control of dynamical systems. This work has applications to route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment.

Anticipatory route guidance in traffic networks is based on time-dependent fastest path calculation requiring forecasts of link travel time over a time horizon. These forecasts would be produced by a traffic assignment procedure, which must take into account the behavior of anticipatory vehicles seeking user-optimal route guidance. Thus a conceptual feedback loop occurs. We implement this feedback loop iteratively using simulation for the assignment phase. When the iteration terminates with a fixed-point assignment, user-optimality is achieved. We study the benefits accrued by individual anticipatory vehicles and the system as a whole, as a function of the proportion of vehicles which have anticipatory route guidance, i.e. the market penetration. We observe individual and system benefits at market penetrations up to 40% or higher.