A dynamical system model for traffic assignment in networks

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.