DYNAMIC SYSTEM-OPTIMAL TRAFFIC ASSIGNMENT USING A STATE-SPACE MODEL

We propose a new mathematical formulation for the problem of optimal t raffic assignment in dynamic networks with multiple origins and destin ations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assum e that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minim ize the total travel time experienced by all the vehicles using the ne twork. We model the traffic network over the time horizon as a discret e-time dynamical system. The system state at each time instant is defi ned in a way that, without loss of optimality, avoids complete microsc opic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, fink outflow function s, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied i n the context of this model. These optimization problems are optimal c ontrol problems for nonlinear discrete-time dynamical systems, and thu s they are amenable to algorithmic solutions based on dynamic programm ing. The computational challenges associated with the exact solution o f these problems are discussed and some heuristics are proposed.