Equilibrium traffic assignment using recurrent backpropagation

The paper presents a discrete time equilibrium traffic assignment model for urban road networks. The equilibrium state can be chosen either user optimized (in the sense of Wardrop's first principle) or system optimized. The model is capable of taking into account various kinds of network characteristics and constraints like o-d-matrices, link capacities, traffic counts and known intersection splitting rates. Congestion phenomena are modeled by traffic dependent link speed and link inflow restrictions. The task is interpreted as a nonlinear dynamic system control problem and a special recurrent neural network, together with its associated error-propagation network, is used for both identification and control of the system. Flow splitting rates serve as control parameters which have to be adjusted according to the minimization of some objective function (comprising the sum of link travel times). The necessary gradient information can be computed very rapidly by means of a modified version of the recurrent backpropagation algorithm. Because of the use of neural-network-like-structures, the process should be suitable to get implemented on massively parallel hardware.