This paper reports on the evaluation of alternative algorithms for dynamic, or time-varying, equilibrium traffic assignment. The algorithms are used for pre-trip assignment, which reflects driver familiarity with expected traffic conditions, and are appropriate for off-line applications which require a more detailed analysis than can be well served with a static assignment model – such as temporal network flows and sensitivity to traffic control measures. The model is formulated as a time discrete variational inequality and two approaches for solution algorithms are developed. The determination of time-dependent path input flows is modeled as a master problem inspired from a simplicial decomposition approach. The determination of path travel times for a given set of path flows, called the network-loading subproblem, is done by simulating the resulting traffic on the network using the computationally efficient space-time queuing approach of Mahut. The complexity of the traffic simulation, results in an assignment map that is discontinuous and difficult to characterize analytically. Nevertheless, the algorithms presented in this paper have been found to work in practice for finding approximate dynamic equilibrium conditions on real-world networks of significant size. The routing algorithms are compared primarily on the proximity of the converged assignment to the dynamic equilibrium conditions. The reported applications of this model include references to studies carried out in several cities around the world and some detailed model calibration results for the cities of Bakersfield, USA and Montreal, Canada. The results show that this model may be calibrated for medium-size networks and the dynamic flows obtained with very reasonable computing times.
Abstract