Comparison of assignment methods for simulation- based dynamic-equilibrium traffic assignment

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 – such as temporal network flows and sensitivity to traffic control measures – and thus are not well served by static assignment models. The model is formulated as a time discrete variational inequality and a solution algorithm is 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 is the network-loading sub-problem, which is solved using the computationally efficient space-time queuing approach of Mahut. This solution method to the traffic flow problem is combined with heuristic driver behavior models to produce a fully-featured traffic simulation model. The complexity of the traffic simulation, which is motivated by a desire for a realistic representation of the system, results in an assignment map that is discontinuous and difficult to characterize analytically. Nevertheless, algorithms inspired from static network assignment have been found to work in practice for finding approximate dynamic equilibrium conditions on realworld networks of significant size. The routing algorithms are evaluated primarily on the proximity of the converged assignment to the dynamic equilibrium conditions. Other measures of algorithm performance include the speed of convergence (number of iterations), computational burden (per iteration), and computer memory requirements. 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. Index Terms – dynamic traffic assignment, method of successive averages, projected gradient, traffic simulation, queuing models