STAQ: Static Traffic Assignment with Queuing

Because of computation time issues on large networks, most strategic regional and urban transport models today use static instead of dynamic traffic assignment procedures. Mathematical models of traffic assignment are usually based upon Wardrop’s principle. To solve this static traffic equilibrium problem almost all applied static assignment models follow Beckmann who formulated it as a convex optimization problem containing a link travel time function (Beckmann 1956). This function has the form of a polynomial whose degree and coefficients are specified from statistical analysis of real data. The best known polynomial is the BPR function (US bureau of Public Roads, 1964). Although widely used, traffic assignment models based on Beckmann’s formulation have several drawbacks. Firstly, these models penalize but not explicitly constrain link flows to their respective link capacities. This can result in a solution where traffic flows exceed link capacities. Secondly, models derived from Beckmann’s formulation do not account for queuing and spillback on the network as a result of high demand, resulting in poor travel times and route choice on congested networks. Related drawbacks are that congestion is modelled downstream instead of upstream from the bottleneck and that upstream bottlenecks do not influence downstream traffic demand. These drawbacks not only yield incorrect link flows and travel times, they also prevent proper network and matrix calibration using traffic counts on congested links. Given the ever increasing levels of structural congestion, these drawbacks will only become more relevant in the future.