Static Traffic Assignment with Queuing (STAQ) ? Static Assignment Revisited
L Brederode, Goudappel Coffeng BV, NL; M Bliemer, Goudappel Coffeng BV/Delft University of Technology, NL; L Wismans, Goudappel Coffeng BV/University of Twent, NL
STAQ is a new static traffic assignment model, taking both queuing as well as spillback into account. STAQ is a special case of the LTM model, with stationary travel demand in one time period, providing realistic travel times.
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.
In order to overcome the drawbacks of Beckmann?s formulation of the static traffic equilibrium problem, models that explicitly constrain link flows to their respective capacities have been proposed, both in literature (e.g. Marcotte et al (2003), De Palma and Nesterov (2000), Larsson and Patriksson (1999), Bifulco and Chrisali (1998)), and practice (e.g. Bundschuh et al (2006), 4Cast (2009)). All these models cope with queuing thereby producing more accurate travel times and placing congestion upstream from the bottleneck. However, these models still have drawbacks, such as using heuristic or approximate traffic delay rules and/or lack spillback-effects.
Given these drawbacks and the ever increasing levels of structural congestion, there is a great need for a static traffic assignment model which can be applied on both regional and urban regions, taking both queuing as well as spillback into account. Instead of improving existing traffic assignment models, we propose to start with a dynamic assignment model and construct the special case of a static traffic assignment model. This leads to STAQ (Static Traffic Assignment with Queuing), a specific case of the link transmission model (Yperman 2007), with the added assumptions that there is only one time period in which there is a stationary travel demand. While the iterative (equilibrium) route choice model is the same as existing methods (e.g., solving the deterministic or stochastic equilibrium problem with MSA or Frank-Wolfe), STAQ replaces the traffic flow and travel time computations (basically the static equivalent of dynamic traffic propagation) and is event-based. STAQ exhibits many favourable properties of dynamic models (such as horizontal dynamic queuing, shockwaves, spillback, using the complete fundamental diagram) but simplified such that it is suitable for strategic planning studies on large scale networks.
In this paper the concept of STAQ is explained and discussed, as well as some case studies on some smaller hypothetical networks and a real life network.
Association for European Transport