## Quasi Dynamic Assignment on the Large Scale Congested Network of Noord-Brabant

### Authors

Luuk Brederode, DAT.mobility / Delft University of Technology, Martijn Heynickx, Provincie Noord Brabant, Rogier Koopal, Goudappel Coffeng

### Description

Research on the quasi dynamic assignment model STAQ applied to the strategic transport model of Noord-Brabant. Even using synthetic OD matrices, most congestion patterns where reproduced and the user equilibrium was reached within 30 minutes.

### Abstract

This paper describes research on the quasi dynamic assignment model STAQ (first described in Brederode et al (2010)) applied on the province wide traffic model of Noord-Brabant. Noord-Brabant is the second largest urban region in the Netherlands with some 2 million inhabitants, a large concentration of high-tech companies and the highest patent density of all European regions.

In 2014 the province of Noord-Brabant commissioned an audit on the current regional traffic model system (BBMA: 3300 zones, 140000 links, 100000 nodes, 1900 junctions modelled). One of the main recommendations from the audit was to replace the traditional static traffic assignment (STA) model with an assignment model that better captures the physical effects of congestion, mainly to improve modelled travel times and broaden opportunities for analysis. Further recommendations included that junction modelling should remain an integral part of the assignment model to realistically model urban areas.

The audit clearly revealed the major disadvantage of traditional STA models: they cannot describe the physical effects of congestion (flow metering and queue formation). This is caused by 1) their cost function, which does not correspond to empirically supported traffic flow theory describing the relation between flow, speed and density and 2) lack of a proper node model that enables the inclusion of hard capacity constraints.

Although dynamic traffic assignment (DTA) models do capture the physical effects of congestion, their application is limited to operational and tactical models, because of 1) their limited scalability: the high computational cost and memory usage prohibit application on large models (in terms of number of OD-pairs and routes); and 2) their use of a time dimension, which introduces temporal interaction effects within the (implicit) cost functions, for which –to the best of the authors knowledge- no algorithms exist to calculate the user equilibrium (the network wide steady-state needed to be able to fairly compare model outcomes in strategic model applications). Furthermore, the existence of a time dimension means that much more input data (e.g.: OD-matrices, traffic counts) is needed.

The quasi dynamic traffic assignment model STAQ was developed to overcome the problems of DTA and STA models described above. STAQ explicitly captures flow metering and queue formation due to congestion (just like DTA models do), but assumes stationary demand during a single time period (e.g. a whole peak hour, just like STA models do) and is therefore much more scalable and mathematically tractable. Furthermore, STAQ does not need any additional input data compared to STA models. STAQ is implemented in OmniTRANS transport planning software.

STAQ was applied on the STA models network (links, nodes and junction definitions), although network link capacities needed refinement on some locations where slip lanes and buffer-space in front of traffic lights turned out to be omitted in the STA network. Furthermore, a limited number of large roundabouts coded as multiple nodes needed to be recoded into one node, to prevent formation of unrealistic gridlocks.

In order to be able to reach the user equilibrium, spillback was only included in the last iteration, in the other iterations vertical queues where assumed. The stochastic duality gap (Bliemer et al (2013)) was used as convergence measure because of its consistency with the definitions of stochastic user equilibrium and the multinomial route choice model used together with STAQ. A threshold value of 5E-04 proved to provide a short calculation time whilst reaching a level of convergence that is considered to be good enough for all strategic applications in a STA context (Boyce Ralevic and Bar-Gera (2004)).

The synthetic OD-matrices from the STA model were used, however bucket rounding was applied to increase matrix sparsity (and thus reduce the number of routes to be evaluated). This greatly improved calculation times, whereas extensive comparisons proved that it had negligible effects on trip length frequency distribution, route choice, flow propagation and link flows. To further speed up convergence, the self regulating average (Liu et al (2007) was used to average route demands over iterations.

With only the limited network refinement described above, and without any ODmatrix calibration, STAQ clearly exhibited the physical congestion effects and replicated 6 of the top 10 of structural congestion locations in Noord-Brabant, whereas the STA model only replicated 2 locations. All four ‘missing’ locations where due to coarseness of the zoning structure and/or network coding. Calculation time needed to reach the user equilibrium was less than 30 minutes which is faster than current STA implementation!

Future research focusses on convergence of STAQ using spillback in all iterations and development of an ODmatrix estimation method using STAQ.

#### Publisher

Association for European Transport