VACANCY INTERNSHIP PROJECT An improved algorithm to solve the fixed-point problem of the STAQ traffic model Problem description This project focuses on the Static Traffic Assignment with Queuing (STAQ) assignment model for road traffic. STAQ was developed as an alternative to traditional static traffic assignment (STA) models, providing more accuracy on congested networks without reducing robustness, applicability and accountability and without increasing input requirements, whilst keeping computational requirements to acceptable levels (Bliemer et al., 2014; Brederode et al., 2019). Like STA models, STAQ assumes stationary travel demand during a single study period (typically the AM or PM peak) and instantaneous flow propagation, but contrary to traditional STA models it adheres to strict road capacity constraints. Picture to the left: STAQ results on the strategic transport model of the province of Noord-Brabant Legend: Bandwidth widths: flow [veh/h] during AM peak Bandwidth colors: speed [% of free flow speed]: 0 %
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Pie chart diameters: vertical queue sizes [vehicle loss hours]:
Solving STAQ is comprised of two phases: first, the static traffic assignment with capacity constraints is solved in the squeezing phase, which is followed by the queuing phase in which the (vertical) queues are dealt with. Solving STAQ squeezing amounts to solving a fixed-point problem of a compound function (Bliemer et al., 2014), which may result in convergence problems for real-life networks. An improved algorithm may be obtained by using the approach of Raadsen and Bliemer (2018) to separate the fixed-point problems in three fixed-point subproblems and iteratively solve these. The aim of the project is to apply this approach to the STAQ assignment model. This master project focuses on the mathematical analysis, implementation, and practical performance evaluation of the fixedpoint subproblems approach to solving STAQ squeezing.
Master thesis assignment The central question of this project is whether the fixed-point subproblems approach to solving STAQ squeezing as proposed in Raadsen and Bliemer (2018) has better convergence properties than solving the integrated fixed-point problem as is done in Bliemer et al. (2014). The following points will be addressed: 1. Mathematical analysis of convergence properties of both fixed-point problem approaches in the STAQ context, by means of Karush–Kuhn–Tucker conditions. 2. Implementation of the fixed-point subproblems approach in an existing C++ implementation of STAQ squeezing (which uses the integrated fixed-point problem approach). This does not require producing a lot of new code and close supervision is provided. 3. Evaluating the performance of both fixed-point solvers on several real-life networks as well as toy examples provided in the literature. Actual convergence, convergence speed, and computational time are the main indicators of interest. 4. (Optional) Solving the fixed-point problem(s) involves looping over routes. The computational time of the C++ implementation is expected to decrease significantly if the looping can be done using a multithreaded approach. This improvement, if possible, can be implemented additional to point 2.
Research group DAT.mobility Deventer Daily supervisors: Alwin Stegeman, Jeroen van Oorspronk
When interested in this Master thesis assignment, please contact Dr. Alwin Stegeman (astegeman@DAT.nl, +31 (0) 6 15903132)
Literature Bliemer, M.C.J., Raadsen, M.P.H., Smits, E.-S., Zhou, B., Bell, M.G.H. 2014. Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model. Transportation Research Part B, 68, 363-384. Raadsen, M.P.H, Bliemer, M.C.J. 2018. General solution scheme for the Static Link Transmission Model. Working Paper ITLSWP-18-21. https://ses.library.usyd.edu.au/handle/2123/19143 Brederode, L., Pel, A., Wismans, L., de Romph, E., Hoogendoorn, S., 2019. Static Traffic Assignment with Queuing: model properties and applications. Transp. Sci. 15, 179–214. https://doi.org/10.1080/23249935.2018.1453561