Distributed Control of Dynamic Flows in Traffic Networks
Abstract: In today’s society, traffic congestion is a major problem in several aspects. Apart from the obvious problem that people are losing valuable time due to the resulting delays, it also has negative impact on as well the economy as the local and global environment. With the development of sensors and navigation support, it has now become possible and thus of interest to study optimal routing of vehicles in a traffic network, in order to reduce the congestion-related problems. In this master’s thesis, a distributed algorithm for solution of optimal dynamic traffic flow control problems is derived, implemented and tested. Traffic networks are modelled with the cell transmission model (CTM), and the solution algorithm is based on a generalization of the alternating direction method of multipliers (ADMM). The algorithm is tested for one simple and one more complicated traffic network. The tests include both cases with time-varying external inflow of traffic as well as cases where the flow capacity of a specific road segment is varied with time, in order to simulate temporary traffic incidents. The tests show that if the cost function is chosen as the sum of squares of the traffic volumes at the cells (road segments) of the network, the algorithm converges to the optimal solution if a specific parameter (the penalty parameter, or step length) is chosen sufficiently small. The report starts with a description and examples from the simpler case of static traffic flow optimization. It also contains a summary of the concepts used from optimization theory. After this, the approach for dynamic traffic flow modelling and optimization is described. Finally, a description and derivation of the algorithm is provided, after which the implementation is tested for different cases involving the two different traffic networks.
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