Minimizing Total Delay in Fixed-Time Controlled Traffic Networks

We present two different approaches to minimize total delay in signalized fixed-time controlled inner city traffic networks. Firstly, we develop a time discrete model where all calculations are done pathwise and vehicles move on "time trajectories" on their routes. Secondly, an idea by Gartner, Little, and Gabbay is extended to a continuous, linkwise operating model using "Link Performance Functions" to determine delays. Both models are formulated as mixed-integer linear programs and are compared and evaluated by PTV AG's simulation tool VISSIM 3.70

Hybrid Petri net model of a traffic intersection in an urban network

Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the red-to-green switching times of traffic signals. Different techniques have been proposed and commercially implemented, ranging from heuristic methods to model-based optimization. However, given the complexity of the dynamics and the scale of urban traffic networks, there is still a lot of scope for improvement. In this work, a new hybrid model for the traffic behavior at an intersection is introduced. It captures important aspects of the flow dynamics in urban networks. It is shown how this model can be used in order to obtain control strategies that improve the flow of traffic at intersections, leading to the future possibility of controlling several connected intersections in a distributed way

The Network Improvement Problem for Equilibrium Routing

In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average delay have received substantial attention, including network tolls, Stackelberg routing, and edge removal. A related approach with arguably greater practical relevance is that of making investments in improvements to the edges of the network, so that, for a given investment budget, the average delay at equilibrium in the improved network is minimized. This problem has received considerable attention in the literature on transportation research and a number of different algorithms have been studied. To our knowledge, none of this work gives guarantees on the output quality of any polynomial-time algorithm. We study a model for this problem introduced in transportation research literature, and present both hardness results and algorithms that obtain nearly optimal performance guarantees. - We first show that a simple algorithm obtains good approximation guarantees for the problem. Despite its simplicity, we show that for affine delays the approximation ratio of 4/3 obtained by the algorithm cannot be improved. - To obtain better results, we then consider restricted topologies. For graphs consisting of parallel paths with affine delay functions we give an optimal algorithm. However, for graphs that consist of a series of parallel links, we show the problem is weakly NP-hard. - Finally, we consider the problem in series-parallel graphs, and give an FPTAS for this case. Our work thus formalizes the intuition held by transportation researchers that the network improvement problem is hard, and presents topology-dependent algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure