Traffic Signal Optimization: Combining Static and Dynamic Models

Abstract

In this paper, we present a cyclically time-expanded network model for simultaneous optimization of traffic assignment and traffic signal parameters, in particular offsets, split times, and phase orders. Since travel times are of great importance for developing realistic solutions for traffic assignment and traffic signal coordination in urban road networks, we perform an extensive analysis of the model. We show that a linear time-expanded model can reproduce realistic travel times especially for use with traffic signals and we verify this by simulation. Furthermore, we show how exact mathematical programming techniques can be used for optimizing the control of traffic signals. We provide computational results for real world instances and demonstrate the capabilities of the cyclically time-expanded by simulation results obtained with state-of-the-art traffic simulation tools. MotivationTraffic signals can be seen as a backbone in the control of traffic flows in urban areas. Since the appearance of the first signalized intersections over 100 years ago, the improvement of signal control strategies has been an important subject for research. Friedrich [13] and Papageorgiou et al. [24] provide overviews of the main research lines over the last years.Recently, we presented a model for traffic signal coordination based on cyclically timeexpanded networks (see [20,21,32]). In contrast to most of the previous mathematical approaches, we focused not only on optimizing the offsets of signals, but also optimizing the implied traffic assignment. Each change in the signal parameters may influence the travel times in the network. Consequently, road users will quickly adapt to a new signal coordination and they will switch to faster routes if they suffer from the last intervention 1 arXiv:1509.08709v1 [cs.DM] 29 Sep 2015 in the signal plans. The traffic assignment, i.e., the distribution of traffic in the road network, may change significantly.Contrary to previous practical approaches based on non-linear models and heuristics, we focus on a model which allows for the use of exact programming techniques. Hence, proving optimality of a solution or bounding the gap between primal and dual solution was given a higher priority than modeling every effect of real traffic. Thus, this paper is particularly addressing the underlying theoretical questions of traffic signal optimization and the corresponding hardness.In this paper, we present an extensive analysis of the cyclically time-expanded model. It is a hybrid between a static, i.e., time independent, and a dynamic, i.e., time dependent, network flow approach. Although this time-expanded model is based on a linear program, it can reproduce very realistic non-linear flow-dependent travel times for urban traffic networks with signal control. In particular, both typical convex link performance functions and the time-dependent behavior of traffic, necessary for traffic signal coordination, are realistically mapped in this model. Additionally, the propagation of platoons of cars that is ...

Special Issue on Recent Advances in Urban Transport and Logistics Through Optimization and Analytics

“…With this approach, the authors demonstrate the efficiency of their traffic light control strategy. "Traffic Signal Optimization: Combining Static and Dynamic Models" presents a cyclically time-expanded network model for simultaneous optimization of traffic assignment and traffic signal parameters (Köhler and Strehler 2019). The developed mixed-integer programming models are tested on real-world instances and evaluated with simulation.…”

State-of-art review of traffic signal control methods: challenges and opportunities

“…References, [79][80][81][82][83] formulated the TST optimization problem as mixed-integer linear programming (MILP) whereas references [84,85] presented as the non-linear programming models…”

“…Based on the vehicle trajectory data in urban road networks, Yan et al [82] formulated a network-level multiband signal coordination scheme as MILP to provide progression bands for major traffic streams. For optimizing TST parameters Köhler et al [81] presented an approach based on a cyclically time-expanded network model. The model was able to optimize traffic assignment problems at the same time.…”

A Coordination Algorithm for Signalized Multi-Intersection to Maximize Green Wave Band in V2X Network

“…Traffic lights, first used in 1928 [7], are still the most extensive application of traffic management systems by now [8][9][10][11]. One of the ways to manage traffic flow at urban intersections is to provide traffic light signal optimization.…”

“…In [9], C Costa et al proposes a bi-objective optimization of fixed-time traffic signals using an improved genetic algorithm to improve the performance of vehicle speed. Kohler and Strehler [8,10] have developed a model that optimizes the fixed-time signal plan in a cyclically expanded network. They considered the coordination of multiple traffic signals and presented a corresponding mixed-integer linear programming formulation for simultaneously optimizing both the coordination of traffic signals and the traffic assignment.…”