Traffic jams cause economical damage which has been estimated between 10 and 100 billion Euros per year in Germany, also due to inefficient urban traffic. It is currently open how the situation will change with upcoming technological advances in autonomous and electric mobility. On the one hand, autonomous cars may lead to an increased number of vehicles on the road with implied consequences. On the other hand, the availability of Vehicle2X (V2X) communication and smart algorithms might make the traffic flow more efficient, especially at natural bottlenecks such as urban traffic-light-controlled intersections. To be able to quantify this anticipated potential to reduce waiting time, energy consumption, and CO2 emissions, we developed mathematical models and tailored optimization algorithms. Mathematically optimal solutions provide bounds on what could be achieved. This versatile tool can be used to analyze a large variety of scenarios, including infrastructure investments, changes of traffic-light legislation, or the interplay between humans and autonomous vehicles. Numerical results indicate that the performance indicators time, energy, and emissions could be concurrently reduced by almost 50%. Potentially, the same models and algorithms might be the basis for future traffic control systems. To calculate optimal switching of traffic lights and optimal autonomous driving of participants, we have been developing a mixed-integer optimization model and a variety of techniques that allow an efficient computation. Scenarios include fully-autonomous as well as mixed traffic, which leads to the additional challenge of incorporating realistic and uncertain human driving behavior into the model. To this end, we have been combining methods from different areas such as discrete and continuous mathematical optimization, control theory, and machine learning. Parts of the derived algorithms were successfully implemented and tested in a car of our industrial project partner Volkswagen Aktiengesellschaft.
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