I. Introduction
In 2020, one hundred years will pass since the first traffic lights based on the use of three lights red, yellow and green designed by William Potts were applied in practice. This system is a foundation of the currently operating traffic lights around the world. Certainly, it does not mean that this is a perfect solution. In fact, the time wasted at intersections with traffic lights is significant. They cause not only financial but also social and increasingly noticeable environmental losses. Other adverse aspect of intersections with traffic lights relates to risks associated with the need to take rapid decisions while the signal changes from green to yellow and to decide on whether to start braking maneuver to stop before a stop line or to continue driving to cross the intersection. It is very often a complex and difficult decision since when the signal is changing from green to yellow, a vehicle moving at a permissible speed at a distance from the signaling device may be in a so-called dilemma zone. The dilemma zone concept was developed by the team of Gazis, Herman and Maradudin already in the 1960s [9]. A dilemma zone is an area near to an intersection where a driver has a problem of taking right decisions when the yellow signal appears. He cannot safely cross the intersection, since the distance that can be covered by the vehicle during the yellow signal is shorter than the distance needed to reach the stop line. In such a situation, the driver must take the decision on whether to continue and enter the intersection at the red signal. It is also not possible to stop safely before the stop line and brake with a delay recognized as a safe breaking delay, since the calculated distance covered by the vehicle during transmission of the yellow signal is longer than the stopping distance to the stop line. The range of the dilemma zone varies depending on the vehicle speed, delay and acceleration, driver reaction time, road conditions affecting the braking distance and conditions associated with the vehicle itself, its mass, duration of the yellow signal, whose length is regulated by law in Poland and is 3 seconds. Extending the duration of the yellow signal could reduce the dilemma zone but it may adversely affect an intersection capacity. Some studies [25] show that collisions and accidents at intersections constitute about 30% of all accidents on urban roads, and half of them involve collisions (rearward collisions, side collisions) due to indecision and drivers' problems with taking right decisions in the dilemma zone. Hence the search for solutions for providing better capacity while reducing dangers at intersections with traffic lights. The problem arises from the sudden change of the signal from green to yellow and lack of adequate information ahead. This problem is more noticeable, especially for larger vehicles (for example a bus or a tram, when the driver cannot perform a maneuver with a high braking delay due to the comfort and safety of passengers who are not seat belted safely) when permissible speeds are higher. The next problem is also the fact that a driver can be surprised by a sudden change of the signal to green, the lack of information about the change of the transmitted signal before the yellow with red light signal appears whose transmission time in Poland is set to 1s.