In this paper a new approach for designing controllers of traffic crossings is developed. The aim of the paper is not to design a specific controller, but rather to show how this design can be done in a systematic way. The work presented here is part of a bigger project. The overall goal is to provide the traffic engineer with a tool for designing 'intelligent' controllers for traffic lights.
Due to the structure of Swiss cities – The streets are not built in a chess-board like grid, for which the stationary solution of the switching sequence of the traffic lights can be calculated from traffic-flow considerations. – it takes more than flow analysis to control the crossings. Today's control is often done by using a combination of fixed cycles and traffic dependency. The control mechanism works like the barrel of a musical box, but the pins are switching the traffic lights of the crossing. In a first approach traffic dependency, actually time dependency, has been implemented by a fixed schedule of barrel-changes. But, because of its lack of adaptability to fast changing situations this control has not worked satisfactory. Therefore, in a second approach a dynamic barrel has been introduced whose pins can be shifted within a given range (typically within ten seconds for a cycle time of about one minute). In addition, the dynamic barrel can be slowed down or speeded up what makes up a quite flexible control-mechanism. However, the problem what indications should be used to shift the pins and to change the speed of the barrel is left up to the actual design.
As for usual control systems a controlled traffic system consists of the plant (here representing the crossing), the observer which reconstructs/estimates its state, and the controller which makes the decisions. This control structure is sketched in figure 1. All road users (we call them customers below) are considered as disturbances entering and driving the system. As the control-goal is the flushed system (no customers in the system), we omit the reference-input in figure 1. Arrivals and departures of customers are called input events, and accordingly switching commands of the traffic lights are called output events. By the way, it is noted that only in absence of measuring noise and detector failures the sensor readings report accurately the input events.
Figure 1: block-diagram of the controlled system consisting of plant, observer, and controller
In order to formulate a control problem, an objective has to be defined. Two common objectives are the total waiting time and the throughput:
In general, the two objectives lead to different control rules. A well known result from queuing theory which will be shown later. Actually, one is concerned with both issues in real traffic systems, as the public-transportation is mostly not separated from the individual traffic. Although using different lanes they interfere at crossings. To promote the public transportation in the city of Zurich, it is given an almost absolute priority over the individual traffic. Therefore, the total waiting time of the public transportation is minimized on the top level of the hierarchical decision making, while on a second level, given the constraints, the throughput is maximized in order to maintain the individual traffic flowing as well as possible.
The paper is organized as follows: The basic model is introduced in section 2 and discussed in section 3. In section 4 the control algorithm is presented, followed by some concluding remarks in section 5.