2. INTRODUCTION

During rush hours many intersections get saturated (temporarily unstable). Saturated intersections can be optimally controlled using an off-line calculated steady state of traffic light switching sequences. But in the case of low traffic, it takes more than flow analysis to control the intersection. A frequently used control mechanism works like the barrel of a musical box, but the pins are switching the traffic lights of the intersection. In a first approach traffic dependency has been implemented by a fixed schedule of barrel-changes. But, because of its poor 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. 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. In this paper an alternative approach is proposed.

As for usual control systems a controlled traffic system consists of the plant (here representing the intersection), the observer which reconstructs/estimates its state, and the controller which makes the decisions. This control structure is sketched in Fig. 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 Fig. 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.

Block-diagram of the controlled system, consisting of plant, observer, and controller.

Fig. 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 the former case the accumulated waiting times of all customers flowing through the system is minimised. We choose this objective for the trams (or buses) to achieve that they operate on schedule.

In the other case the throughput of the system (and so the capacity) is maximised. We choose this objective to maintain the individual traffic flowing.

In general, the two objectives lead to different control rules (Riedel, 1991; Riedel and Brunner, 1992). 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. In the city of Zurich, the public transportation is given an almost absolute priority over the individual traffic. Therefore, the total waiting time of the public-transportation is minimised on the top level of the hierarchical decision making, while on a second level, given the constraints, the throughput is maximised.

The paper is organised as follows: In the next two sections the example and the modelling technique are introduced. Then the control algorithm is presented and discussed. Finally it is applied to the example.