(without frames contens library)
During rush hour many crossings get saturated (temporarily unstable). Saturated crossings 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 crossing. In a first approach traffic dependency was implemented by a fixed schedule of program changes. It has poor adaptability to fast changing situations. In a second approach dynamic program changes have been introduced exchanging only parts of the switching sequence. However, the problem what indications should be used to modify the program is left up to the actual design. In this paper an alternative approach is proposed.
Fig. 1. Block-diagram of the controlled system, consisting of plant, observer, and controller
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 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.
In order to formulate a control problem, an objective is 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, when public-transportation is not separated from 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. 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 of the individual traffic 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.