Modeling and Optimization of Traffic Flow in Urban Areas - Czech ...

10 Chapter 2 Simple Light Controled Intersection Modelphase 2phase 1Fig. 2.3: Simple intersection model2.3 Simple Intersection ModelThe queue model described above will now be used to construct a simpleintersection model (see Fig. 2.3). The intersection consists of two streets(i.e., two queues) and one crossing area (which is a shared resource). Theoutgoing flow q for each queue is controlled by the intersection lights.The simple intersection model is described byx M (k + 1) = F (x M (k), q(k), h(k)) , (2.9)where x M (k) = (x 1 (k), x 2 (k)) T contains the state vectors of the two queues.The full intersection state vector is hence given byx M (k) = (n 1 (k), E 1 (k), n 2 (k), E 2 (k)) T (2.10)Here, F is a non-linear function given by (2.3) and (2.4). The vector q(k) =(q 1 (k), q 2 (k)) T represents the outgoing flow for the queues and the vectorh(k) = (h 1 (k), h 2 (k)) T represents the incoming flow.2.3.1 Linear modelA linear model is constructed via linearization of the function F around anequilibrium point (Subsection 2.2.3). The equilibrium point was selected