Pattern formation in traffic microscopic model

Pattern formation in traffic microscopic model

audiovizuální tvorba

čeština

Long-range patterns can be often observed in dynamic systems where only the short-range interactions between components exist. The progress in nonlinear dynamics theory within the past twenty years has helped us to understand the emergence of order in such complex systems. Nobel Prize winner Ilya Prigogine has coined the term dissipative structure for the ordered spatial patterns that emerge in dynamic systems. These patterns are independent on the geometry of system boundaries and often become time-dependent even when all the system parameters are time independent. There are three necessary conditions for such pattern-producing systems: Energy flow between the parts (the system is driven sufficiently far from equilibrium), energy dissipation which allows the system to settle into definite structures, presence of nonlinearity in interactions between the parts of the system. All properties mentioned above can be found in single-lane microscopic models of traffic as well even in case of vehicles with identical properties. In our paper we investigated behavior of such model from the point of view of nonlinear dynamic theory. Intelligent Driver Model (IDM) has been studied with respect to finite reaction interval (retarded interaction between vehicles). We used mean density of the vehicles as the main external parameter of the system. During the extensive set of simulation experiments we detected general properties of the system stationary behavior.

Long-range patterns can be often observed in dynamic systems where only the short-range interactions between components exist. The progress in nonlinear dynamics theory within the past twenty years has helped us to understand the emergence of order in such complex systems. Nobel Prize winner Ilya Prigogine has coined the term dissipative structure for the ordered spatial patterns that emerge in dynamic systems. These patterns are independent on the geometry of system boundaries and often become time-dependent even when all the system parameters are time independent. There are three necessary conditions for such pattern-producing systems: Energy flow between the parts (the system is driven sufficiently far from equilibrium), energy dissipation which allows the system to settle into definite structures, presence of nonlinearity in interactions between the parts of the system. All properties mentioned above can be found in single-lane microscopic models of traffic as well even in case of vehicles with identical properties. In our paper we investigated behavior of such model from the point of view of nonlinear dynamic theory. Intelligent Driver Model (IDM) has been studied with respect to finite reaction interval (retarded interaction between vehicles). We used mean density of the vehicles as the main external parameter of the system. During the extensive set of simulation experiments we detected general properties of the system stationary behavior.

traffic flow, microscopic traffic model, IDM model

traffic flow, microscopic traffic model, IDM model

APELTAUER, T.

19. 6. 2007

Université Paris-Sud 11

Université Paris-Sud 11, Orsay cedex, France