ar X iv : c on d - m at / 9 71 20 77 v 1 5 D ec 1 99 7 A 1 d Traffic Model with Threshold Parameters

The basic properties of traffic flow are analyzed using a simple deterministic one dimensional car following model with continuous variables based on a model introduced by Nagel and Herrmann [Physica A 199 254–269 (1993)] including a few modifications. As a first case we investigate the creation and propagation of jams in a platoon generated by a slow leading vehicle. In a second case we look at a system with the size L, periodic boundary conditions and identical vehicles. A strong dependence on the initial configuration of the fundamental diagram’s shape can be found. 1 Definition of the Model To get a parallel update of all vehicles, the first step is to change the velocity of all vehicles taking into account the threshold parameters α and β according to the rules defined below. In the second step the position of all vehicles is changed using the velocity calculated in the first step. Position, velocity and threshold parameters of the vehicles are continuous variables. ∆t is the time step used in the simulations. 1st step velocity: A vehicle decelerates if the headway distance ∆xi(t) is smaller than a safety distance α. The headway distance after the deceleration step is determined by δ. ∆xi(t)− vi(t)∆t < α vi(t+∆t) = max (