Modeling vehicular speed fluctuations as a stochastic process with exponentially decaying memory Free

In this study, the temporal fluctuation of the speed of a vehicle plying in traffic is modelled as a stochastic process with an exponentially decaying memory function. Results of the stochastic modeling are compared with simulations using a two-lane Nagel-Schreckenberg cellular automata traffic model for speeds involving different traffic scenarios. Vehicular speeds were also obtained from the position of actual vehicles in real-world scenarios using a Global Positioning System (GPS) data logger which records the position with one second time interval. The mean squared displacements (MSD) of the speed's temporal fluctuation for both the simulation and the GPS data match the theoretical MSD given by, MSD(T) = C(1−e^−T/Tc). The simulation confirms that the values of the two parameters, Tc and C, of the MSD indicate sensitivity to the different vehicular densities. The time constant Tc decreases as the density increases while the relation between C and density shows a similar behavior to that of the traffic flow-density relation where two traffic regimes can be clearly defined. The dependence of the parameters to the vehicular density allows the stochastic model to determine the density and flow at any section of the road in real-time. The stochastic model of a single vehicle's speed fluctuation is especially useful in traffic forecasting and management since this enables the gathering of essential traffic data with high spatial and temporal resolution.