Continuous time stochastic models for vehicular traffic on highways

Abstract

We have simulated a continuous time version of the Nagel-Schreckenberger model of vehicular traffic on highways and calculated the flux as a function of vehicle density. In the low density regime the flux increases linearly with density but becomes a power law when velocities are allowed to increase without bounds. We have simulated also a modified version in which the state of a vehicle depends on the velocity of the vehicle moving ahead. This model displays a phase transition from a state with nonzero flux to a jammed state at a critical density which is strictly less than the closed-packed density. We also study the relationship of this model with self-organized criticality.

Generating Pseudo-Random Discrete Probability Distributions

“…As a consequence, it is also an essential aspect of our science and technology. The related research theme, that was motivated initially mainly by gambling and led eventually to probability theory [4,5], is nowadays a crucial part of many different fields of study such as computational simulations, information theory, cryptography, statistical estimation, system identification, and many others [6,7,8,9,10,11,12].…”