| Popis: |
We introduce a novel lattice-free stochastic process which models vehicular traffic at the microscopic level. Vehicles are allowed to advance freely within their lane or change lanes without the limitation of lattice cells. Vehicles move under the influence of modified yet classical stochastic spin-flip and spin-exchange Arrhenius dynamic potentials. A modification of the well-known kinetic Monte Carlo algorithm produces the solution for these dynamics in real-time even for the case of a large traffic stream.An interesting, yet not-widely known discrepancy is revealed between lattice-based solutions and those produced by this new lattice-free approach. This discrepancy is mainly visible for high vehicle densities while both solutions agree otherwise. Employing the Palasti conjecture however reveals that indeed the new proposed lattice-free process is correct in predicting traffic densities while avoiding the overestimates produced by classic Cellular Automata type, lattice-based, approaches. |
