Lane Preference in a Simple Traffic Model

We examine the effect of lane preference on a quasi one-dimensional three-state driven lattice gas, consisting of holes and positive and negative particles, and periodic boundary conditions in the longitudinal direction. Particles move via particle-hole and, with a lesser rate, particle-particle exchanges; the species are driven in opposite directions along the lattice, each preferring one of the lanes with a given probability, <I>p</I>. The model can be interpreted as traffic flow on a two-lane beltway, with fast cars preferring the left lane and slow cars preferring the right, viewed in a comoving frame. In steady-sate, the system typically exhibits a macroscopic cluster containing a majority of the particles. At very high values of <I>p</I>, a first order transition takes the system to a spatially disordered state. Using Monte Carlo simulations to analyze the system, we find that the size of the cluster increases with lane preference. We also observe a region of negative response, where increasing the lane preference <I>decreases</I> the number of particles in their favored lane, against all expectations. In addition, simulations show an intriguing sequence of density profiles for the two species. We apply mean-field theory, continuity equations, and symmetries to derive relationships between observables to make a number of predictions verified by the Monte Carlo data.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2004

Author dc:creator

• Krometis, Justin

Chairs dc:contributor.committeechair

• Hagedorn, George A.
• Schmittmann, Beate

Committee member dc:contributor.committeemember

• Zia, Royce K. P.

• driven lattice gas
• Monte Carlo simulations
• phase transition
• non-equilibrium steady-state
• highway traffic

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-04302004-120043

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/42365