Title page for ETD etd-04302004-120043

Type of Document Master's Thesis
Author Krometis, Justin
Author's Email Address krometis@vt.edu
URN etd-04302004-120043
Title Lane Preference in a Simple Traffic Model
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Hagedorn, George A. Committee Chair
Schmittmann, Beate Committee Co-Chair
Zia, Royce K. P. Committee Member
  • driven lattice gas
  • Monte Carlo simulations
  • phase transition
  • non-equilibrium steady-state
  • highway traffic
Date of Defense 2004-04-23
Availability restricted
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, p. 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 p, 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 decreases 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.
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