One-Dimensional Traffic Flow Models: Theory and Computer Simulations

TL;DR

This paper reviews theoretical and simulation studies of one-dimensional driven lattice gases, especially the TASEP model, exploring phase transitions, power spectra, and network effects in steady states.

Contribution

It provides new simulation results on the power spectrum of particle number fluctuations and theoretical approximations within the domain-wall picture, along with phase analysis on network models.

Findings

Power spectrum varies across different phases.

Coexistence line shows cross-correlations between branches.

Phase structures depend on boundary rates and network topology.

Abstract

Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion process (TASEP) with open boundary conditions: particles are injected at the left end with rate alpha and removed at the right end with rate beta. Depending on the values of these parameters, the model exhibits three stationary phases, separated by lines of first- and second-order non-equilibrium phase transitions. New simulation results on the power spectrum of the fluctuating total number of particles in the different phases of the system are presented. Our theoretical contribution concerns the approximate evaluation of the power spectrum in the domain-wall picture of the coexisting low- and high-density phases. Finally, we review some of our recent results on the TASEP defined on an open network containing a double-chain section in the middle. With the aid of a simple theory, which neglects correlations at the junctions of the chain segments, the possible phase structures of the model are found. Density profiles and nearest-neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained by means of computer simulations. On the coexistence line cross-correlations are found to exist between equivalent sites in the branches of the middle section.