Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model

Approximating the BRMPU as a generalization of the NaSch model, the steady-state distribution of the time headways (TH) is calculated which are defined as the time intervals between the departures (or arrivals) of two successive particles on the model route.

Abstract

\n \nA Bus Route Model (BRM) can be defined on a \none-dimensional lattice, where buses are represented by \n"particles"that are driven forward from one site to the \nnext with each site representing a bus stop. We replace \nthe random sequential updating rules in an earlier BRM by parallel \nupdating rules. In order to elucidate the connection between \nthe BRM with parallel updating (BRMPU) and the Nagel-Schreckenberg \n(NaSch) model, we propose two alternative extensions of the NaSch \nmodel with space-/time-dependent hopping rates. Approximating \nthe BRMPU as a generalization of the NaSch model, we calculate \nanalytically the steady-state distribution of the time \nheadways (TH) which are defined as the time intervals between \nthe departures (or arrivals) of two successive particles (i.e., \nbuses) recorded by a detector placed at a fixed site (i.e., bus \nstop) on the model route. We compare these TH distributions \nwith the corresponding results of our computer simulations of \nthe BRMPU, as well as with the data from the simulation of the \ntwo extended NaSch models. We also investigate interesting kinetic \nproperties exhibited by the BRMPU during its time evolution \nfrom random initial states towards its steady-states.\n\n\n