Reconciliation of stability analysis with simulation in a bus route model

Abstract

In a recent paper (Physica A 296, 320 (2001)), T. Nagatani proposes a time-headway model for buses on a bus route, and studies the stability of that model's homogeneous solutions. While investigating the phase diagram gotten by varying the rate of passenger arrival and the initial spacing of buses, he discovers a discrepancy between the results of simulation and those of linear stability analysis. In this paper, we reconcile the discrepancy by noting the existence of three types of phase diagrams, and present simulational results which confirm the stability analysis.