The complexity in transportation systems: the study of a bus loop

Abstract

We present a study of buses serving commuters through bus stops located in a loop as a complex system. We adopt the approaches of mathematical analysis, agent-based simulations, and machine learning in this study. Our aim is to attain bus scheduling configurations that minimise the average waiting time of the commuters. By performing simplified dynamical and statistical formulations, we delve into the essence of bus-to-bus and bus-to-commuters interactions. Our mathematical analysis cum computer simula- tions uncovered the effects of the interactions on (a) the rate at which buses bunches; (b) the efficiency of a proposed synchronized bunched bus configuration in serving a bus loop where commuters arrive in periodic spikes in one of the bus stops; and (c) the benefits of decoupling a set of bus stops to form the express bus configuration. Through the ma- chine learning technique of reinforcement learning, we found that holding and no-boarding strategies emerge as the elementary low-level actions for active control of staggered buses to optimally serve regular bus stops. Moreover, reinforcement learning had revealed that a novel semi-express bus configuration is an optimal set-up for an autonomous bus loop system, with the enhanced performance a consequence of the system situating at the edge-of-chaos.