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Title: Bus bunching as a synchronisation phenomenon
Authors: Pang, Ian Yi En
Chew, Lock Yue
Saw, Vee-Liem
Chung, Ning Ning
Quek, Wei Liang
Keywords: Bus Bunching
Kuramoto Model
Issue Date: 2019
Source: Saw, V.-L., Chung, N. N., Quek, W. L., Pang, I. Y. E., & Chew, L. Y. (2019). Bus bunching as a synchronisation phenomenon. Scientific Reports, 9, 6887-. doi:10.1038/s41598-019-43310-7
Series/Report no.: Scientific Reports
Abstract: Bus bunching is a perennial phenomenon that not only diminishes the efficiency of a bus system, but also prevents transit authorities from keeping buses on schedule. We present a physical theory of buses serving a loop of bus stops as a ring of coupled self-oscillators, analogous to the Kuramoto model. Sustained bunching is a repercussion of the process of phase synchronisation whereby the phases of the oscillators are locked to each other. This emerges when demand exceeds a critical threshold. Buses also bunch at low demand, albeit temporarily, due to frequency detuning arising from different human drivers’ distinct natural speeds. We calculate the critical transition when complete phase locking (full synchronisation) occurs for the bus system, and posit the critical transition to completely no phase locking (zero synchronisation). The intermediate regime is the phase where clusters of partially phase locked buses exist. Intriguingly, these theoretical results are in close correspondence to real buses in a university’s shuttle bus system.
DOI: 10.1038/s41598-019-43310-7
Rights: © 2019 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Te images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit
Fulltext Permission: open
Fulltext Availability: With Fulltext
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