Bus bunching as a synchronisation phenomenon

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.

No-boarding buses: Synchronisation for efficiency

“…Without any intervention, the two buses cannot remain staggered because such a configuration is unstable. This would be exemplified by systems with the buses moving at different natural frequencies, where frequency detuning leads to periodic bunching during lull periods, otherwise sustained bunching is the outcome during busy periods [1]. To prevent bunching, some form of intervention has to be executed.…”

“…Ref. [1] found that for the system served by N = 2 buses with f Let us now investigate the no-boarding policy applied to these situations in the NTU shuttle buses. We shall run simulations with the following setups:…”

“…Therefore, we describe a simple algorithm for picking θ 0 which is adaptive towards real-world stochasticity and varying demand levels k j for each bus stop. Before we present this algorithm, we first give some real-world parameters measured from the NTU campus shuttle buses [1]. With this, we can use these parameters to define our simulation environment to mimic a realistic system, where we then implement the adaptive algorithm to dynamically pick θ 0 which minimises the average waiting time.…”

“…In many bus systems, bus bunching is a natural repercussion where an initially staggered configuration of buses ends up with multiple buses getting closer to each other [1][2][3][4][5][6]. An intuitive mechanism that explains this phenomenon is that if there is some perturbation in the spacing between buses or the number of people at bus stops waiting to board a bus, then a bus may have to stop a bit longer to pick up people as well as allow people to alight.…”

“…Recently, work by Ref. [1] modelled a system of buses serving a loop of bus stops as a system of coupled oscillators [33], where each bus is represented by an autonomous oscillator.…”