Chaotic semi-express buses in a loop

TL;DR

This paper models a simplified urban bus loop with one normal and one semi-express bus, revealing that chaotic dynamics in the semi-express system lead to improved efficiency and reduced waiting times compared to traditional bus configurations.

Contribution

It introduces a novel semi-express bus system model demonstrating how chaotic dynamics can enhance efficiency in urban bus loops.

Findings

Semi-express system exhibits chaotic dynamics.

Chaotic behavior leads to anti-bunching of buses.

Semi-express configuration reduces average waiting time.

Abstract

Urban mobility involves many interacting components: buses, cars, commuters, pedestrians, trains etc., making it a very complex system to study. Even a bus system responsible for delivering commuters from their origins to their destinations in a loop service already exhibits very complicated dynamics. Here, we investigate the dynamics of a simplified version of such a bus loop system consisting of two buses serving three bus stops. Specifically, we consider a configuration of one bus operating as a normal bus which picks up passengers from bus stops $A$ and $B$, and then delivers them to bus stop $C$, whilst the second bus acts as an express bus which picks up passengers only from bus stop $B$ and then delivers them to bus stop $C$. The two buses are like asymmetric agents coupled to bus stop $B$ as they interact via picking up passengers from this common bus stop. Intriguingly, this \emph{semi-express} bus configuration is more efficient and has a lower average waiting time for buses, compared to a configuration of two normal buses or a configuration of two express buses. We reckon the efficiency arises from the chaotic dynamics exhibited in the semi-express system, where the tendency towards anti-bunching is greater than that towards bunching, in contradistinction to the regular bunching behavior of two normal buses or the independent periodic behaviour of two non-interacting express buses.