Chaotic semi-express buses in a loop

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 that picks up passengers from bus stops A and B and then delivers them to bus stop C, while the second bus acts as an express bus that 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 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 that the efficiency arises from the chaotic dynamics exhibited in the semi-express system, where the tendency toward anti-bunching is greater than that toward bunching, in contradistinction to the regular bunching behavior of two normal buses or the independent periodic behavior of two non-interacting express buses.