Bunching Dynamics of Buses in a Loop

TL;DR

This paper presents an analytical approach to predict bus bunching in loop systems, providing insights into the timing of bunching events and passenger waiting times to improve transit efficiency.

Contribution

It introduces a novel analytical method to determine the number of revolutions before buses bunch and characterizes passenger waiting times in idealized bus loops.

Findings

Predicts the number of revolutions before bus bunching occurs.

Characterizes average passenger waiting times during bunching.

Offers design recommendations for bus loop systems.

Abstract

Bus bunching is a curse of transportation systems such as buses in a loop. Here we present an analytical method to find the number of revolutions before two buses bunch in an idealised system, as a function of the initial distance and the crowdedness of the bus stops. We can also characterise the average waiting time for passengers as the buses bunch. The results give a better understanding of the phenomenon of bus bunching and design recommendations for bus loops.