Accounting for passenger loss in bus bunching reduction: a robust real-time speed control method

Bus bunching is a common phenomenon resulting from the inherent instability influenced by factors such as traffic and passenger behaviour. However, the issue of passenger loss caused by extended waiting time, is often overlooked despite being a significant concern for passengers. This paper addresses this problem by modelling passenger arrival and loss as a Markov birth–death process. We present a transit route model that incorporates passenger loss while considering additional factors, such as stochasticity, overtaking, passenger alighting, and bus capacity constraints. The primary objective of our model is to minimise passenger loss. To achieve this, we conduct an analysis about the characteristics of passenger loss. Under mild assumptions, we prove that passenger loss increases as the headways between buses exhibit greater variance. We also develop a robust optimisation (RO) method and corresponding algorithms to minimise passenger loss. To validate the effectiveness of our control method, we conduct numerical experiments using both computer-generated and real-world data. The results demonstrate that our method effectively reduces bus bunching, passenger loss, and waiting time compared to the existing literature.