2021/01/16 by Luca Vismara, Lock Yue Chew, Vee-Liem Saw
Engineering · Mathematics · Physics and Astronomy · Social Sciences · #Address bus #Artificial intelligence #Bus network #Computer hardware #Computer science #Control bus #Disjoint sets #Engineering #Local bus #Mathematics #Real-time computing #Reinforcement learning #School bus #System bus #Traffic control and management #Transport engineering #Transportation Planning and Optimization #Transportation and Mobility Innovations #physics.soc-ph
paper · pdf · doi:10.1016/j.physa.2021.126268
21 pages, 5 figures
arxiv created 2021/01/16 · openalex publication_date 2021/07/20 · arxiv updated 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Bus systems involve complex bus-bus and bus-passengers interactions. We study the problem of assigning buses to bus stops to minimise the average waiting time of passengers, W. An analytical theory for two specific cases of interactions is formulated: normal situation where all buses board passengers from every bus stop, versus novel express buses where disjoint subsets of non-interacting buses serve disjoint subsets of bus stops. Our formulation allows exact calculation of W for general loops in the two cases examined. Compared with regular buses, we present scenarios where express buses show improvement in W. Useful insights are obtained from our theory: 1) there is a minimum number of buses needed, 2) splitting a crowded bus stop into two less crowded ones always increases W for regular buses, 3) changing the destination of passengers and location of bus stops do not influence W. In the second part, we introduce a reinforcement-learning platform that overcomes limitations of our analytical method to search for better allocations of buses to bus stops that minimise W. Compared with the previous cases, any possible interaction between buses is allowed, unlocking novel emergent strategies. We apply this tool to a simple toy model and three empirically-motivated bus loops, based on data collected from the Nanyang Technological University shuttle bus system. In the simplified model, we observe an unexpected strategy emerging that could not be analysed with our mathematical formulation and displays chaotic behaviour. The possible configurations in the three empirically-motivated scenarios are approximately 1011, 1011 and 1020, so a brute-force approach is impossible. Our algorithm reduces W by 12% to 32% compared with regular buses and 12% to 29% compared with express buses. This tool has practical applications because it works independently of the specific characteristics of a bus loop.