Stochastic collective model of public transport passenger arrival process

It is essential to understand how transit passengers arrive at stops, as it enables transit operators and researchers to anticipate the number of waiting passengers at stops and their waiting time. However, the literature focuses more on predicting the total passenger demand, rather than simulating individual passenger arrivals to transit stops. When an arrival process is required especially in public transport planning and operational control, existing studies often assume a deterministic uniform arrival or a homogeneous Poisson process to model this passenger arrival process. This study generalises the homogeneous Poisson process (HPP) to a more general non‐HPP (NHPP) in which the arrival rate varies as a function of time. The proposed collective NHPP (cNHPP) simulates the passenger arrival using less time regions than the HPP, takes less time to compute, while providing more accurate simulations of passenger arrivals to transit stops. The authors first propose a new time‐varying intensity function of the transit passenger arrival process and then a maximum likelihood estimation method to estimate the process. A comparison study shows that the proposed cNHPP is capable of capturing the continuous and stochastic fluctuations of passenger arrivals over time.