A Markov process model for capacity-constrained transit assignment

Motivated by transit environments in cities where the transit vehicles are small and do not run to timetables, this study aims to represent the finite capacity constraints imposed by such vehicles in a transit assignment model. The objectives of this study are: to specify the requirements of a transit assignment model that accounts for both strict capacity constraints and the day-to-day dynamics of passengers' route choice, to develop such a model, and to identify its properties and conduct numerical tests on it. To position this research in relation to the wide-ranging existing literature required a comprehensive literature review including: general frequency-based (FB) and schedule-based (SB) assignment models, different approaches for including capacity constraints and modelling passengers' route choice. It is noted that no existing FB assignment model gives a consistent account of the waiting time and attractive-line boarding probability impacts of strict capacity constraints, including the asymmetric interactions of different groups of passengers competing for capacity. SB models require timetables and are thus not applicable. The proposed model, MPTRANSIT, is formulated as a Markov process model. It accounts for: the strict capacity constraints of transit vehicles, passengers' learning processes, differences in passengers' cost perceptions, and the day-to-day variability in demand and line frequencies. A microsimulation model is used to enforce capacity constraints at the level of each individual vehicle and represent the day-to-day .variability in line frequencies. The model outputs include distributions of route flows, route costs, and line loadings. For cases where total demand does not exceed total capacity, a theoretical proof is given for the stationarity of the route cost distributions, independent of initial conditions. A route enumeration algorithm is also proposed and tested on small artificial networks. The numerical experiments conducted on artificial networks illustrate the theoretical result and show that MPTRANSIT converges to the same stationary distribution, independent of initial conditions. MPTRANSIT is shown to converge to a stationary distribution even where multiple route flow attractors exist. The difficulty in calibrating congestion functions to consistently account for strict capacity constraints is, discussed. The estimation errors arising when such constraints are not. represented consistently are illustrated. The sensitivity of the model to key parameters and assumptions is also presented.EThOS - Electronic Theses Online ServiceGBUnited Kingdo