Stochastic modelling for evaluation of impacts of headway variability on public transit performance

摘要

This thesis investigates stochastic factors influencing reliability of public transit (particularly bustransit) and examines performance indicators using probabilistic considerations such as the effectof randomness in passenger arrival, boarding, alighting and vehicle travel time on the regularityof headway along the route with multiple stops. The primary objective of this research is todevelop an analytical modeling framework to evaluate transit service performance understochastic environment.This research lays out an approach to study stochastic effects of public transit operation based onresults from theory of bulk queues. Stochastic flows over the system are characterized by theflow of passengers, with particular interest on the headway distribution of vehicles. Waitingpassenger line at stops are described as individual queues and the theory of bulk queues areapplied to find statistics of performance measures over a particular segment of a route. Threetypes of passenger waiting behavior have been taken into account to develop formulations. Thesepassenger behavior are: (a) passengers wait for the first bus after they joined the queue andabandon the system if unable to board the bus, (b) passengers wait at transit stop until they areserved and (c) passengers are unwilling to wait for bus if they do not receive service within theirexpected limit of waiting time budget. Based on passenger waiting behavior, polynomialequations and probability generating function of probability vectors of waiting passengers arederived along with moments of queue length for random outbound capacity of vehicles.Moreover, mean and variance of headway and occupancy, covariance of occupancy and headwayfor a given capacity of vehicles are derived. New performance measures are proposed.A single route consists of two terminals with multiple intermediate stops are considered for theanalytical modelling purpose. Empty buses of same size begine to serve passengers from the firststop to the last stop allowing passenger boarding and alighting in intermediate stops in onedirection. Step by step procedure for implementation of analytical model as a computer programis described. Application of the models is illustrated with number of numerical examples offeringinsights into factors that affect reliability of bus transit systems. The inputs of models arepassenger boarding and alighting demand at stops, marginal boarding and alighting time ofpassengers, mean and variance of travel time between stops, mean headway and vehicle size.The models produce a range of outputs that are interest of transit operations such as mean,variances and covariance of headway and occupancy, distribution of passenger load on bus,mean of number of waiting passengers, delay of passenger leftover and abandoned passengers atstops and utilization of transit routes. The developed modelling framework can be applied, ingeneral, for various transit operating strategies in a cheaper and convenient means oversimulations. More particularly, the computer application programs based on the analytical modelconstitute a research tool that would assist to accomplish planning and analyzing tasks withinpublic transit domain with detailed analysis at stop and route level.The analytical modeling framework, in its mathematical study of dynamics of bus routeoperations is a significant contribution to the states of the art. This investigation provides abetter understanding of determinants of reliability of public transit systems and the model can beused as an analysis tool by transit planners to evaluate effectiveness of various policies.