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

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Copyright: Islam, Md Kamrul
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Abstract
This thesis investigates stochastic factors influencing reliability of public transit (particularly bus transit) and examines performance indicators using probabilistic considerations such as the effect of randomness in passenger arrival, boarding, alighting and vehicle travel time on the regularity of headway along the route with multiple stops. The primary objective of this research is to develop an analytical modeling framework to evaluate transit service performance under stochastic environment. This research lays out an approach to study stochastic effects of public transit operation based on results from theory of bulk queues. Stochastic flows over the system are characterized by the flow of passengers, with particular interest on the headway distribution of vehicles. Waiting passenger line at stops are described as individual queues and the theory of bulk queues are applied to find statistics of performance measures over a particular segment of a route. Three types of passenger waiting behavior have been taken into account to develop formulations. These passenger behavior are: (a) passengers wait for the first bus after they joined the queue and abandon the system if unable to board the bus, (b) passengers wait at transit stop until they are served and (c) passengers are unwilling to wait for bus if they do not receive service within their expected limit of waiting time budget. Based on passenger waiting behavior, polynomial equations and probability generating function of probability vectors of waiting passengers are derived along with moments of queue length for random outbound capacity of vehicles. Moreover, mean and variance of headway and occupancy, covariance of occupancy and headway for 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 the analytical modelling purpose. Empty buses of same size begine to serve passengers from the first stop to the last stop allowing passenger boarding and alighting in intermediate stops in one direction. Step by step procedure for implementation of analytical model as a computer program is described. Application of the models is illustrated with number of numerical examples offering insights into factors that affect reliability of bus transit systems. The inputs of models are passenger boarding and alighting demand at stops, marginal boarding and alighting time of passengers, 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 at stops and utilization of transit routes. The developed modelling framework can be applied, in general, for various transit operating strategies in a cheaper and convenient means over simulations. More particularly, the computer application programs based on the analytical model constitute a research tool that would assist to accomplish planning and analyzing tasks within public transit domain with detailed analysis at stop and route level. The analytical modeling framework, in its mathematical study of dynamics of bus route operations is a significant contribution to the states of the art. This investigation provides a better understanding of determinants of reliability of public transit systems and the model can be used as an analysis tool by transit planners to evaluate effectiveness of various policies.
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Author(s)
Islam, Md Kamrul
Supervisor(s)
Dixit, Vinayak
Vandebona, Upali
Sharma, Ashish
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Publication Year
2014
Resource Type
Thesis
Degree Type
PhD Doctorate
UNSW Faculty
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