Holistic approach to stochastic analysis of public transportation networks - Colgan, Stasia Arnae (Kansas State University, 2023)
Evaluating multi-modal public transportation networks is complicated and often the data needed to conduct detailed analysis is not available or difficult to attain. Much research has been done on methods to improve efficiency and redesign networks using mathematical and simulated models, but there is a lack of holistic analysis on the state of current networks. Holistic analysis allows efficient analysis requiring minimal equipment or software and can be used to test different scenarios that affect traffic through the network easily. It can also be used to determine where more critical analysis should be conducted. This thesis develops a network of queues to evaluate parameters of a transportation network consisting of multiple modes of transportation on a station-by-station basis, focusing on wait times, station utilization, and queue lengths. The first formulation defines the network as a set of nodes and arcs that are used to conduct the analysis. Second, an open Jackson network is used to evaluate the effective arrival rate to then calculate the different performance measures of the network. Finally, simulation using SIMIO is used to determine the interarrival time data of passengers entering each station that is not available in published data sets. Using a case study and numerical experiments, this thesis analyzes both a network with one mode of transportation and one with multiple modes. It also analyzes the impact of changing aspects of these networks on performance measures of each station within it. We observe what happens when passengers select a different transportation mode and how flow is affected when stations are closed. Overall, we demonstrate that queueing theory provides a method to quickly analyze a network without requiring complicated software.
Keywords: Stochastic; Queueing; Jackson network; Transportation