Application of Graph-Theoretic Indicators in Multi-Modal Public Transportation Networks by Bryan Whited A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Transportation Engineering Department of Civil and Environmental Engineering University of Alberta © Bryan Whited, 2018 ABSTRACT This thesis extends the current research on graph theory-based techniques to meet the needs of planners of multimodal transit networks. Graph theory was originally developed in the 1700s to study transportation systems although it was not adapted to study public transportation networks until the 1980s. Since then it has been primarily used to study rail and metro transit networks, resulting in numerous metrics being developed. Bus networks much larger and operate very differently from rail networks and so while many researchers have applied those metrics to bus networks, there remains a notable gap between the needs of bus transit planners and the graph theory-based tools seen in the current literature. This gap is bridged using graph representations of Edmonton’s multimodal transit network to understand the limitations of the current methodology and develop new methods specific to bus transit. The public transportation network operated by Edmonton Transit Service (ETS) is analyzed in five time periods, each of which is represented using four graph types, four edge types, both with and without pedestrian links for a total of thirty-two graph configurations. A common battery of indicators was calculated using each of these to investigate the effect of graph type, edge type, and pedestrian links, as well as changes in the network between time periods. The results indicate the metrics commonly used in the current literature provide more information about the choice in graph representation than in the underlying transit service. The needs of transit planners are identified, and four new metrics are developed specifically to meet those needs. Each of these metrics uses shortest paths through Time-Expanded graph representations of the Edmonton Transit Service (ETS) transit network. The simplest new metric, “Directional Speed” combines travel times with the distance travelled toward the downtown core. As stops are not equally important, the remaining three indicators are also weighted by ridership. “Weighted Potential” (WP) is a connectivity indicator which combines weighting by ridership with schedule availability between each stop-stop O-D pair. “Potential Travel Time” (PTT) is the average travel time between stop-stop O-D pairs, which is also weighted by ridership. The final metrics, “Effective Travel Time” (ETT), combines Weighted Potential and Potential Travel Time to provide a single indicator that reflects travel times and schedule availability. These metrics are used to quantify the quality of service in Edmonton’s public transit network to both demonstrate the utility of the indicators and provide information to planners who are redesigning the bus network. ii Acknowledgements I could never have done this without the help and support from a number of individuals, to whom I owe many thanks. More than anyone, I want to thank my academic supervisor Dr. Karim El-Basyouny, who has provided guidance and endless patience since first convincing me to take on a thesis. His knowledge and advice have been critical to developing this thesis. I also want to thank my coworkers at ETS, who provided data, inspiration, insight, and support over the past few years. Most notably, I want to thank my supervisor Andrew Gregory, and Directors Bill Sabey and Sarah Feldman, who have been flexible and supportive. Thanks also to Brian Korthius for countless conversations about the nuances and quirks of the GTFS and ridership data for the ETS network. Brian, along with Richard Leclerc, introduced me to KNIME and helped me obtain and clean numerous ridership data sets. In addition, I want to thank Dr. Tae Kwon for his time, effort and willingness to serve on my examination committee, and Dr. Manish Shirgoakar for providing a very useful compilation of GIS data, in addition to serving on my examination committee. Finally, I want to give special thanks to my wife Christy for her unwavering encouragement, and my friends and family who have been supportive and understanding over these past few years. iii TABLE OF CONTENTS ABSTRACT .............................................................................................................................................................. II ACKNOWLEDGEMENTS ......................................................................................................................................... III TABLE OF CONTENTS ............................................................................................................................................. IV LIST OF TABLES .................................................................................................................................................... VII LIST OF FIGURES .................................................................................................................................................. VIII LIST OF ABBREVIATIONS ....................................................................................................................................... XI LIST OF VARIABLES & METRIC VALUES ................................................................................................................. XII 1 INTRODUCTION ............................................................................................................................................. 1 1.1 BACKGROUND .................................................................................................................................................. 1 1.2 OBJECTIVES AND EXPECTED CONTRIBUTIONS .......................................................................................................... 3 1.3 THESIS STRUCTURE ............................................................................................................................................ 3 2 LITERATURE REVIEW ..................................................................................................................................... 5 2.1 TRANSIT QUALITY OF SERVICE .............................................................................................................................. 5 2.2 HISTORY OF PUBLIC TRANSPORTATION AS A GRAPH ................................................................................................. 6 2.3 GRAPHS AND THEIR COMPONENTS ....................................................................................................................... 8 2.4 DECISIONS ON GRAPH CONFIGURATIONS ............................................................................................................. 10 2.4.1 Graph Type ............................................................................................................................................ 11 2.4.2 Edge Type ............................................................................................................................................... 14 2.4.3 Pedestrian Links ..................................................................................................................................... 15 2.5 ANALYZING TRANSIT NETWORKS WITH GRAPH THEORY .......................................................................................... 16 2.6 ANALYSIS OF THE UNDERLYING TRANSIT SYSTEM ................................................................................................... 17 2.6.1 Global System Properties ....................................................................................................................... 17 2.6.2 Frequency of Service .............................................................................................................................. 19 2.6.3 Connectivity between Stops .................................................................................................................. 20 2.6.4 Shortest Path Length (SPL) and Average Path Length (APL) .................................................................. 22 2.7 ANALYSIS OF THE GRAPH .................................................................................................................................. 23 2.7.1 Global Graph Properties ........................................................................................................................ 24 2.7.2 Partition Analysis ................................................................................................................................... 26 2.7.3 Node Properties and Distributions ........................................................................................................ 29 2.7.4 Small-world and Scale-Free Networks ................................................................................................... 31 iv 2.8 LIMITATIONS IN CURRENT RESEARCH .................................................................................................................. 35 3 METHODOLOGY .......................................................................................................................................... 38 3.1 DATA SOURCES ............................................................................................................................................... 38 3.1.1 Google Transit Feed Specification