Application of Graph-Theoretic Indicators in Multi-Modal Public Transportation Networks

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 Edmontonâs 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, âDirectional Speedâ 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. âWeighted Potentialâ (WP) is a connectivity indicator which combines weighting by ridership with schedule availability between each stop-stop O-D pair. âPotential Travel Timeâ (PTT) is the average travel time between stop-stop O-D pairs, which is also weighted by ridership. The final metrics, âEffective Travel Timeâ (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 Edmontonâs public transit network to both demonstrate the utility of the indicators and provide information to planners who are redesigning the bus network.