University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2018 Essays in network theory applications for transportation planning Jeremy David Auerbach University of Tennessee, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Recommended Citation Auerbach, Jeremy David, "Essays in network theory applications for transportation planning. " PhD diss., University of Tennessee, 2018. https://trace.tennessee.edu/utk_graddiss/5027 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Jeremy David Auerbach entitled "Essays in network theory applications for transportation planning." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Geography. Hyun Kim, Major Professor We have read this dissertation and recommend its acceptance: Eugene C. Fitzhugh, Yingjie Hu, Shih-Lung Shaw Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Essays in network theory applications for transportation planning A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Jeremy David Auerbach August 2018 © by Jeremy David Auerbach, 2018 All Rights Reserved. ii Acknowledgments I would like to thank my advisor Hyun Kim (Associate Professor of Geography at the University of Tennessee) for his patience and mentorship and my committee members, Eugene Fitzghugh, Shih-Lung Shaw, and Yingjie Hu, for their valuable input. I would like to thank Alex Zendel (GIS Analyst at the Knoxville-Knox County Metropolitan Planning Commission) for compiling the school network data used for the case study in the se- cond chapter “Optimization of network connectivity: An evaluation of heuristics applied to random networks and a transportation case study”. For the third chapter “Small changes in street connectivity result in big gains for student walking” I would like to thank Ellen Zaviska (Senior Transportation Planner at the Knoxville Regional Transportation Planning Organization) for comments and advice, Alex Zendel (GIS Analyst at the Knoxville-Knox County Metropolitan Planning Commission) for compiling the school network data, and Rickey Grubb (Director of Enrollment and Transportation at Knox County Schools) for relevant information about school busing. iii Abstract Throughout the dissertation, network methods are developed to address pressing issues in transportation science and geography. These methods are applied to case studies to highlight their use for urban planners and social scientists working in transportation, mobility, housing, and health. The first chapter introduces novel network robustness mea- sures for multi-line networks. This work will provide transportation planners a new tool for evaluating the resilience of transportation systems with multiple lines to failures. The se- cond chapter explores optimizing network connectivity to maximize the number of nodes within a given distance to a focal node while minimizing the number and length of addi- tional connections. These methods can be used to identify optimal thoroughfare design around important facilities, such as schools. The third chapter utilizes the network optimi- zation heuristics presented in Chapter 2 to identify the impact of thoroughfare connectivity on student active commuting. Housing developers can incorporate these findings when planning new residential developments around schools. The dissertation concludes with future directions in this research domain. iv Table of Contents Introduction 1 1 Hiking Eulerian Forests: Measuring Robustness and Coverage in Multi-line Networks 4 Abstract . .5 Introduction . .7 Index Development . 11 Eulerian Forests . 11 Modified Traditional Global Connectivity Indexes (αF ; βF ; γF )......... 14 Multi-Line Eigenvalue Robustness Index (ΛF )................. 15 Line Coverage Similarity Index (JF )....................... 16 Edge Comparison Index (CF ).......................... 17 Hub-Stress Index (HSI)............................. 18 Numerical Experiments . 19 Simulated Forests . 19 Case Study with US City Rail Systems . 24 Conclusion and Future Work . 30 Appendix . 31 2 Network Connectivity Optimization: An Evaluation of Heuristics Applied to Complex Networks and a Transportation Case Study 35 Abstract . 36 Introduction . 38 Methods and Results . 42 Network Connectivity Optimization . 42 v Local Search Methodology . 44 Network Connectivity Optimization Heuristics . 46 Simulated Data: Complex Random Networks . 49 Empirical Data: Street Networks Around Schools . 50 Results . 50 Discussion . 52 Appendix . 58 Additional Figures and Tables . 58 Optimization Algorithms . 64 3 Small Changes in Street Connectivity can Result in Big Gains for Student Walking 70 Abstract . 71 Introduction . 72 School Active Commuting: Importance and Recent Decline in the U.S. 72 School Active Commuting Policy Case Study . 74 Scope of Research . 75 Methods . 77 Data........................................ 77 School Selection and Optimal Location of Connections . 78 Energy Expenditure . 80 Busing Costs . 80 Health Economics . 81 Connection Costs . 81 Results . 82 Discussion . 84 Limitations . 84 Conclusions . 85 vi Appendix . 87 Additional Results . 87 Data Engineering . 87 Optimal Connection Search Algorithm . 90 Conclusion 92 References 97 Vita 114 vii List of Tables 1.1 List of symbols and their definitions. .6 1.2 Network characteristics and global connectivity and robustness measures. 21 1.3 Correlations between the global measures for the simulated Forests. 25 1.4 Network characteristics and robustness index values for the twelve largest United States city rail systems with multiple lines. 26 1.5 Correlations between the global measures for the twelve US rail networks. 27 2.1 List of symbols and their definitions. 37 2.1 Correlation coefficients for the nodal characteristics and the solution bene- fits for the experimental networks. 54 2.A1 Local search criteria. 59 2.A2 Measures of network complexity. 60 2.A3 Delaunay and Voronoi random network characteristics. 60 2.A4 School street network characteristics. 61 2.A5 Random network parameters. 61 3.1 Active commuting characteristics and optimal results for the ten schools. 83 viii List of Figures 1.1 Comparison of three Eulerian Forests with the same number and length of trails. 13 1.2 Characteristics of the Hub Stress index. 20 1.3 Distributions of the various global robustness measures applied to the same set of simulated Forests (10000 random networks). 23 1.4 Plots of the largest and second largest eigenvalues for different Forest sizes and trails lengths. 24 1.5 Comparison of Hub Stress index values for the twelve heavy rail networks. 29 1.6 The ranges of Hub Stress index values for the hubs of each of the twelve rail networks. 30 1.A1 Additional numerical results. 34 2.1 Diagram of the network connectivity optimization problem. 43 2.2 Diagram of the local search methodology. 45 2.3 Examples of the street networks used for the analysis. 51 2.4 The relationship between select nodal characteristics and the cost and be- nefits for each solution for different networks. 53 2.5 Termination times and optimal solution deviations for the heuristics. 55 2.A1 Examples of the random graphs used for the analysis. 58 2.A2 Termination times for the heuristics applied to random networks. 62 2.A3 Cost and benefit deviations for the heuristics applied to random networks. 63 3.1 A cartoon description of the connectivity problem. 76 3.2 Map of the study area. 78 3.3 Student active commuting potential for Knox County schools. 79 ix 3.4 Optimal connection results for the two example schools. 82 3.A1 Optimal connection results for the ten schools. 87 x List of Algorithms 2.1 Exhaustive search pseudocode . 64 2.2 Hill climbing . 65 2.3 Stochastic hill climbing . 66 2.4 Hill climbing with a variable neighborhood . 67 2.5 Simulated annealing . 68 2.6 Genetic algorithm . 69 3.1 Exhaustive search pseudocode . 90 xi Introduction Transportation studies and geography have benefited greatly from network science (Lar- son and Odoni, 1981, Magnanti and Wong, 1984, Derrible and Kennedy, 2010a) but there are still many questions and issues in the field which need to be addressed. Measuring the resilience of systems that have multiple connections between nodes, such as rail sy- stems with several lines between stations, and optimizing the thoroughfare connectivity around important facilities, such as greenways around schools, are examples of problems still not fully explored. Utilizing network theory approaches to address these questions can help urban planners and social scientists make more informed policy recommendations for improving healthcare, infrastructure, and security. The dissertation is composed of several chapters, each exploring a different aspect of transportation research and network theory with the emphasis on developing new metho- dology and written in separate manuscript formats. Each