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Models for Networks with Consumable Resources: Applications to Smart Cities Hayato Montezuma Ushijima-Mwesigwa Clemson University, [email protected]

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Models for Networks with Consumable Resources: Applications to Smart Cities Hayato Montezuma Ushijima-Mwesigwa Clemson University, Hmwesigwa@Hotmail.Com Clemson University TigerPrints All Dissertations Dissertations 12-2018 Models for Networks with Consumable Resources: Applications to Smart Cities Hayato Montezuma Ushijima-Mwesigwa Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_dissertations Recommended Citation Ushijima-Mwesigwa, Hayato Montezuma, "Models for Networks with Consumable Resources: Applications to Smart Cities" (2018). All Dissertations. 2284. https://tigerprints.clemson.edu/all_dissertations/2284 This Dissertation is brought to you for free and open access by the Dissertations at TigerPrints. It has been accepted for inclusion in All Dissertations by an authorized administrator of TigerPrints. For more information, please contact [email protected]. Models for Networks with Consumable Resources: Applications to Smart Cities A Dissertation Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Computer Science by Hayato Ushijima-Mwesigwa December 2018 Accepted by: Dr. Ilya Safro, Committee Chair Dr. Mashrur Chowdhury Dr. Brian Dean Dr. Feng Luo Abstract In this dissertation, we introduce different models for understanding and controlling the spreading dynamics of a network with a consumable resource. In particular, we consider a spreading process where a resource necessary for transit is partially consumed along the way while being refilled at special nodes on the network. Examples include fuel consumption of vehicles together with refueling stations, information loss during dissemination with error correcting nodes, consumption of ammunition of military troops while moving, and migration of wild animals in a network with a limited number of water-holes. We undertake this study from two different perspectives. First, we consider a network science perspective where we are interested in identifying the influential nodes, and estimating a nodes’ relative spreading influence in the network. For this reason, we propose generalizations of the well-known centrality measures to model such a spreading process with consumable resources. Next, from an optimization perspective, we focus on the application of an Electric Vehicle road network equipped with wireless charging lanes as a resource allocation problem. The objective is this case is to identify a set of nodes for optimal placement of the wireless charging lanes. For this reason, we propose an integer programming model formulation and use it as a building block for different realistic scenarios. We conclude this dissertation by giving an approach to improve route selection for the optimization model proposed by using feedback data while giving comparisons to different realistic scenarios. ii Dedication This dissertation is dedicated to my father, mother, Savannah, Cresto, Keiko, and Christa. In memory of Mbabazi Sherurah for her unwavering encouragement throughout different periods of my life. iii Acknowledgments First and foremost, this dissertation would not have been possible without the help and guidance of my advisor, Dr. Ilya Safro. I am very thankful for his patience and guidance throughout the years. I also greatly appreciate him for encouraging me to expand the scope of my research to other areas such as quantum computing and combinatorial scientific computing. This has subse- quently led to many exciting opportunities and has greatly broadened my research experience. I am thankful that he took me on as his student and we have successfully worked on very many exciting research problems! I am thankful to members of my dissertation committee: Dr. Mashrur Chowdhury, Dr. Feng Luo, and Dr. Brian Dean for their help and guidance with my dissertation. I am grateful to Dr. Dean for introducing me to the School of Computing when I attended his weekly Algorithms seminars. His enthusiasm for algorithms and teaching has inspired me in my own research and presentation. I am thankful to my Masters’ thesis advisors, Dr. Neil Calkin and Dr. Beth Novick, for not only advising me on my thesis but also for their guidance and wisdom which has helped me become a better researcher. I am honored to have been their student. My family has been very supportive of me throughout my entire academic journey. I would like to thank my parents: John Patrick and Hatsuko Mwesigwa, my brothers Savannah and Cresto, and my sister Keiko for being an absolutely encouraging family. Special thanks to Keiko for always being supportive of me from the first day of kindergarten, through graduate school applications to graduation day preparations! I am very thankful for my wonderful fiancée Christa Peterson (Mwesigwa) for being extremely understanding, loving and kind throughout this journey (#cyato19). I would also like to thank my friends and colleagues during my time in graduate school. Thank you Thilo Strauss, Yubo Zhang, Michael Dowling, Ehsan Sadrfaridpour, Varsha Chauhan, iv Justin Sybrandt, and Ruslan Shaydulin to name a few. Last but definitely not least, I would like to thank the Karoro family and my family and friends in Los Angeles and Uganda. Special thanks to Terry and Vince Flynn, Charles Twagira, Charlene Twagira, Harunah Ntege, Steed Kiboneka, and Yasin Sebaggala. v Table of Contents Title Page ............................................ i Abstract ............................................. ii Dedication............................................ iii Acknowledgments........................................ iv List of Tables ..........................................vii List of Figures..........................................viii 1 Introduction......................................... 1 1.1 Research Objectives .................................... 2 1.2 Contributions........................................ 2 2 Network Analytic Models................................. 4 2.1 Introduction......................................... 4 2.2 Applications......................................... 5 2.3 Related Work........................................ 8 2.4 Graph Model........................................ 10 2.5 Katz Centrality....................................... 12 2.6 Betweenness Centrality................................... 13 2.7 Random-Walk Betweenness Centrality.......................... 20 2.8 Computational Experiments................................ 23 2.9 Conclusion ......................................... 38 3 Optimization Models....................................40 3.1 Introduction......................................... 40 3.2 Optimization Model Development............................. 46 3.3 Computational Results................................... 60 3.4 Conclusion ......................................... 74 4 Feedback-Based Optimization ..............................75 4.1 Survey............................................ 76 4.2 Computational Experiments................................ 79 5 Conclusion..........................................83 vi List of Tables 2.1 Experimental graph datasets: dmin; davg; dmax represents the minimum, average and maximum degree. ..................................... 23 3.1 Road category with corresponding speed in Miles/Hr.................. 67 vii List of Figures 2.1 Kendall comparison of nodes’ spreading influence according to the generalized SIR model and SOC Katz centrality on the routers network. Each boxplot represents 30 random choices of the set Ω with spreading probability α = 0:03, and κ = 5 . 26 2.2 Spearman comparison of nodes’ spreading influence according to the generalized SIR model and SOC Katz centrality on the routers network. Each boxplot represents 30 random choices of the set Ω with spreading probability α = 0:03, and κ = 5 . 27 2.3 Kendall correlation scores for expected versus realized centrality for SOC-betweenness centrality for the Gnutella network. Each boxplot represents 30 random choices of the set Ω, with κ = 4 .................................... 28 2.4 Spearman correlation scores for expected versus realized centrality for SOC-betweenness centrality for the Gnutella network. Each boxplot represents 30 random choices of the set Ω, with κ = 4 .................................... 29 2.5 Kendall correlation scores for expected versus realized centrality for SOC RWBC for the Gnutella network. Each boxplot represents 30 random choices of the set Ω, with κ = 4 ............................................. 30 2.6 Spearman correlation scores for expected versus realized centrality for SOC RWBC for the Gnutella network. Each boxplot represents 30 random choices of the set Ω, with κ = 4 .......................................... 31 2.7 Kendall correlation scores for expected versus realized centrality for SOC-betweenness centrality for the Minnesota road network. Each boxplot represents 30 random choices of the set Ω, with κ = 20 .................................. 32 2.8 Comparison of BC and SOC-BC. (a) Standard BC; (b) SOC-BC with Ω = ;; κ = 4; (c) - (f) SOC-BC with κ = 4, where diamond-shaped nodes represent nodes in Ω. 33 2.9 Comparison of Katz and SOC-Katz; (a) Standard Katz centrality; (b) SOC-BC with Ω = ;; κ = 4; (c) - (f) SOC-BC with κ = 4, where diamond-shaped nodes represent nodes in Ω. ......................................... 34 2.10 SOC-Katz Vs. Katz for 10 × 10 Grid graph. ...................... 35 2.11 SOC-BC Vs BC for Minnesota Road Network ..................... 35 2.12 Comparison of RWBC with SOC-RWBC for a single s-t pair over the Minnesota road network. The top-left and center black nodes represent the source
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