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ESTIMATION OF THE OPTIMAL SPEED LIMIT TO MAXIMIZE THE TRAFFIC FLOW AT GIVEN DENSITY Master’s Thesis Zhang Wenjun Aalto University School of Business Information and Service Management Fall 2021 Aalto University, P.O. BOX 11000, 00076 AALTO www.aalto.fi Abstract of master’s thesis Author Zhang Wenjun Title of thesis Estimation of the Optimal Speed Limit to Maximize the Traffic Flow at Given Density Degree Master of Science in Economics and Business Administration Degree programme Information and Service Management Thesis advisor(s) Timo Kuosmanen Year of approval 2021 Number of pages 62 Language English Abstract Traffic congestion on road networks has become increasingly problematic since the 1950s. During the past several decades, it has caused various serious problems. Governments and other parties have already carried out many kinds of policies to mitigate it. Variable speed limit (VSL) is one of these strategies and used on the roads to reduce traffic accidents because higher free speeds would be more likely to cause traffic congestion and to manage the traffic flows with the intention of improving capacity and then throughout the traffic. For many years the research investigations about the relationship between traffic flow and speed limit have been being a popular topic in the transportation field. However, there still exist some conflicts on the traffic capacity and flow-density model under VSLs, some researchers proposed decreasing traffic capacity with decreasing VSL, while some induced increasing traffic capacity with decreasing VSL. The flow-density model is related to speed, traffic flow, and density, which are the main three elements of the fundamental equation in traffic flow theory. However, for all of these earlier literatures, researchers are just hypothesizing of how the flow-density diagram could look like using the simulator without considering the real-world data directly. This thesis explored the flow-density model under VSLs based on the real-world traffic flow dataset collected from the Finnish Transport Infrastructure Agency (FTIA) with different methodology convex regression to estimate the flow-density diagram and find the optimal speed limit to maximize the traffic flow at a given density. This project refers to two remarkable results that the estimated patterns look very different from those depicted in previous theoretical speculations. Firstly, the slopes of the congestion region above the critical density reveal large seasonal differences in the flow-density model. Secondly, at lower density, a lower speed limit could keep higher traffic flow. Keywords traffic congestion, traffic accident, variable speed limit (VSL), flow-density model, traffic flow theory, convex regression i Acknowledgements I thank my thesis supervisor, professor Timo Kuosmanen, who allowed me to follow the topic I am interested in. Because I have never learned traffic flow theory and convex regression in system, professor Timo is so nice to help me in the related documents collection and the understanding of these professional terminologies and methodologies. In addition, professor Timo arranged enough meeting chances to discuss with me and help me find the interesting thesis topic at the earlier period and he always help me focus on these wonderful fields and remarkable results. Professor Timo always provides valuable comments on my useful findings and criticizes the meaningless parts to make sure the thesis more wonderful. I also thanks to my family members, especially my husband Zhu Chao who accompanied me all the time during the special COVID 2019 period. It’s hard to keep healthy mood and focus on the master thesis writing during this period that we only can stay at home. He also helps me collect traffic data used in the thesis, such as the speed limit in highways and the exact locations of sensors. Meanwhile, I thank my husband to help me fix my computer when it crashed this summer. Last, but not least, I thank my friends Du Lei and Qu Ling who often encourage me when I meet some difficulties in my thesis or encounter bad mood during this period. Whenever I go to them, they always encourage that I can do it so that I can finish my thesis. ii Table of Contents Acknowledgements ......................................................................................................... ii 1 Introduction............................................................................................................. 1 2 Earlier Research...................................................................................................... 5 2.1 The VSL and Flow-density Model ............................................................................. 6 2.2 The Traffic Flow Theory............................................................................................ 9 3 Methodology.......................................................................................................... 13 3.1 Convex Regression ................................................................................................... 14 3.2 Convex Regression in Traffic Flow Theory............................................................. 17 4 Application ............................................................................................................ 19 4.1 Data Collection and Preprocessing.......................................................................... 20 4.1.1 Data Collection from Väylävirasto ......................................................................... 22 4.1.2 Data preprocessing with Python ............................................................................. 24 4.1.3 Calculation of Flow Rate and Density .................................................................... 27 4.2 Estimation of the Optimal Speed Limit to Maximize the Traffic Capacity at Given Density with Convex Regression .......................................................................................... 30 4.2.1 Flow-density Illustrations with Real Data............................................................... 31 4.2.2 Application of Convex Regression in Traffic Flow Theory ..................................... 34 5 Results and Discussion .......................................................................................... 37 5.1 Statistical Analysis of Experimental Data ............................................................... 38 5.2 Monthly Comparisons of Flow-density Model ........................................................ 41 5.3 Monthly Comparisons of Flow-density Models under VSLs .................................. 45 6 Conclusions............................................................................................................ 48 References ..................................................................................................................... 50 Appendix A: Appendix Title......................................................................................... 52 Appendix B: Simple Mass Downloader........................................................................ 53 Appendix C: Code of downloading data from URLs file............................................. 54 Appendix D: The Abnormal Points.............................................................................. 55 iii List of Tables Table 1: The features of raw data .................................................................................... 24 Table 2: The remaining features...................................................................................... 25 Table 3: Two DataFrames............................................................................................... 26 Table 4: Final two DataFrames ....................................................................................... 29 Table 5: Four sensors selected......................................................................................... 32 Table 6: Monthly flow rate and median slope of four sensors.......................................... 38 iv List of Figures Figure 1. Existing models regarding VSL effects on the flow-occupancy diagram............. 2 Figure 2. VSL sign in the United States in the late 1960s .................................................. 6 Figure 3. Cremer (1979) based on the data from Zackor (1972)......................................... 7 Figure 4. Distribution between density and traffic flow under VSL ................................... 8 Figure 5. A typical example of the fundamental diagram................................................. 10 Figure 6. Discontinuous Fundamental Diagram, Said Easa (1982)................................... 11 Figure 7. Least-squares fit of convex function to given data ............................................ 16 Figure 8. Least-squares fit of concave function to given data........................................... 18 Figure 9. The main loop for data collection and preprocessing ........................................ 20 Figure 10. the yearly flow-density scatterplots of four sensors......................................... 32 Figure 11. the capacity inference diagram of four sensors in October 2019 ..................... 36 Figure 12. the capacity inference of flow-density model for sensor 116, 126................... 41 Figure 13. the seasonal flow-density scatterplots for sensor 116, 126 .............................. 43 Figure 14. the capacity inference of flow-density model for sensor 183, 172................... 43 Figure 15. Comparisons of flow-density

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