Modeling complex processes: street traffic

elective seminars

Blended learning
Classroom
Field classes
Remote learning

The idea behind our seminar is to use mathematics and programming tools to solve civilization problems in the modern world. We will look at the issues related to road traffic and the impact of traffic jams on air quality, economy and safety from a perspective of mathematical and IT tools, e.g. game theory, machine learning, quantum computing, differential equations and cellular automata.

Contemporary societies struggle with many civilization problems, and mathematics and computer science have enormous potential to deal with them. Air pollution, traffic jams, the climate crisis, the global pandemic and the fight against cancer are just a few of the challenges in which mathematical modeling is key to developing effective action strategies. Addressing these challenges goes beyond narrow research fields and requires an interdisciplinary effort. It is necessary to create an effective link between the theoretical / mathematical aspect of problem description, e.g. using differential equations or game theory, and the tangible result of the analysis based on data, algorithms and programming. This requires a combination of skills that are customarily developed in the academic curriculum in unrelated courses. Therefore, we invite to our seminar those who:

a) are interested in issues inspired by real problems, b) have some experience in the following areas (at least 1 of them): game theory, machine learning, data analysis, Big Data, differential equations (ordinary and / or partial), graphs, cellular automata , programming, algorithms, databases, quantum computing c) are ready and willing to work in task teams on specific research projects.

In the 2022/2023 academic year, we will focus on road traffic. Daily traffic jams at rush hour significantly affect air quality, economic indicators, safety and public mood. One of the key problems of traffic management is the attitude of the drivers themselves, who follow the selfish goal of optimizing their own passage without taking into account the broader aspects of traffic. Collective strategies can significantly improve the total flow of traffic. Currently, as part of the tests, autonomous cars are joining the public traffic. Their intelligent and collective behavior offers new opportunities to improve the current, strained system. Significant improvements can also be achieved at the infrastructure level by means of surprising planning decisions, an example of which is the so-called Braess's paradox that removing a road from the transport network could improve overall car flow. The essence of this intriguing phenomenon can be explained with the help of game theory. However, this is not only a theoretical construct, but a phenomenon observed in practice.

As part of the seminar, students will have the opportunity to learn about professional tools for modeling and analyzing road traffic (eg Visum) and carry out research work under the CoMobility project https://comobility.edu.pl. Lectures by invited speakers from other universities and practitioners from institutions related to road management and control are also planned. We plan to conduct some classes remotely, regardless of the mode, the course has its website on moodl: https://moodle.mimuw.edu.pl/course/view.php?id=1077.

● David Easley, Jon Kleinberg: Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press, 2010. ● Filippo Santambrogio: Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling, Progress in Nonlinear Differential Equations and Their Applications, Birkhauser, 2015.

● D. Braess: On a paradox of traffic planning (english translation by, A. Nagurney, and T. Wakolbinger) Journal of Transportation Science, volume 39, 2005, pp. 446–450.

● Nagel, K.; Schreckenberg, M. (1992). "A cellular automaton model for freeway traffic" (PDF). Journal de Physique I. 2 (12), pp. 2221-2229.

● Kerner, B. S (1998). "Experimental Features of Self-Organization in Traffic Flow". Physical Review Letters. 81 (17), pp. 3797–3800.

● Skowronek Ł., Gora P., Możejko M., Klemenko A., "Graph-based Sparse Neural Networks for Traffic Signal Optimization", Proceedings of the 29th International Workshop on Concurrency, Specification and Programming (CS&P 2021), 2021.

● Szejgis W., Warno A., Gora P., "Predicting times of waiting on red signals using BERT", in NeurIPS 2020 Workshop on Machine Learning for Autonomous Driving

● Borowski M., Gora P., Karnas K., Błajda M., Król K., Matyjasek A., Burczyk D., Szewczyk M., and Kutwin M., "New Hybrid Quantum Annealing Algorithms for Solving Vehicle Routing Problem", Computational Science - ICCS 2020, 2020, pp. 546-561.

● Gora P., Kurach K. "Approximating Traffic Simulation using Neural Networks and its Application in Traffic Optimization", in "NIPS 2016 Workshop on Nonconvex Optimization for Machine Learning: Theory and Practice."

● Gora P., Rüb I. "Traffic Models For Self-driving Connected Cars", in "Transportation Research Procedia", vol. 14, 2016, pp. 2207-2216.

Students can:

● model, using mathematical and / or IT tools, complex processes occurring in nature, find analogies between various phenomena,

● to critically analyze articles and scientific studies,

● plan and carry out simple research / experiments: analyze their results, prepare a research report, prepare a presentation of the obtained results, present data,

● students develop the ability to work in a diverse group, communication and division of tasks.

Rules for crediting:

- students are expected to actively participate in classes

- students are required to prepare a final research report

- students are required to present the developed issues / research results during the classes

Assessment based on:

- attendance at classes

- preparing and delivering presentations

- a report on the work carried out.