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Large-scale simulation of traffic flow using Markov model

Author

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  • Renátó Besenczi
  • Norbert Bátfai
  • Péter Jeszenszky
  • Roland Major
  • Fanny Monori
  • Márton Ispány

Abstract

Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps in understanding and handling traffic problems, optimizing traffic regulations and adapting the traffic management in real time for unexpected disaster events. A mathematically rigorous stochastic model that can be used for traffic analysis was proposed earlier by other researchers which is based on an interplay between graph and Markov chain theories. This model provides a transition probability matrix which describes the traffic’s dynamic with its unique stationary distribution of the vehicles on the road network. In this paper, a new parametrization is presented for this model by introducing the concept of two-dimensional stationary distribution which can handle the traffic’s dynamic together with the vehicles’ distribution. In addition, the weighted least squares estimation method is applied for estimating this new parameter matrix using trajectory data. In a case study, we apply our method on the Taxi Trajectory Prediction dataset and road network data from the OpenStreetMap project, both available publicly. To test our approach, we have implemented the proposed model in software. We have run simulations in medium and large scales and both the model and estimation procedure, based on artificial and real datasets, have been proved satisfactory and superior to the frequency based maximum likelihood method. In a real application, we have unfolded a stationary distribution on the map graph of Porto, based on the dataset. The approach described here combines techniques which, when used together to analyze traffic on large road networks, has not previously been reported.

Suggested Citation

  • Renátó Besenczi & Norbert Bátfai & Péter Jeszenszky & Roland Major & Fanny Monori & Márton Ispány, 2021. "Large-scale simulation of traffic flow using Markov model," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-31, February.
  • Handle: RePEc:plo:pone00:0246062
    DOI: 10.1371/journal.pone.0246062
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    References listed on IDEAS

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    1. Yang Chen & Arturo Ardila-Gomez & Gladys Frame, 2016. "Achieving Energy Savings by Intelligent Transportation Systems Investments in the Context of Smart Cities," World Bank Publications - Reports 24740, The World Bank Group.
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    Cited by:

    1. Alyse K. Winchester & Ryan A. Peterson & Ellison Carter & Mary D. Sammel, 2021. "Impact of COVID-19 Social Distancing Policies on Traffic Congestion, Mobility, and NO 2 Pollution," Sustainability, MDPI, vol. 13(13), pages 1-17, June.
    2. Gunda Singer & Roman Overko & Serife Yilmaz & Emanuele Crisostomi & Robert Shorten, 2021. "Markovian city-scale modelling and mitigation of micro-particles from tires," PLOS ONE, Public Library of Science, vol. 16(12), pages 1-22, December.

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