Skip to main content
SpringerLink
Log in

Mathematical Models of Moving Particles and Their Application for Traffic

  • Conference paper
  • First Online:
Book cover Proceedings of the Eighth International Conference on Management Science and Engineering Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 280))

  • 1986 Accesses

Abstract

The mathematical models of moving particles, describing behavior of traffic systems are constructed. It is shown that Belyaev’s effect about random binomial walk separately considered particle is true for more general cases. Using this fact a reason of appearance a traffic jam is shown. The class of probability distributions between moving particles is found. It is shown that any discrete probability distribution can be approximated by distribution between moving particles. Numerical examples and graphs, demonstrating these theoretical results are given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Belyaev Y, Buslayev A et al (2002) Markov approximation of stochastic model motion by two lines. Proc Inst Traffic Road 32

    Google Scholar 

  2. Belyaev YK (1969) On simplified model of motion without overtaking. Sov J Comput Syst Sci 3:17–21

    Google Scholar 

  3. Gazis D, Eday L (1968) Mathematical models of transport flows. IEEE 4:94–109

    Google Scholar 

  4. Hajiyev A (1990) On a random walk on a circle. Math Notes 47(6):140–144

    Google Scholar 

  5. Hajiyev A, Mammadov T (2011) Mathematical models of moving particles and their applications. Theory Probab Appl 56(4):676–689

    Google Scholar 

  6. Shiryaev A (1995) Probability. Springer

    Google Scholar 

  7. Zahle U (1972) Generalization of model of motion without overtaking. J Comput Syst Sci 5:100–103

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Baku State University, AZ1141, Baku, Azerbaijan

    Narmina Abdullayeva & Mirvari Hasratova

  2. Institute of Cybernetics, Azerbaijan National Academy of Sciences, AZ1141, Baku, Azerbaijan

    Asaf Hajiyev

Authors
  1. Narmina Abdullayeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asaf Hajiyev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mirvari Hasratova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Asaf Hajiyev .

Editor information

Editors and Affiliations

  1. Business School, Sichuan University, Chengdu, China

    Jiuping Xu

  2. Depart de Enge Mecânica e Industrial, Faculdade de Ciências e Tecnologia - Universidade Nova de Lisboa (FCT/UNL), Caparica, Portugal

    Virgílio António Cruz-Machado

  3. LeBow College of Business Department of Decision Sciences, Drexel University, Philadelphia, Pennsylvania, USA

    Benjamin Lev

  4. Institute of Operations Research, Karlsruhe Institute ofTechnology (KIT), Karlsruhe, Germany

    Stefan Nickel

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Abdullayeva, N., Hajiyev, A., Hasratova, M. (2014). Mathematical Models of Moving Particles and Their Application for Traffic. In: Xu, J., Cruz-Machado, V., Lev, B., Nickel, S. (eds) Proceedings of the Eighth International Conference on Management Science and Engineering Management. Advances in Intelligent Systems and Computing, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55182-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-55182-6_18

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55181-9

  • Online ISBN: 978-3-642-55182-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation