Time-Dependent SIR Analysis in Shopping Malls Using Fractal-Based Mobility Models

  • Yuri Orlov
  • Elisabeth Kirina-Lilinskaya
  • Andrey Samuylov
  • Aleksandr Ometov
  • Dmitri MoltchanovEmail author
  • Yulia Gaimamaka
  • Sergey Andreev
  • Konstantin Samouylov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10372)


Shopping malls are characterized by a high density of users. The use of direct device-to-device (D2D) communications may significantly mitigate the load imposed on the cellular systems in such environments. In addition to high user densities, the communicating entities are inherently mobile with very specific attractor-based mobility patterns. In this paper, we propose a model for characterizing time-dependent signal-to-interference ratio (SIR) in shopping malls. Particularly, we use fractional Fokker-Plank equation for modeling the non-linear functional of the average SIR value, defined on a stochastic fractal trajectory. The evolution equation of the average SIR is derived in terms of fractal motion of the tagged receiver and the interfering devices. We illustrate the use of our model by showing that the behavior of SIR is generally varying for different types of fractals.


Mobility Fractal stochastic motion Time-dependent metrics Average SIR evolution Device-to-device communications 



The publication was financially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number 02.a03.21.0008) and RFBR (research projects No. 16-07-00766, 17-07-00845).


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Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  • Yuri Orlov
    • 1
  • Elisabeth Kirina-Lilinskaya
    • 1
  • Andrey Samuylov
    • 2
    • 3
  • Aleksandr Ometov
    • 2
    • 3
  • Dmitri Moltchanov
    • 2
    • 3
    Email author
  • Yulia Gaimamaka
    • 3
    • 4
  • Sergey Andreev
    • 2
  • Konstantin Samouylov
    • 3
    • 4
  1. 1.Department of Kinetic EquationsKeldysh Institute of Applied MathematicsMoscowRussia
  2. 2.Department of Communications EngineeringTampere University of TechnologyTampereFinland
  3. 3.Department of Applied Probability and InformaticsRUDN UniversityMoscowRussia
  4. 4.Institute of Informatics ProblemsFRC CSC RASMoscowRussia

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