Time-Dependent SIR Analysis in Shopping Malls Using Fractal-Based Mobility Models
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.
KeywordsMobility 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).
- 1.Ericsson: Ericsson mobility report: on the pulse of the networked society, July 2015Google Scholar
- 2.Nordrum, A.: Popular internet of things forecast of 50 billion devices by 2020 is outdated. IEEE Spectrum 18 (2016)Google Scholar
- 3.Dohler, M., Nakamura, T., Osseiran, A., Monserrat, J.F., Marsch, P.: 5G Mobile and Wireless Communications Technology. Cambridge University Press, Cambridge (2016)Google Scholar
- 5.Orsino, A., Militano, L., Araniti, G., Iera, A.: Social-aware content delivery with D2D communications support for emergency scenarios in 5G systems. In: Proceedings of 22th European Wireless Conference European Wireless, VDE, pp. 1–6 (2016)Google Scholar
- 6.International Telecommunications Union (ITU): Framework and overall objectives of the future development of IMT for 2020 and beyond. Recommendation ITU-R M.2083-0, September 2015Google Scholar
- 7.International Telecommunications Union (ITU): Minimum requirements related to technical performance for IMT-2020 radio interface(s). DRAFT NEW REPORT ITU-R M.[IMT-2020.TECH PERF REQ], February 2017Google Scholar
- 9.Haneda, K., Tian, L., Asplund, H., Li, J., Wang, Y., Steer, D., Li, C., Balercia, T. Lee, S., Kim, Y., et al.: Indoor 5G 3GPP-like channel models for office and shopping mall environments. In: Proceedings of International Conference on Communications Workshops (ICC), pp. 694–699. IEEE (2016)Google Scholar
- 12.Samuylov, A., Moltchanov, D., Gaidamaka, Y., Begishev, V., Kovalchukov, R., Abaev, P., Shorgin, S.: SIR analysis in square-shaped indoor premises. In: Proceedings of 30th European Conference on Modelling and Simulation, ECMS, pp. 692–697 (2016)Google Scholar
- 17.Orlov, Y., Fedorov, S., Samuylov, A., Gaidamaka, Y., Molchanov, D.: Simulation of devices mobility to estimate wireless channel quality metrics in 5G network. In: Proceedings of the ICNAAM, pp. 19–25 (2016)Google Scholar
- 18.Samuylov, A., Ometov, A., Begishev, V., Kovalchukov, R., Moltchanov, D., Gaidamaka, Y., Samouylov, K., Andreev, S., Koucheryavy, Y.: Analytical performance estimation of network-assisted D2D communications in urban scenarios with rectangular cells. Transactions on Emerging Telecommunications Technologies (2015)Google Scholar
- 21.Zenyuk, D.A., Mitin, N.A., Orlov, Y.N.: Random walks modeling on Cantor set. In: Preprints of the Keldysh Institute of Applied Mathematics, pp. 31–18 (2013)Google Scholar
- 24.Galati, A., Greenhalgh, C.: Human mobility in shopping mall environments. In: Proceedings of the Second International Workshop on Mobile Opportunistic Networking, pp. 1–7. ACM (2010)Google Scholar