Wireless Personal Communications

, Volume 101, Issue 1, pp 491–509 | Cite as

A Simple and Enriched Closed-Form Formula for Cell Residence Time in 5G Heterogeneous Networks

  • Byungjin Jeong
  • Namgi Kim
  • Byoung-Dai Lee
  • Hyunsoo Yoon


Cell residence time is a key system parameter for the performance analysis of cellular mobile systems and their related applications. In order to save cost and time before wide implementation and deployment of a mobile system, various network performance metrics, such as network resource occupancy probabilities, should be calculated through analytical results of the mean cell residence time. However, this is difficult to estimate in 5G heterogeneous networks, due to irregular-shaped multi-tier heterogeneous network topologies introduced by a diverse set of small cells. In order to find an efficient way of calculating the cell residence time for 5G heterogeneous networks, we first examine the well-known conventional formula. Then we propose an enhanced closed-form formula for cell residence time by considering more generalized cellular mobile systems, as well as more generic mobility models. The proposed closed-form formula can be directly applied to various complex and reliable network scenarios. It can be adapted to multi-tier heterogeneous networks with randomly positioned irregular-shaped small cells, even though they overlap with each other. Our simulation results show that the proposed formula provides excellent estimation accuracy for general random mobility models, including the Levy walk, which is known to realistically reflect human mobility.


Modeling and analysis Multi-tier heterogeneous networks Cell residence time Handover rate User mobility General random walk 



This work was partly supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03932696 and NRF-2017R1D1A1B04027874) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2017R1A2B4006026).


  1. 1.
    Chen, Z., Li, T., Fan, P., Quek, T. Q., & Letaief, K. B. (2016). Cooperation in 5G heterogeneous networking: Relay scheme combination and resource allocation. IEEE Transactions on Communications, 64(8), 3430–3443.CrossRefGoogle Scholar
  2. 2.
    Chin, W. H., Fan, Z., & Haines, R. (2014). Emerging technologies and research challenges for 5G wireless networks. IEEE Wireless Communications, 21(2), 106–112.CrossRefGoogle Scholar
  3. 3.
    Ku, B. H., Ren, Y., Weng, J. F., Chen, J. C., & Chen, W. T. (2017). Modeling and analysis of channel holding time and handoff rate for packet sessions in all-IP cellular networks. IEEE Transactions on Vehicular Technology, 66(4), 3331–3344.CrossRefGoogle Scholar
  4. 4.
    Corral-Ruiz, A. L. E., Cruz-Perez, F. A., Hernandez-Valdez, G., & Eksim, A. (2012). Cell dwell time and channel holding time relationship in mobile cellular networks. In A. Eksim (Ed.), Wireless communications and networks—Recent advances, InTech. Rijeka. Available from:
  5. 5.
    Hermann, S. D., Wolisz, A., & Sortais, M. (2006). Expected number of area exits, entrances and crossovers for the investigation of area based push service utilization. In Proceedings of the IEEE ICN/ICONS/MCL 2006 (pp. 136–142).Google Scholar
  6. 6.
    Tang, S. (2012). Performance modeling of an integrated wireless network using WiMAX as Backhaul support for WiFi traffic. International Journal of Wireless Information Networks, 19(1), 73–83.CrossRefGoogle Scholar
  7. 7.
    El-Atty, S. M. A., & Gharsseldien, Z. M. (2017). Performance analysis of an advanced heterogeneous mobile network architecture with multiple small cell layers. Wireless Networks, 23(4), 1169–1190.CrossRefGoogle Scholar
  8. 8.
    Navaratnarajah, S., Dianati, M., & Imran, M. A. (2015). Performance analysis of Cellular-WLAN heterogeneous network based on continuous time markov chain. In Proceedings of the IEEE CAMAD 2015 (pp. 221–225).Google Scholar
  9. 9.
    Xie, H., & Goodman, D. J. (1993). Mobility models and biased sampling problem. In Proceedings of the IEEE ICUPC93 (Vol. 2, pp. 803–807).Google Scholar
  10. 10.
    Yeung, K. L., & Nanda, S. (1996). Channel management in microcell/macrocell cellular radio systems. IEEE Transactions on Vehicular Technology, 45(4), 601–612.CrossRefGoogle Scholar
  11. 11.
    Zonoozi, M. M., & Dassanayake, P. (1997). User mobility modeling and characterization of mobility patterns. IEEE Journal on Selected Areas in Communications, 15(7), 1239–1252.CrossRefGoogle Scholar
  12. 12.
    Hyytia, E., & Virtamo, J. (2007). Random waypoint mobility model in cellular networks. Wireless Networks, 13(2), 177–188.CrossRefGoogle Scholar
  13. 13.
    Zola, E., & Barcelo-Arroyo, F. (2009). Impact of mobility models on the cell residence time in WLAN networks. In Proceedings of the IEEE SARNOFF09 (pp. 1–5).Google Scholar
  14. 14.
    Lin, X., Ganti, R. K., Fleming, P. J., & Andrews, J. G. (2013). Towards understanding the fundamentals of mobility in cellular networks. IEEE Transactions on Wireless Communications, 12(4), 1686–1698.CrossRefGoogle Scholar
  15. 15.
    Shin, S., Lee, U., Dressler, F., & Yoon, H. (2016). Analysis of cell sojourn time in heterogeneous networks with small cells. IEEE Communications Letters, 20(4), 788–791.CrossRefGoogle Scholar
  16. 16.
    Fang, Y. (2005). Modeling and performance analysis for wireless mobile networks: A new analytical approach. IEEE/ACM Transactions on Networking, 13(5), 989–1002.CrossRefGoogle Scholar
  17. 17.
    Ghaderi, M., & Boutaba, R. (2006). Call admission control in mobile cellular networks: A comprehensive survey. Wireless Communications and Mobile Computing, 6(1), 69–93.CrossRefGoogle Scholar
  18. 18.
    Xiao, L., Fuja, T. E., & Costello, D. J. (2010). Mobile relaying: Coverage extension and throughput enhancement. IEEE Transactions on Communications, 58(9), 2709–2717.CrossRefGoogle Scholar
  19. 19.
    Casares-Giner, V., Pla, V., & Escalle-Garca, P. (2011). Mobility models for mobility management. In Proceedings of the Springer Network performance engineering (pp. 716–745). Berlin: Springer.Google Scholar
  20. 20.
    Ge, X., Ye, J., Yang, Y., & Li, Q. (2016). User mobility evaluation for 5G small cell networks based on individual mobility model. IEEE Journal on Selected Areas in Communications, 34(3), 528–541.CrossRefGoogle Scholar
  21. 21.
    Rhee, I., Shin, M., Hong, S., Lee, K., Kim, S. J., & Chong, S. (2011). On the levy-walk nature of human mobility. IEEE/ACM Transactions on Networking (TON), 19(3), 630–643.CrossRefGoogle Scholar
  22. 22.
    Lee, K., Hong, S., Kim, S. J., Rhee, I., & Chong, S. (2012). SLAW: Self-similar least-action human walk. IEEE/ACM Transactions on Networking (TON), 20(2), 515–529.CrossRefGoogle Scholar
  23. 23.
    Fu, H. L., Lin, P., & Lin, Y. B. (2013). Reducing signaling overhead for femtocell/macrocell networks. IEEE Transactions on Mobile Computing, 12(8), 1587–1597.CrossRefGoogle Scholar
  24. 24.
    Yu, Y., & Gu, D. (2013). The cost efficient location management in the LTE picocell/macrocell network. IEEE Communications Letters, 17(5), 904–907.CrossRefGoogle Scholar
  25. 25.
    Maksymyuk, T., Brych, M., & Pelishok, V. (2015). Stochastic geometry models for 5G heterogeneous mobile networks. Smart CR, 5(2), 89–101.CrossRefGoogle Scholar
  26. 26.
    Cox, D. R. (1969). Some sampling problems in technology. In N. L. Johnson & H. Smith Jr. (Eds.), New developments in survey sampling (pp. 506–527). New York: Wiley.Google Scholar
  27. 27.
    Papoulis, A., & Pillai, S. U. (2002). One function of two random variables. In Probability, random variables, and stochastic processes (Ch. 6–2, pp. 180–197), McGraw-Hill Education.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Byungjin Jeong
    • 1
  • Namgi Kim
    • 2
  • Byoung-Dai Lee
    • 2
  • Hyunsoo Yoon
    • 1
  1. 1.School of ComputingKorea Advanced Institute of Science and TechnologyDaejeonRepublic of Korea
  2. 2.Department of Computer ScienceKyonggi UniverisitySuwonRepublic of Korea

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