Erlang Distribution and Exponential Distribution Models in Wireless Networks

  • Lela Mirtskhulava
  • Giorgi Gugunashvili
  • Mzia Kiknadze
Conference paper

Abstract

Two mathematical models of wireless networks are analyzed in the given chapter. We demonstrate that the Erlang family provides more flexibility in modeling that exponential family, which only has one parameter. For this purposes one model has special Erlang distribution and second one is using exponential distribution. In practical situations, the Erlang family provides more flexibility in fitting a distribution to real data that the exponential family provides. The Erlang distribution is also useful in queueing analysis because of its relationship to the exponential distribution. To demonstrate the applicability of the Erlang distribution, we consider two queueing models, represented radio channels where the interarrival times between failure have the Erlang Distribution for FIRS model and Exponential distribution for second model.

Keywords

Erlang distribution Interarrival time between failures Probabilistic approach Queueing model 

References

  1. 1.
    L. Mirtskhulava, Mathematical model of prediction of reliability of wireless communication networks, in UKSim-AMSS 15th International Conference on Computer Modeling and Simulation, Cambridge, UK, 10–12 April 2013. IEEE Trans. 677–681 (2013)Google Scholar
  2. 2.
    W. Jeon, D. Jeong, Call admission control for CDMA mobile communications systems supporting multimedia services. IEEE Trans. Wireless Commun. 1(4), 649–659 (2002)CrossRefGoogle Scholar
  3. 3.
    J.I. Sanchez, F. Bercelo, J. Jordon, Inter-arrival time distribution for channel arrivals in cellular telephony, in Proceedings of the 5th International Workshop on Mobile Multimedia Comm. MoMuc’98, 12–13 October 1998, Berlin, GermanyGoogle Scholar
  4. 4.
    F. Khan, LTE for 4G Mobile Broadband: Air Interface Technologies and Performance (Cambridge University Press, New York, 2009)CrossRefGoogle Scholar
  5. 5.
    S. Parkvall, E. Dahlman, J. Sköld, P. Beming, 3G Evolution: HSPA and LTE for Mobile Broadband (Elsevier Publishers, 2nd edn., 2008Google Scholar
  6. 6.
    J.C. Ikuno, M. Wrulich, M. Rupp, TCP performance and modeling of LTE H-ARQ, in Proceedings of the International ITG Workshop on Smart Antennas (WSA 2009), Berlin, Germany (2009)Google Scholar
  7. 7.
    B. Lin, S. Mohan, A. Noerpel, Queueing priority channel assignment strategies for handoff and initial access for a PCS network. IEEE Trans. Veh. Technol. 43(3), 704–712 (1994)CrossRefGoogle Scholar
  8. 8.
    Y. Fang, I. Chlamtac, Teletraffic analysis and mobility modeling for PCS networks. IEEE Trans. Commun. 47(7), 1062–1072 (1999)CrossRefGoogle Scholar
  9. 9.
    R.E. Haskell, C.T. Case, Transient signal propagation in lossless isotropic plasmas (Report style). USAF Cambridge Research Laboratory, Cambridge, MA Report ARCRL-66-234 (II), vol. 2 (1994)Google Scholar
  10. 10.
    G. Boggia, P. Camarda, N. Di Fonzo, Teletraffic analysis of hierarchical cellular communication networks. IEEE Trans. Veh. Technol. 52(4), 931–946 (2003)CrossRefGoogle Scholar
  11. 11.
    S. Bhattacharya, H.M. Gupta, S. Kar, Traffic model and performance analysis of cellular mobile systems for general distributed handoff traffic and dynamic channel allocation. IEEE Trans. Veh. Technol. 57(6), 3629–3640 (2008)CrossRefGoogle Scholar
  12. 12.
    Y. Iraqi, R. Boutaba, Handoff and call dropping probabilities in wireless cellular networks, in Proceedings of International Conference on Wireless Networks, Communications and Mobile Computing (WIRELESSCOM ’05), Maui, Hawaii, USA, June 2005, pp. 209–213Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Lela Mirtskhulava
    • 1
  • Giorgi Gugunashvili
    • 1
  • Mzia Kiknadze
    • 2
  1. 1.Department of Computer SciencesIvane Javakhishvili Tbilisi State UniversityTbilisiGeorgia
  2. 2.Department of Computer EngineeringGeorgian Technical UniversityTbilisiGeorgia

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