Bayesian Estimation of Network-Wide Mean Failure Probability in 3G Cellular Networks

  • Angelo Coluccia
  • Fabio Ricciato
  • Peter Romirer-Maierhofer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6821)


Mobile users in cellular networks produce calls, initiate connections and send packets. Such events have a binary outcome — success or failure. The term “failure” is used here in a broad sense: it can take different meanings depending on the type of event, from packet loss or late delivery to call rejection. The Mean Failure Probability (MFP) provides a simple summary indicator of network-wide performance — i.e., a Key Performance Indicator (KPI) — that is an important input for the network operation process. However, the robust estimation of the MFP is not trivial. The most common approach is to take the ratio of the total number of failures to the total number of requests. Such simplistic approach suffers from the presence of heavy-users, and therefore does not work well when the distribution of traffic (i.e., requests) across users is heavy-tailed — a typical case in real networks. This motivates the exploration of more robust methods for MFP estimation. In a previous work [1] we derived a simple but robust sub-optimal estimator, called EPWR, based on the weighted average of individual (per-user) failure probabilities. In this follow-up work we tackle the problem from a different angle and formalize the problem following a Bayesian approach, deriving two variants of non-parametric optimal estimators. We apply these estimators to a real dataset collected from a real 3G network. Our results confirm the goodness of the proposed estimators and show that EPWR, despite its simplicity, yields near-optimum performance.


  1. 1.
    Coluccia, A., Ricciato, F., Romirer, P.: On Robust Estimation of Network-wide Packet Loss in 3G Cellular Networks. In: 5th IEEE Broadband Wireless Access Workshop (BWA 2009), Honolulu (November 2009)Google Scholar
  2. 2.
    Kaaranen, H., et al.: UMTS Networks — Architecture, Mobility and Services, 2nd edn. Wiley (2005)Google Scholar
  3. 3.
    Romirer-Maierhofer, P., Ricciato, F., D’Alconzo, A., Franzan, R., Karner, W.: Network-Wide Measurements of TCP RTT in 3G. In: Papadopouli, M., Owezarski, P., Pras, A. (eds.) TMA 2009. LNCS, vol. 5537, pp. 17–25. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  4. 4.
    D’Alconzo, A., Coluccia, A., Ricciato, F., Romirer, P.: A Distribution-Based Approach to Anomaly Detection for 3G Mobile Network. In: IEEE GLOBECOM 2009 (2009)Google Scholar
  5. 5.
    Lehmann, E.L., Casella, G.: Theory of Point Estimation. Springer, Heidelberg (1998)zbMATHGoogle Scholar
  6. 6.
    Wolter, K.M.: Introduction to Variance Estimation. Springer Series in Statistics (2007)Google Scholar
  7. 7.
    Metawin and Darwin projects,
  8. 8.
    Minka, T.P.: Estimating a Dirichlet distribution, Microsoft Technical Report (2003)Google Scholar
  9. 9.
    Robbins, H.: An Empirical Bayes Approach to Statistics. In: Proc. Third Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 157–163. Univ. of California Press (1956)Google Scholar
  10. 10.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, New York (1972)zbMATHGoogle Scholar
  11. 11.
    Yeredor, A.: The Joint MAP-ML Criterion and its Relation to ML and to Extended Least-Squares. IEEE Trans. on Signal Processing 48(12) (December 2000)Google Scholar
  12. 12.
    George, E.I., Makov, U.E., Smith, A.F.M.: Conjugate Likelihood Distributions. Scandinavian Journal of Statistics 20(2), 147–156 (1993)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Kevin, B., Reeds, J.: Compound Multinomial Likelihood functions are unimodal: proof of a conjecture of I. J. Good. The Annals of Statistics 5(1), 79–87 (1977)CrossRefMathSciNetGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2011

Authors and Affiliations

  • Angelo Coluccia
    • 1
  • Fabio Ricciato
    • 1
    • 2
  • Peter Romirer-Maierhofer
    • 2
  1. 1.University of SalentoLecceItaly
  2. 2.FTW Forschungszentrum Telekommunikation WienViennaAustria

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