Telecommunication Systems

, Volume 52, Issue 2, pp 587–600 | Cite as

Logarithmic laws in service quality perception: where microeconomics meets psychophysics and quality of experience

  • Peter ReichlEmail author
  • Bruno Tuffin
  • Raimund Schatz


Utility functions, describing the value of a good or a resource from an end user’s point of view, are widely used as an important ingredient for all sorts of microeconomic models. In the context of resource allocation in communication networks, a logarithmic version of utility usually serves as the standard example due to its simplicity and mathematical tractability. In this paper we argue that indeed there are much more (and better) reasons to consider logarithmic utilities as really paradigmatic, at least when it comes to characterizing user experience with specific telecommunication services. We justify this claim with the help of recent results from Quality of Experience (QoE) research, and demonstrate that, especially for Voice-over-IP and mobile broadband scenarios, there is increasing evidence that user experience and satisfaction follows logarithmic laws. Finally, we go even one step further and put these results into the broader context of the Weber-Fechner Law, a key principle in psychophysics describing the general relationship between the magnitude of a physical stimulus and its perceived intensity within the human sensory system.


Utility function Quality-of-experience Proportional fairness Voice over IP Mobile broadband Weber-Fechner law 


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  1. 1.
    ITU–T Rec. E.800 (2008). Terms and definitions related to quality of service. Google Scholar
  2. 2.
    ITU-T Rec. G.100/P.10 (2008). Vocabulary for performance and quality of service, amendment 2: new definitions for inclusion in Recommendation P.10/G.100. Google Scholar
  3. 3.
    ITU-T Rec. G.107 (2000). The E-model, a computational model for use in transmission planning. Google Scholar
  4. 4.
    ITU-T Rec. P.800 (1996). Methods for subjective determination of transmission quality. Google Scholar
  5. 5.
    ITU-T Rec. P.862 (2001). Perceptual evaluation of speech quality (PESQ), an objective method for end-to-end speech quality assessment of narrow-band telephone networks and speech codecs. Google Scholar
  6. 6.
    GNU: Speex (2004).
  7. 7.
    Fiedler, M., Chevul, S., Radtke, O., Tutschku, K., & Binzenhöfer, A. (2005). The network utility function: a practicable concept for assessing network impact on distributed services. In Proc. ITC-19, Beijing, China, Sept. 2005 (pp. 1465–1474). Google Scholar
  8. 8.
    Fiedler, M., & Hossfeld, T. (2010). Quality of experience-related differential equations and provisioning-delivery hysteresis. In Proc. 21st ITC specialist seminar, Miyazaki, Japan, March 2010. Google Scholar
  9. 9.
    Fiedler, M., Kilkki, K., & Reichl, P. From quality of service to quality of experience. Executive Summary, Seminar 09192, Dagstuhl Seminar Proceedings, available at URL:
  10. 10.
    Fiedler, M., Hossfeld, T., & Tran-Gia, P. (2010). A generic quantitative relationship between quality of experience and quality of service. IEEE Network, special issue “Improving QoE for Network Services”, pp. 36–41. Google Scholar
  11. 11.
    Hayel, Y., Maillé, P., & Tuffin, B. (2005). Modelling and analysis of Internet pricing: introduction and challenges. In Proc. international symposium on applied stochastic models and data analysis (ASMDA), Brest, France, May 2005. Google Scholar
  12. 12.
    Hayel, Y., Rubino, G., Tuffin, B., & Varela, M. (2006). A new way of thinking utility in pricing mechanisms: a neural network approach. In Proc. CLAIO’06, Montevideo, Uruguay. Google Scholar
  13. 13.
    Hossfeld, T., Tran-Gia, P., & Fiedler, M. (2007). Quantification of quality of experience for edge-based applications. In Proc. 20th international teletraffic congress (ITC20), Ottawa, Canada, June 2007. Google Scholar
  14. 14.
    Hossfeld, T., Hock, D., Tran-Gia, P., Tutschku, K., & Fiedler, M. (2008). Testing the IQX hypothesis for exponential interdependency between QoS and QoE of voice codecs iLBC and G.711. In Proc. 18th ITC specialist seminar on quality of experience, Karlskrona, Sweden, May 2008. Google Scholar
  15. 15.
    Ibarrola, E., Liberal, F., Taboada, I., & Ortega, R. (2009). Web QoE evaluation in multi-agent networks: validation of ITU-T G.1030. In Proc. ICAS’09, Valencia, Spain, April 2009. Google Scholar
  16. 16.
    Kelly, F. P. (2003). Fairness and stability of end-to-end congestion control. European Journal of Control, 9, 159–176. CrossRefGoogle Scholar
  17. 17.
    Kilkki, K. (2008). Quality of experience in communications ecosystems. Journal of Universal Computer Science, Special issue on socio-economic aspects of next generation Internet, Spring. Google Scholar
  18. 18.
    Longo, M. R., & Lourenco, S. F. (2007). Spatial attention and the mental number line: evidence for characteristic biases and compression. Neuropsychologia, 45, 1400–1406. CrossRefGoogle Scholar
  19. 19.
    Lopez, D., Gonzalez, F., Bellido, L., & Alonso, A. (2006). Adaptive multimedia streaming over IP based on customer oriented metrics. In Intern. symposium on computer networks, Istanbul, June 2006. Google Scholar
  20. 20.
    Odlyzko, A. (1999) Paris metro pricing for the Internet. In Proc. of the ACM conference on electronic commerce (EC’99), London, UK (pp. 140–147). CrossRefGoogle Scholar
  21. 21.
    Keeney, R., & Raiffa, H. (1976). Decisions with multiple objectives: preferences and value tradeoffs. New York: Wiley. Google Scholar
  22. 22.
    Reichl, P., Thissen, D., & Linnhoff-Popien, C. (1996). How to enhance service selection in distributed systems. In Proc. DCCN’96, Tel Aviv, Israel, Nov. 1996. Google Scholar
  23. 23.
    Reichl, P. (2010). From charging for quality-of-service to charging for quality-of-experience. Annals of Telecommunications, 65(3), 189–199. Special issue on “Quality of Experience and Socio-Economic Issues of Network-Based Services”. CrossRefGoogle Scholar
  24. 24.
    Reichl, P., Egger, S., Schatz, R., & D’Alconzo, A. (2010). The logarithmic nature of QoE and the role of the Weber-Fechner law in QoE assessment. In Proc. IEEE ICC’10, Cape Town, South Africa, May 2010. Google Scholar
  25. 25.
    Reichl, P., Fabini, J., Kurtansky, P., & Stiller, B. (2006). A stimulus-response mechanism for charging enhanced quality-of-user experience in next generation all-IP networks. In Proc. CLAIO’06, Montevideo, Uruguay, Nov. 2006. Google Scholar
  26. 26.
    Ricciato, F. (2006). Traffic monitoring and analysis for the optimization of a 3G network. IEEE Wireless Communications Magazine, 13(6). Google Scholar
  27. 27.
    Robinson, J. (1962). Economic philosophy. Chicago, Aldine. Google Scholar
  28. 28.
    Rubino, G., Tirilly, P., & Varela, M. (2006). Evaluating users’ satisfaction in packet networks using random neural networks. In ICANN (vol. 1, pp. 303–312). Google Scholar
  29. 29.
    Sun, L., & Ifeachor, E. C. (2002). Perceived speech quality prediction for voice over IP-based networks. In Proc. IEEE ICC’02, New York, USA, April/May 2002. Google Scholar
  30. 30.
    Soldani, D., Li, M., & Cuny, R. (2006). QoS and QoE management in UMTS cellular systems. New York: Wiley. CrossRefGoogle Scholar
  31. 31.
    Takahashi, T. (2006). Time-estimation error following Weber-Fechner law may explain subadditive time-discounting. Medical Hypotheses, 67(6), 1372–1374. CrossRefGoogle Scholar
  32. 32.
    Tuffin, B. (2003). Charging the Internet without bandwidth reservation: an overview and bibliography of mathematical approaches. Journal of Information Science and Engineering, 19(5), 765–786. Google Scholar
  33. 33.
    Varela, M. (2005). Évaluation pseudo–subjective de la qualité d’un flux multimédia. PhD Thesis, University of Rennes 1, France. Google Scholar
  34. 34.
    Varela, M., Marsh, I., & Grönvall, B. (2006). A systematic study of PESQ’s behavior (from a networking perspective). In Proc. MESAQIN’06, Prague, Czech Republic, June 2006. Google Scholar
  35. 35.
    Weber, E. H. (1834). De pulsu, resorptione, auditu et tactu. Annotationes anatomicae et physiologicae. Leipzig: Koehler. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Telecommunications Research Center Vienna (FTW)ViennaAustria
  2. 2.Université Européenne de BretagneRennesFrance
  3. 3.INRIA Rennes Bretagne-AtlantiqueRennes CedexFrance

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