A Simple Approximation for the Response Times in the Two-Class Weighted Fair Queueing System

  • Dhari Ali Mahmood
  • Gábor HorváthEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10378)


The weighted fair queueing (WFQ) service discipline provides a flexible way to share bandwidth among two or more traffic classes. Some variants of the basic WFQ principle are used in the practice in computer networks in routers, switches, etc. Unfortunately, the analytical modeling of the related queues turned out to be notoriously difficult. This paper presents approximation expressions for the mean response times in a two-class (ideal) WFQ system with Poisson arrival process and exponentially distributed service times. The approximation is based on simulation. The results are very simple, explicit, yet reasonably accurate, ideal to use in self organizing networks where the weights associated with the different traffic classes need to be recalculated to adapt to the changing network conditions.



Dhari Ali Mahmood would like to thank to the Tempus Public Foundation (TPF) – Stipendium Hungaricum program and University of Technology – Iraq for the support for his PhD scholarship.


  1. 1.
    Al-Sawaai, A., Awan, I., Fretwell, R.: Analysis of the weighted fair queuing system with two classes of customers with finite buffer. In: International Conference on Advanced Information Networking and Applications Workshops, WAINA 2009, pp. 218–223. IEEE (2009)Google Scholar
  2. 2.
    Bolch, G., Greiner, S., de Meer, H., Trivedi, K.S.: Queueing Networks and Markov Chains: Modeling and Performance Evaluation with Computer Science Applications. Wiley, Hoboken (2006)CrossRefGoogle Scholar
  3. 3.
    Fayolle, G., Iasnogorodski, R.: Two coupled processors: the reduction to a Riemann-Hilbert problem. Probab. Theory Relat. Fields 47(3), 325–351 (1979)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Golestani, S.J.: A self-clocked fair queueing scheme for broadband applications. In: 13th Proceedings IEEE Networking for Global Communications, INFOCOM 1994, pp. 636–646. IEEE (1994)Google Scholar
  5. 5.
    Guillemin, F., Pinchon, D.: Analysis of generalized processor-sharing systems with two classes of customers and exponential services. J. Appl. Probab. 41(03), 832–858 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Horváth, G., Telek, M.: An approximate analysis of two class WFQ systems. In: Workshop on Preformability Modeling of Computer and Communication Systems-PMCCS, pp. 43–46. Citeseer (2003)Google Scholar
  7. 7.
    Kraemer, W., Langenbach-Belz, M.: Approximate formulae for the delay in the queueing system GI/G/1. In: Proceedings of the 8th International Teletraffic Congress, pp. 235–1 (1976)Google Scholar
  8. 8.
    Resing, J.: A tandem queueing model with coupled processors. Oper. Res. Lett. 31(5), 383–389 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Shortle, J.F., Fischer, M.J.: Approximation for a two-class weighted fair queueing discipline. Perform. Eval. 67(10), 946–958 (2010)CrossRefGoogle Scholar
  10. 10.
    Shreedhar, M., Varghese, G.: Efficient fair queuing using deficit round-robin. IEEE/ACM Trans. Netw. 4(3), 375–385 (1996)CrossRefGoogle Scholar
  11. 11.
    Varga,A., Hornig, R.: An overview of the omnet++ simulation environment. In: Proceedings of the 1st international conference on Simulation tools and techniques for communications, networks and systems & workshops, p. 60, ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering) (2008)Google Scholar
  12. 12.
    Vitale, C., Rizzo, G., Rengarajan, B., Mancuso, V.: An analytical approach to performance analysis of coupled processor systems. In: 2015 27th International Teletraffic Congress (ITC 27), pp. 89–97. IEEE (2015)Google Scholar
  13. 13.
    Whitt, W.: The queueing network analyzer. Bell Labs Tech. J. 62(9), 2779–2815 (1983)CrossRefGoogle Scholar
  14. 14.
    Zhang, L.: Virtual clock: a new traffic control algorithm for packet switching networks. In: ACM SIGCOMM Computer Communication Review, vol. 20, pp. 19–29. ACM (1990)Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Networked Systems and ServicesBudapest University of Technology and EconomicsBudapestHungary
  2. 2.MTA-BME Information Systems Research GroupBudapestHungary
  3. 3.University of TechnologyBaghdadIraq

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