Wireless Networks

, Volume 20, Issue 5, pp 805–816 | Cite as

Loss-based proportional fairness in multihop wireless networks

  • Pablo Jesus Argibay-Losada
  • Kseniia Nozhnina
  • Andrés Suárez-González
  • Cándido López-García
  • Manuel Fernández-Veiga
Article

Abstract

Proportional fairness is a widely accepted form of allocating transmission resources in communication systems. For wired networks, the combination of a simple probabilistic packet marking strategy together with a scheduling algorithm aware of two packet classes can meet a given proportional vector of n loss probabilities, to an arbitrary degree of approximation, as long as the packet loss gap between the two basic classes is sufficiently large. In contrast, for wireless networks, proportional fairness is a challenging problem because of random channel variations and contention for transmitting. In this paper, we show that under the physical model, i.e., when receivers regard collisions and interference as noise, the same packet marking strategy at the network layer can also yield proportional differentiation and nearly optimal throughput. Thus, random access or interference due to incoherent transmissions do not impair the feasibility of engineering a prescribed end-to-end loss-based proportional fairness vector. We consider explicitly multihop transmission and the cases of Markovian traffic with a two-priority scheduler, as well as orthogonal modulation with power splitting. In both cases, it is shown that sharp differentiation in loss probabilities at the link layer is achievable without the need to coordinate locally the transmission of frames or packets among neighboring nodes. Given this, a novel distributed procedure to adapt the marking probabilities so as to attain exact fairness is also developed. Numerical experiments are used to validate the design.

Keywords

Proportional fairness Quality of service Packet marking Loss proportional service Two class queues 

References

  1. 1.
    Argibay-Losada, P. J., Suárez-González, A., López-García, C., & Fernández-Veiga, M. (2010). A new design for end-to-end proportional loss differentiation in IP networks. Computer Networks, 54(9), 1389–1403.CrossRefMATHGoogle Scholar
  2. 2.
    Banchs, A., Serrano, P., & Vollero, L. (2007). Proportional fair throughput allocation for multirate 802.11e EDCA wireless LANs. Wireless Networks, 13(5), 649–662.Google Scholar
  3. 3.
    Biglieri, E., Proakis, J., Shamai(Shitz), S. (1998). Fading channels: Information-theoretic and communications aspects. IEEE Transactions on Information Theory, 44(6), 2619–2692.CrossRefMATHGoogle Scholar
  4. 4.
    Boche, H., & Schubert, M. (2009). Nash bargaininh and proportional fairness for wireless systems. IEEE/ACM Transactions on Networking, 17(5), 1453–1466.CrossRefGoogle Scholar
  5. 5.
    Cheng, H. T., & Zhang, W. (2008). An optimization framework for balancing throughput and fairness in wireless networks with QoS support. IEEE Transactions on Wireless Communications, 7(7), 584–593.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Cohen, J. E. (1979). Random evolutions and the spectral radius of a nonnegative matrix. Mathematical Proceedings of the Cambridge Philosophical Society., 86, 345–350.CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Dovrolis, C., Stiliadis, D., & Ramanathan, P. (2002). Proportional differentiated services: Delay differentiation and packet scheduling. IEEE/ACM Transactions on Networking, 10(1), 12–26.CrossRefGoogle Scholar
  8. 8.
    Elwalid, A. I., & Mitra, D. (1993). Effective bandwidth of general Markovian sources and admission control of high speed networks. IEEE/ACM Trans. Networking, 1(3), 329–343.CrossRefGoogle Scholar
  9. 9.
    El Gamal, A., & Kim, Y. H. (2011). Network information theory. Cambridge: Cambridge University Press.CrossRefMATHGoogle Scholar
  10. 10.
    Gantmacher, F. R. (1960). The theory of matrices, (2 edn.). New York: Chelsea.Google Scholar
  11. 11.
    Georgiadis, L., Neely, M. J., & Leandros, T. (2006). Resource allocation and cross layer control in wireless networks. Foundations and trends in networking, Vol. 1. Hanover: Now Publishers.Google Scholar
  12. 12.
    Gupta, P., & Kumar, P. R. (2000). The capacity of wireless networks. IEEE Transaction on Information Theory, 33(2), 388–404.CrossRefMathSciNetGoogle Scholar
  13. 13.
    Jiang, L., Leconte, M., Ni, J., Srikant, R., & Walrand, J. (2012). Fast mixing of parallel glauber dynamics and low-delay CSMA scheduling. IEEE Transaction on Information Theory, 58(10), 6541–6555.CrossRefMathSciNetGoogle Scholar
  14. 14.
    Kelly, F. P., Maulloo, A., & Tan, D. (1998). Rate control for communication networks: Shadow prices, proportional fairness and stability. Journal of the Operational Research, 49(3), 237–252.CrossRefMATHGoogle Scholar
  15. 15.
    Kunniyur, S., & Srikant, R. (2003). End-to-end congestion control: Utility functions, random losses and ECN marks. IIEEE/ACM Transactions on Networking, 11(5), 689–702.CrossRefGoogle Scholar
  16. 16.
    Liu, J., Stolyar, A. L., Chiang, M., & Poor, H. V. (2009). Queue back-pressure random access in multihop wireless networks: Optimality and stability. IEEE Transaction on Information Theory, 55(9), 4087–4099.CrossRefMathSciNetGoogle Scholar
  17. 17.
    Lu, S., Bharghavan, B., & Srikant, R. (1999). Fair scheduling in wireless packet networks. IEEE/ACM Transactions on Networking, 7(4), 473–489.CrossRefGoogle Scholar
  18. 18.
    Laurent, M. (2007). Structural properties of proportional fairness: Stability and insensitivity. The Annals of Applied Probability, 17(3), 809–839.CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Menache, I., & Shinkin, N. (2008). Capacity management and equilibrium for proportional QoS. IEEE/ACM Transactions on Networking, 16(5), 1025–1037.CrossRefGoogle Scholar
  20. 20.
    Mushkin, M., & Bar-David, I. (1989). Capacity and coding for the gilbert-elliott channels. IEEE Transaction on Information Theory, 35(6), 1277–1290.CrossRefMATHGoogle Scholar
  21. 21.
    Neely, M. J., Modiano, E., & Li, C. (2005). Fainess and optimal stochastic control for heterogeneous networks. In Proceedings on IEEE INFOCOM, Vol. 3, pp. 1723–1734.Google Scholar
  22. 22.
    Padhye, J., Firoiu, J., Towsley, D. F., & Kurose, J. F. (2000). Modeling TCP Reno performance: A simple model and its empirical validation. IEEE/ACM Transactions on Networking, 8(2), 133–145.CrossRefGoogle Scholar
  23. 23.
    Stiliadis, D., & Varma, A. (1998). Rate-proportional servers: A design methodology for fair queueing algorithms. IEEE/ACM Transactions on Networking, 6(2), 164–174.CrossRefGoogle Scholar
  24. 24.
    Subramanian, V., Duffy, K., & Leith, D. (2009). Existencee and uniqueness of fair rate allocations in lossy wireless networks. IEEE Transactions on Wireless Communications, 8(7), 3401–3406.CrossRefGoogle Scholar
  25. 25.
    Tse, D., & Viswanath, P. (2005). Fundamentals of wireless communications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  26. 26.
    Tulino, A. M., Caire, G., Shamai, S., & Verdú, S. (2010). Capacity of channels with frequency-selective and time-selective fading. IEEE Transaction on Information Theory, 56(3), 1187–1215.CrossRefGoogle Scholar
  27. 27.
    Verdú, S., & Han, T. S. (1994). A general formula for channel capacity. IEEE Transaction on Information Theory, 40(4), 1147–1157.CrossRefMATHGoogle Scholar
  28. 28.
    Wang, P., Jiang, H., Zhang, W., & Poor, H. V. (2009). Redefinition of max-min fairness in mutlihop wireless networks. IEEE Transactions on Wireless Communications, 7(12), 4786–4791.CrossRefGoogle Scholar
  29. 29.
    Zhang, Y. J., & Chan Liew, S. (2008). Proportional fairness in multi-channel multi-rate wireless networks–Part ii: the case of time-varying channels with application to OFDM systems. IEEE Transactions on Wireless Communications, 7(9), 3457–3467.CrossRefGoogle Scholar
  30. 30.
    Zwillinger, D. (1997). Handbook of differential equations, chapter Lyapunov functions, (3 edn.). Boston, MA: Academic Press.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Pablo Jesus Argibay-Losada
    • 1
    • 2
  • Kseniia Nozhnina
    • 3
  • Andrés Suárez-González
    • 1
  • Cándido López-García
    • 1
  • Manuel Fernández-Veiga
    • 1
  1. 1.Department of Telematics EngineeringUniversity of VigoVigoSpain
  2. 2.LANDERState University of New York at BuffaloBuffaloUSA
  3. 3.State University of Information and Communication TechnologiesKievUkraine

Personalised recommendations