, Volume 56, Issue 2, pp 477–496 | Cite as

A matrix analytic approach to study the queuing characteristics of nodes in a wireless network

  • Sweta Dey
  • T. G. DeepakEmail author
Theoretical Article


In this paper, we propose a model to study the queueing characteristics of nodes in a wireless network in which the channel access is governed by the well known binary exponential back off rule. By offering the general phase type (PH) distributional assumptions to channel idle and busy periods and assuming Poisson packet arrival processes at nodes, we represent the model as a quasi birth death process and analyse it by using matrix analytic methods. Stability of the system is examined. Several important queueing characteristics that help in efficient design of such systems are derived. Extensive simulation analysis is performed to establish the validity of our theoretical results.. It is shown that both the simulated and theoretical results agree on some important performance measures. Some real life data has been used to get approximate PH representations for channel idle and busy period variates, which in turn are used for numerical illustrations.


Queueing model Binary exponential back off rule Phase type distribution Matrix analytic methods 

Mathematics Subject Classification

60J27 60K25 



We acknowledge the great help received from Prof. B.S. Manoj, Department of Avionics, IIST for availing us the data from IIST campus network as well as on its usage.


  1. 1.
    Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: IEEE Standards 802.11-1997. The Institute of Electrical and Electronics Engineers, New York (1997)Google Scholar
  2. 2.
    Tobagi, F., Kleinrock, L.: Packet switching in radio channels: part 2. The hidden terminal problem in carrier sense multiple-access and the busy - tone solution. IEEE Trans. Commun. 23, 1417–1433 (1975)CrossRefGoogle Scholar
  3. 3.
    Boroumand, L., Khokhar, R.H., Bakhtiar, L.A., Pourvahab, M.: A review of techniques to resolve the hidden node problem in wireless networks. Smart Comput. Rev. 2, 95–110 (2012)Google Scholar
  4. 4.
    Bisnik, N., Abouzeid, A.: Queueing network models for delay analysis of multihop wireless adhoc networks. Ad Hoc Netw. 7(1), 79–97 (2009)CrossRefGoogle Scholar
  5. 5.
    Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1981). (Reprinted by Dover Publications, 1994)Google Scholar
  6. 6.
    Neuts, M.F.: Probability distribitions of Phase type. In: Liber Amicorum Prof. Emeritus H. Florin, pp. 173–206; Department of Mathematics. University of Louvain, Belgium (1975)Google Scholar
  7. 7.
    Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modelling. The Society for Industrial and Applied Mathematics, Philadelphia, Pensylvania (1999)CrossRefGoogle Scholar
  8. 8.
    Kobayashi, H.: Application of the dissusion approximation to queuing networks: equilibrium queue distributions. J. ACM 21(2), 316–328 (1974)CrossRefGoogle Scholar
  9. 9.
    Bianchi, G.: Performance analysis of the IEEE 802.11 distributed coordination function. IEEE J. Sel. Commun. 18(3), 535–547 (2000)CrossRefGoogle Scholar
  10. 10.
    Asmussen, S., Nerman, O., Olsson, M.: Fitting phase-type distributions via the EM algorithm. Scand. J. Stat. 23, 419–441 (1996)Google Scholar
  11. 11.
    Deepak, T.G.: A queueing network model for delay and throughput analysis in multi-hop wireless Ad Hoc networks. Reliab. Theory Appl. 12(2), 68–81 (2017)Google Scholar
  12. 12.
    Zhou, J., Mitchell, K.: A scalable delay based analytical framework for CSMA/CA wireless mesh networks. Comput. Netw. 54(2), 304–318 (2010)CrossRefGoogle Scholar
  13. 13.
    Yunbo Wang, M.C., Vuran, S.: Goddard: cross-layer analysis of the end-to-end delay distribution in wireless sensor networks. IEEE ACM Trans. Netw. 20(1), 305–318 (2012)CrossRefGoogle Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Space Science and TechnologyThiruvananthapuramIndia

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