A matrix analytic approach to study the queuing characteristics of nodes in a wireless network
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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.
KeywordsQueueing model Binary exponential back off rule Phase type distribution Matrix analytic methods
Mathematics Subject Classification60J27 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.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
- 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
- 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.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
- 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.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