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An analytical framework for reliability evaluation of d-dimensional IEEE 802.11 broadcast wireless networks

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Abstract

In this paper, we validate that the deterministic distance-based analytical model can be used to estimate the reliability of one-dimensional (1-D) 802.11 broadcast wireless networks compared with the interference-based analytical model. Therefore, we propose a deterministic distance-based reliability analytical framework for such networks in d-dimensional (d-D, \(d \ge 1\)) scenarios. This framework takes into account the fading channel and hidden terminal problem and makes three commonly used reliability metrics able to be resolved, including point-to-point packet reception probability (NRP), packet delivery ratio (PDR), and packet reception ratio (PRR). There are two key factors involved in deducing the effect of hidden terminals. One is to measure the hidden terminal transmission probability during the vulnerable period, which can be calculated based on the approximate solution of the semi-Markov process model capturing the channel contention and the back-off behavior. Another is the challenge to determine the size of the area to which the hidden terminals belong. First, we give a general mathematical expression on the size of the hidden terminal coverage affecting NRP which is an important part of the closed-form solution of NRP/PRR. Second, we adopt the Monte-Carlo method to solve the size of general hidden terminal coverage affecting PDR, making it possible to approximate PDR, as well as control the efficiency and accuracy by constraining the relative error. Finally, we adopt a multi-parameter optimization scheme to find the optimum settings for the network to ensure the quality of service and maximize channel utilization. A series of experimental results show that the framework can be used to access the reliability of 802.11 based d-D broadcast wireless network and pave the way for further optimization.

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Acknowledgements

We thank anonymous reviewers for their invaluable comments and suggestions on improving this work. This work is supported by the National Natural Science Foundation of China (NSFC) (Grant No. 61572150), and Central Fund of Dalian University of Technology (No. DUT17RC(3)097).

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Correspondence to Jing Zhao or Yanbin Wang or Xiaomin Ma.

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Appendix A PDR/PRR results of the interference-based model and the deterministic distance-based model

Appendix A PDR/PRR results of the interference-based model and the deterministic distance-based model

Figures 23, 24, 25, 26, 27, 28, 29 and 30 present PDR/PRR results of the interference-based model and the deterministic distance-based model with the data rate of 3 Mbps, 6 Mbps, 12 Mbps, and 24 Mbps. PRR results show the same behavior with NRP in Sect. 2.4. We witness that PDRs are almost identical in the low-to-medium density at each data rate. When the density increases, the deterministic distance model obtains better PDRs. This is because that the hidden terminals beyond the interference range in the deterministic distance-based analytical model do not be considered. But in the interference-based model, they can also lead to reception failure. At the same time, the definition of PDR shows that it is the most stringent evaluation metric which requires that a packet is received successfully by all neighbors. Therefore, the phenomenon happens.

Fig. 23
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PRR comparisons of the two models with the data rate of 3 Mbps

Fig. 24
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PRR comparisons of the two models with the data rate of 6 Mbps

Fig. 25
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PRR comparisons of the two models with the data rate of 12 Mbps

Fig. 26
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PRR comparisons of the two models with the data rate of 24 Mbps

Fig. 27
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PDR comparisons of the two models with the data rate of 3 Mbps

Fig. 28
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PDR comparisons of the two models with the data rate of 6 Mbps

Fig. 29
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PDR comparisons of the two models with the data rate of 12 Mbps

Fig. 30
figure30

PDR comparisons of the two models with the data rate of 24 Mbps

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Zhao, J., Li, Z., Wang, Y. et al. An analytical framework for reliability evaluation of d-dimensional IEEE 802.11 broadcast wireless networks. Wireless Netw (2020). https://doi.org/10.1007/s11276-020-02268-5

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Keywords

  • Reliability evaluation
  • d-D broadcast wireless networks
  • Fading channel
  • Hidden terminal problem
  • Monte-Carlo method