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Four-dimensional Markov chain model of single-hop data aggregation with IEEE 802.15.4 in wireless sensor networks

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Abstract

This paper introduces a new 4D Markov chain model for IEEE 802.15.4 wireless transmission, which corrects and extends an existing 3D model, providing more accurate and comprehensive results. It also introduces an analytical technique for calculating both the pdf and mean of the number of timeslots required to complete all transmissions, when a set of nodes contend for the channel at the beginning of a superframe. It is assumed that transmission takes place in beacon mode but without acknowledgement (NACK mode). The model can be used to determine the optimum value of the MAC attribute macSuperframeOrder (SO) required for saving energy, and the shortest delay required to receive all transmitted packets with a specified probability. It can also specify an upper threshold on the number of nodes and the packet length required, in order to achieve acceptable end-to-end delay. The potential creation of a traffic model for the aggregated data generated by the coordinating node is also discussed.

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Acknowledgments

This work was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) under the TRAMSNOD project.

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Authors and Affiliations

  1. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, University Town of Shenzhen, Shenzhen, China

    Xiaoyun Li

  2. School of Computer Science and Electronic Engineering, University of Essex, Colchester, CO4 3SQ, UK

    David K. Hunter

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  1. Xiaoyun Li
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Correspondence to Xiaoyun Li.

Appendix

Appendix

The attempt probability has been successfully used to analyze the truncated binary exponential backoff algorithm in both Ethernet [23] and in the IEEE 802.11 Distributed Coordination Function. This is the probability that an IEEE 802.15.4 node senses the channel or makes an attempt to access it in a particular slot n. Assuming the channel is always busy before the current timeslot n, it can be approximated as [20]:

$$ P_{n} = \sum\limits_{m = 0}^{M} {P_{n} (m)} ,\quad {\text{where }}n \ge 1 $$
(16)

where M is equal to macMaxCSMABackoffs, and P n (m) denotes the attempt probability that a node chooses slot n for its mth attempt:

$$ \begin{aligned} P_{n} (0) & = \left\{ {\begin{array}{*{20}c} {\frac{1}{{W_{\min } }}} & {{\text{where }}1 \le n < W_{\min } } \\ 0 & {\text{otherwise}} \\ \end{array} } \right. \\ P_{n} (m) & = \frac{1}{W}\sum\limits_{k = \max (1,n - W + 1)}^{n} {P_{k} (m - 1)} ,\quad {\text{where }}m > 0 \\ \end{aligned} $$
(17)

where W min = 2macMinBE, and W = min(2m W min, 2macMaxBE). Figure 10 shows P n for macMinBE = 2 and macMinBE = 3, with macMaxBE = 5. Figure 11 shows P n (m) and P n for macMinBE = 3 and macMaxBE = 5.

Fig. 10
figure 10

Attempt probability P n , the probability that a node chooses slot n for a transmission attempt, without considering m

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Fig. 11
figure 11

Attempt probability P n (m), the probability that a node chooses slot n for its mth transmission attempt

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Li, X., Hunter, D.K. Four-dimensional Markov chain model of single-hop data aggregation with IEEE 802.15.4 in wireless sensor networks. Wireless Netw 18, 469–479 (2012). https://doi.org/10.1007/s11276-011-0412-1

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