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A Novel Recursive Algorithm to Calculate the Parameters of Markov Model for IEEE 802.15.4 in Sensor Applications
Hossein Hadaidian Nejad Yousefi, Yousef Seifi Kavian and Alimorad Mahmoudi

The influence of the internet of things (IoT) has been dramatically increasing on various applications. In the recent trend, wireless sensor networks (WSN) will become an important technology of IoT. Clustering methods are a common way to improve the performance of these networks, and IEEE 802.15.4 becomes a more popular technology for WSNs. In this paper, a discrete-time Markov model is proposed for a sensor node in a cluster based on the non-acknowledge non-beacon-enabled IEEE 802.15.4. This paper calculates the probability of the busy channel using a proposed recursive method and conditional probabilities. Moreover, the cumulative distribution function of the packet delivery delay, packet delivery ratio, and energy consumption per bit are obtained by proposing an absorbing Markov model. The model is investigated for various network conditions, and the results are verified in different cases using the Monte Carlo algorithm, which points to the accuracy and precision of the model.

Keywords: Clustering network, Internet of Things, IEEE 802.15.4, Wireless Sensor Networks, Markov chain, Network Modeling.

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