Markov Chain Based Modeling Bandwith States of the Wireless Sensor Networks of Monitoring System
In this paper, a mathematical model of the operation process of the ZigBee standard wireless network for remote monitoring systems based on the Markov chain apparatus was developed. Using the model was evaluated of the operation process of the CSMA/CA algorithm of the MAC level of the IEEE 802.15.4 ZigBee standard. The peculiarity of this mathematical model is that it takes into account the level of loading of network elements and potential distortions in the transmitted packets as a result of the influence of interference. Using the developed mathematical model, the main characteristics of the network operation process, such as dependence of the probability of successful transmission of packets on the system load (on the number of nodes, on the minimum length of the “competition window”), the dependence of the bandwidth on system load (on the number of nodes, on the minimum length of the “competition window”) for the case where there is noise in the channel and for the absence of noise in the channel were obtained.