Delay distribution analysis of Wireless Personal Area Networks

Characterizing the network delay distribution is a fundamental step to properly compensate the delay of Networked Control Systems (NCSs). Due to the random backoff mechanism employed by Wireless Personal Area Network (WPAN) protocols, it is difficult to derive such a distribution. In this paper, the probability distribution of the delay for successfully received packets in WPANs is characterized. The analysis uses a moment generating function method based on an extended Markov chain model. The model considers the exponential backoff process with retry limits, acknowledgements, unsaturated traffic, and variable packet size, and gives an accurate explicit expression of the probability distribution of the network delay. The probability distribution of the delay is a function of the traffic load, number of nodes, and parameters of the communication protocol. Monte Carlo simulations validate the analysis for different network and protocol parameters. We show that the probability distribution of the delay is significantly different from existing network models used for NCS design. Furthermore, the parameters of the communication protocol result to be critical to stabilize control systems.