On the Relation Between Peak Age and Stability in Control Loops Over Non-Beacon Enabled CSMA/CA

The proliferation of the Internet of Things has enabled implementing control loops using low-capable devices over non-deterministic networks. This letter addresses the use of non-beacon enabled CSMA/CA and motivates the need of minimizing the probability of peak age surpassing a bound, given in terms of two indicators of control over networks: the maximum allowable transmit interval and the maximum allowable delay. A concrete analytical result for calculating the probability is given, which represents an improvement of 50% with respect to a known bound at the optimal rate in a 5-loops control system.