Minimization of peak age of information in LoRaWAN-based monitoring systems

We study the communication network based on LoRaWAN technology. The communication network consists of N nodes and carries out one-way transmission of monitoring data to the base station (BS). The messages from each node are sent to the BS at random time intervals and independently of each other. If they have the same spreading factor (SF) and airtimes of messages from two or more nodes overlap, a collision occurs and none of the messages reaches the operator. We assume that the importance of information from each node is different, and the peak age of information (PAoI) is used to measure its freshness. We define the functional as the maximum PAoI among all nodes in the system, and our task is to find the parameters under which its minimization is achieved. We choose various message intensities to account for different freshness of information from each node and formulate the problem of optimal SF allocation.