Joint Optimization of PAoI and Queue Backlog with Energy Constraints in LoRa Gateway Systems

Peak Age of Information(PAoI), as a performance indicator representing the freshness of information, has attracted the attention of researchers in recent years. The data packet transmission rate in the LoRa network determines the information freshness level for system packets. In order to study the optimal scheduling of data packets, we try to use the PAoI to describe the real-time level of the end devices( \( EDs \) ) and reduce it. We use edge servers to process monitoring data packets at the edge of the network to improve the efficiency of \( EDs \) and the information freshness level of data. Since packet transmission will be constrained by \( EDs \) battery queue energy and gateway queue backlog, we propose an optimization problem that aims to minimize the long-term average PAoI of \( EDs \) while ensuring network stability. With the Lyapunov optimization framework, the long-term stochastic optimization problem is transformed into a single-slot optimization problem. Furthermore, to avoid the problem of too large search space, we propose a dynamic strategy space reduction algorithm (SSDR) to shrink the strategy space. The simulation experiments show that our SSDR algorithm can optimize the PAoI index of \( EDs \) in various situations and satisfy the constraints of long-term optimization.