Effective age of information in real-time wireless feedback control systems

Ultra-reliable and low-latency communication (URLLC) is one of the most important scenarios in forthcoming fifth generation (5G) cellular networks to ensure timely exchange of information and realize real-time wireless control. In URLLC, timely information update needs to be guaranteed since control performance, e.g., control cost and stability, is directly determined by timely control information update. In this paper, we introduce an effective age of information (EAoI) to evaluate the timeliness of information update in control process. We consider the control process with two phases: sensor to controller phase and controller to actuator phase. We adopt first-generate-first-serve (FGFS) M/M/1/1 → M/M/1/2 and FGFS M/M/1/1* → M/M/1/2* tandem queuing models to represent control process and we use finite-state Markov chains to describe control information updates. By studying state transitions, we calculate the average EAoI for both tandem queuing models. More importantly, we analyze throughput of wireless control systems and its relationship with average EAoI, which provides a guideline for URLLC system design in real-time feedback control systems. Simulation results show the advantage of using EAoI.