Age-of-Event Aware: Sampling Period Optimization in a Three-Stage Wireless Cyber-Physical System With Diverse Parallelisms

With the emergence of parallel computing systems and distributed time-sensitive applications, it is urgent to provide statistical guarantees for age of information (AoI) in wireless cyber-physical systems (WCPS) with diverse parallelisms. However, most of the existing research on AoI have tended to focus on serial transmission, and the AoI performance of multi-stage parallel systems remains unclear. To help address these research gaps, in this work, we set out to investigate the age of event (AoE) violation probability in a three-stage WCPS with diverse parallelisms such as fork-join and split-merge. We analyze both transient and steady-state characteristics of AoE violation probability (AoEVP). Using these characteristics, we transform the AoEVP minimization problem into an equivalent minimization problem. Moreover, we develop a queuing model to capture the queue dynamics under the max-plus theory of stochastic network calculus (SNC) approach. Based on the max-plus model, we derive a closed-form Chernoff upper bound for the equivalent problem by applying the union bound and the Chernoff inequality. Furthermore, we characterize the service process for different parallelisms applicable to each stage. By solving the Chernoff upper bound with the service moment generation functions (MGFs), we obtain heuristic update period solutions for minimizing the AoEVP of three-stage WCPS. Simulation results validate our analysis and demonstrate that our heuristic update period solutions are near optimal for minimizing the AoEVP of three-stage WCPS with diverse parallelisms.