AoI and PAoI in the IoT-Based Multisource Status Update System: Violation Probabilities and Optimal Arrival Rate Allocation
Tianci Zhang, Shutong Chen, Zhengchuan Chen, Zhong Tian, Yunjian Jia, Min Wang, Dapeng Wu
Abstract
Abundant real-time applications over Internet of Things (IoT) have imperative demands on timely information. Compared to average Age of Information (AoI), distribution of AoI characterizes the timeliness in more details. This article studies the timeliness of an IoT-based multisource status update system. By modeling the system as a multisource M/G/1/1 bufferless preemptive queue, general formulas of violation probabilities and probability density functions (p.d.f.s) of AoI and PAoI are derived based on a time-domain approach. For the case with exponentially distributed service time, the violation probabilities and p.d.f.s are obtained in closed form. To fully characterize the overall timeliness of the multisource system, the maximal violation probabilities of AoI and PAoI are proposed. To improve the overall timeliness under the resource constraint of IoT device, the arrival rate allocation is optimized to control the maximal violation probabilities. It is proved that the optimal arrival rates can be found by convex optimization. In particular, we show that the minimum of maximal violation probability of AoI (PAoI) is achieved only if all violation probabilities of AoI (PAoI) are equal. Finally, numerical results verify the theoretical analysis and show the effectiveness of the arrival rate allocation in improving the overall timeliness.