AoI and PAoI in the IoT-based Multi-Source Status Update System : Violation Probabilities and Optimal Arrival Rate Allocation

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 paper studies the timeliness of an IoT-based multi-source status update system. By modeling the system as a multi-source 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 multi-source 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. © 2023 IEEE