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

TL;DR

This paper analyzes violation probabilities of AoI and PAoI in IoT status update systems, deriving formulas and proposing optimal arrival rate allocation to enhance information freshness under resource constraints.

Contribution

It introduces a novel modeling approach for violation probabilities of AoI and PAoI in multi-source IoT systems and proposes an optimal resource allocation scheme based on convex optimization.

Findings

Derived closed-form violation probability formulas for specific service time distributions.

Proposed an optimal arrival rate allocation scheme to minimize maximal violation probabilities.

Numerical results confirm the effectiveness of the proposed scheme and theoretical analysis.

Abstract

Lots of real-time applications over Internet of things (IoT)-based status update systems have imperative demands on information freshness, which is usually evaluated by age of information (AoI). Compared to the average AoI and peak AoI (PAoI), violation probabilities and distributions of AoI and PAoI characterize the timeliness in more details. This paper studies the timeliness of the 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 with a time-domain approach. For the case with negativeexponentially distributed service time, the violation probabilities and p.d.f.s are obtained in closed form. Moreover, the maximal violation probabilities of AoI and PAoI are proposed to characterize the overall timeliness. To improve the overall timeliness under the resource constraint of IoT-device, the arrival rate allocation scheme is used to minimize the maximal violation probabilities. It is proved that the optimal arrival rates can be found by convex optimization algorithms. In addition, it is obtained that the minimum of maximal violation probability of AoI (or PAoI) is achieved only if all violation probabilities of AoI (or PAoI) are equal. Finally, numerical results verify the theoretical analysis and show the effectiveness of the arrival rate allocation scheme.