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.
翻译:在互联网上大量实时应用基于事物(IoT)的状态更新系统对信息新鲜度提出了迫切的要求,通常根据信息年龄(AoI)来评估。与平均AoI和峰值AoI(PaoI)相比,AoI和PaoI(PaoI)的违规概率和分布更详细地说明了其及时性。本文研究基于IoT的多源状态更新系统的及时性。通过将该系统建为多源M/G/1/1无缓冲性先发制人排队,AoI和PaoI的违规概率和概率密度功能的一般公式(p.d.f.s)通常用时间-视距方法来评估。对于服务时间分布为负差的AoI和PaoI的违规概率和分布模式以封闭形式获取。此外,AoI和PaoI的最大违反概率的概率概率,如果A的到达率得到最接近,则使用Arblority比率的比值最高。