存在分组错误的多源抢占式M/PH/1/1队列：信息年龄及其峰值的精确分布
The Multi-Source Preemptive M/PH/1/1 Queue with Packet Errors: Exact Distribution of the Age of Information and Its Peak
AI总结：
针对状态更新系统的信息新鲜度分析问题，提出多源概率抢占式无缓冲M/PH/1/1排队模型，通过矩阵分析等方法得到各源AoI与PAoI的精确分布，比现有仅求均值的SHS方法更具通用性。
摘要：
信息年龄（Age of Information, AoI）和峰值信息年龄（Peak AoI, PAoI）及其分析模型，近期在信息论与无线通信领域受到广泛关注，用于对状态更新系统中的信息新鲜度进行定性评估。本文采用排队论方法，研究一种具有N个独立信息源到达的概率抢占式无缓冲$M/PH/1/1$排队系统，旨在对通用状态更新系统进行建模。在该模型中，来自源m的新信息分组到达时，允许以取决于n和m的概率抢占正在服务的源n的分组。为使模型比现有模型更具通用性，我们假设每个信息源具有不同的PH型服务时间分布和不同的分组错误概率。随后，我们利用矩阵分析算法，特别是马尔可夫流体队列理论和样本路径论证，得到了每个信息源的AoI和PAoI的精确分布。这与现有依赖随机混合系统（Stochastic Hybrid Systems, SHS）的方法形成对比，后者仅能得到平均值，且适用场景的通用性更低。本文还提供了数值算例，以验证所提方法的有效性，并给出抢占概率对若干AoI和PAoI性能指标影响的工程见解。
英文摘要：
Age of Information (AoI) and Peak AoI (PAoI) and their analytical models have recently drawn substantial amount of attention in information theory and wireless communications disciplines, in the context of qualitative assessment of information freshness in status update systems. We take a queueing-theoretic approach and study a probabilistically preemptive bufferless $M/PH/1/1$ queueing system with arrivals stemming from $N$ separate information sources, with the aim of modeling a generic status update system. In this model, a new information packet arrival from source $m$ is allowed to preempt a packet from source $n$ in service, with a probability depending on $n$ and $m$. To make the model even more general than the existing ones, for each of the information sources, we assume a distinct PH-type service time distribution and a distinct packet error probability. Subsequently, we obtain the exact distributions of the AoI and PAoI for each of the information sources using matrix-analytical algorithms and in particular the theory of Markov fluid queues and sample path arguments. This is in contrast with existing methods that rely on Stochastic Hybrid Systems (SHS) which obtain only the average values and in less general settings. Numerical examples are provided to validate the proposed approach as well as to give engineering insight on the impact of preemption probabilities on certain AoI and PAoI performance figures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
