In this paper we analyze the distribution of the Age of Information (AoI) of a tagged data stream sharing a processor with a set of other data streams. We do so in the highly general setting in which the interarrival times pertaining to the tagged stream can have any distribution, and also the service times of both the tagged stream and the background stream are generally distributed. The packet arrival times of the background process are assumed to constitute a Poisson process, which is justified by the fact that it typically is a superposition of many relatively homogeneous streams. The first major contribution is that we derive an expression for the Laplace-Stieltjes transform of the AoI in the resulting GI+M/GI+GI/1 model. Second, we use stochastic ordering techniques to identify tight stochastic bounds on the AoI. In addition, when approximating the tagged stream's inter-generation times through a phase-type distribution (which can be done at any precision), we present a computational algorithm for the mean AoI. As illustrated through a sequence of numerical experiments, the analysis enables us to assess the impact of background traffic on the AoI of the tagged stream.

翻译：本文分析了一组标记数据流在与其他数据流共享处理器时的信息时效（AoI）分布特征。我们在高度泛化的设定下开展研究：标记数据流的到达间隔时间可服从任意分布，同时标记流与背景流的服务时间也均为一般分布。假设背景数据流的数据包到达时间遵循泊松过程，这一假设的合理性在于其通常是多个相对均匀数据流的叠加效应。本文的首要贡献是针对GI+M/GI+GI/1模型推导出AoI的拉普拉斯-斯蒂尔切斯变换表达式；其次，采用随机排序技术识别AoI的紧致随机边界。此外，当通过相位型分布（可达到任意精度）近似标记流的数据生成间隔时，我们提出了平均AoI的计算算法。通过系列数值实验表明，本分析框架能够评估背景流量对标记流AoI的影响程度。