A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues
A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues
复制标题
DOI：
10.1109/tit.2019.2938171
复制
发表时间：
2019-12-01
影响因子：
2.5
通讯作者：
Tanaka, Toshiyuki
中科院分区：
文献类型：
--
作者：
Inoue, Yoshiaki;Masuyama, Hiroyuki;Tanaka, Toshiyuki
本文考虑信息更新系统中信息年龄（AoI）的稳态分布。我们首先推导出AoI稳态分布的一个通用公式，该公式适用于一大类信息更新系统。该公式表明，AoI的稳态分布由系统延迟的稳态分布和峰值AoI的稳态分布给出。为了证明其适用性和有用性，我们分析了具有四种不同服务规则的单服务器队列中的AoI：先到先服务（FCFS）、抢占式后到先服务（LCFS）以及两种非抢占式LCFS服务规则的变体。对于FCFS和抢占式LCFS服务规则，考虑了GI/GI/1、M/GI/1和GI/M/1队列；对于非抢占式LCFS服务规则，考虑了M/GI/1和GI/M/1队列。通过这些结果，我们进一步展示了在这些服务规则下M/GI/1和GI/M/1队列中平均AoI的比较结果。
This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update systems. The formula indicates that the stationary distribution of the AoI is given in terms of the stationary distributions of the system delay and the peak AoI. To demonstrate its applicability and usefulness, we analyze the AoI in single-server queues with four different service disciplines: first-come first-served (FCFS), preemptive last-come first-served (LCFS), and two variants of non-preemptive LCFS service disciplines. For the FCFS and the preemptive LCFS service disciplines, the GI/GI/1, M/GI/1, and GI/M/1 queues are considered, and for the non-preemptive LCFS service disciplines, the M/GI/1 and GI/M/1 queues are considered. With these results, we further show comparison results for the mean AoI's in the M/GI/1 and GI/M/1 queues under those service disciplines.