Research on Age of Information for Discrete-Time System with Ber/Geo/1/1

doi:10.19678/j.issn.1000-3428.0064478

Abstract

Abstract: Due to the dynamic changes in the environment of real-time monitoring systems，such as the Internet of Vehicles（IoV） and remote surgery，it is inevitable for such systems to focus on the freshness of received information.The infrastructure in the Internet of Things（IoT） system is typically performed according to the time slot. An Age of Information（AoI） evaluation method for the discrete time-status update system is proposed to resolve the information freshness in the system.First，a discrete-time Ber/Geo/1/1 system based on the AoI，which consists of a source，server，and destination，is constructed.Based on the queueing theory，a two-dimensional state vector is introduced to simultaneously track the AoI of the destination node and the server status update packet.The steady-state probability of each two-dimensional AoI vector can be determined by solving the state transition equation.Furthermore，the probability distribution of the system AoI can be obtained.However，the complex AoI state transition equation makes it difficult to determine the steady-state probability of the two-dimensional AoI vector，and in some cases，solutions may not exist.Therefore，an AoI evaluation method for a discrete status update system based on the Probability Generating Function（PGF） is proposed. This method only requires using a simple derivative or expanding the corresponding PGF into a power series to obtain the AoI and its probability distribution of the system.The experimental results show that when the packet arrival probability is 0.2，the packet service probability increases from 0.1 to 0.3，which reduces the average AoI by 44.4%.The proposed method has higher calculation accuracy and a simpler calculation process than the traditional method.

Key words: Age of Information（AoI）, discrete time queue, probability generating function, stationary probability, queueing theory

摘要： 车联网、远程手术等实时监控系统所处环境的动态变化性，导致关注接收信息的新鲜度成为此类系统的必然选择。物联网系统中基础设施通常按照时隙进行离散操作，针对离散时间状态更新系统中的信息新鲜度表征问题，提出一个面向离散时间状态更新系统的信息年龄(AoI)评估方法。构建一个基于AoI的单源-单服务器-目的节点的离散时间Ber/Geo/1/1系统，根据排队理论，引入二维状态向量同时追踪目的节点AoI及服务器状态更新包的年龄。每个二维AoI向量的稳态概率可通过求解状态转化方程来确定，继而可得到系统AoI的概率分布。然而复杂的AoI状态转化方程使二维AoI向量的稳态概率难以求解甚至在某些情况下无解，为此，提出基于概率生成函数(PGF)的离散状态更新系统AoI评估方法，通过对相应的PGF进行简单的求导运算或将其展开为幂级数的形式，确定系统AoI及AoI的概率分布。实验结果表明，当数据包到达概率为0.2时，所提方法的数据包服务概率由0.1增加至0.3，平均AoI降低44.4%，相比传统方法具有较高的计算精度和较简单的计算过程。

关键词: 信息年龄, 离散时间队列, 概率生成函数, 稳态概率, 排队理论

CLC Number:

TP391

WEI Zhemin, JIA Xiangdong, CHEN Zhi, ZHAO Yuhua. Research on Age of Information for Discrete-Time System with Ber/Geo/1/1[J]. Computer Engineering, 2023, 49(6): 284-291.

魏哲敏, 贾向东, 陈智, 赵玉华. 离散时间Ber/Geo/1/1系统的信息年龄研究[J]. 计算机工程, 2023, 49(6): 284-291.

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