离散时间Ber/Geo/1/1系统的信息年龄研究

doi:10.19678/j.issn.1000-3428.0064478

摘要/Abstract

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

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

中图分类号:

TP391

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.

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.

https://www.ecice06.com/CN/Y2023/V49/I6/284

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参考文献

[1] LATVA-AHO M,LEPPÄNEN K.Key drivers and research challenges for 6G ubiquitous wireless intelligence[EB/OL].[2022-03-10].https://www.semanticscholar.org/paper/Key-drivers-and-research-challenges-for-6G-wireless-Latva-aho-Lepp%C3%A4nen/51e153f10d15bdaf85a8e56ea52c990495d6b230.
[2] ABD-ELMAGID M A,PAPPAS N,DHILLON H S.On the role of age of information in the internet of things[J].IEEE Communications Magazine,2019,57(12):72-77.
[3] 王恒,段思勰,谢鑫.基于信息年龄优化的多信道无线网络调度方法[J].电子与信息学报,2022,44(2):702-709.WANG H,DUAN S X,XIE X.Scheduling method for multi-channel wireless networks based on optimization of age of information[J].Journal of Electronics and Information Technology,2022,44(2):702-709.(in Chinese)
[4] KAUL S,YATES R,GRUTESER M.Real-time status:how often should one update?[C]//Proceedings of IEEE INFOCOM.Washington D.C.,USA:IEEE Press,2012:2731-2735.
[5] 李保罡,武文静,段晓,等.基于NOMA-MEC系统的信息年龄最小化研究[J].通信学报,2021,42(10):222-232.LI B G,WU W J,DUAN X,et al.Research on the minimizing of information age based on NOMA-MEC system[J].Journal on Communications,2021,42(10):222-232.(in Chinese)
[6] YATES R D,SUN Y,BROWN D R,et al.Age of information:an introduction and survey[J].IEEE Journal on Selected Areas in Communications,2021,39(5):1183-1210.
[7] 熊轲,胡慧敏,艾渤,等.6G时代信息新鲜度优先的无线网络设计[J].物联网学报,2020,4(1):80-91.XIONG K,HU H M,AI B,et al.Information freshness orientated wireless network design for 6G[J].Chinese Journal on Internet of Things,2020,4(1):80-91.(in Chinese)
[8] 赵悦超,杨涛,胡波.无线传感器网络中基于信息年龄的状态更新策略[J].微电子学与计算机,2020,37(11):29-34.ZHAO Y C,YANG T,HU B.A status updating policy based on age of information in wireless sensor network[J].Microelectronics & Computer,2020,37(11):29-34.(in Chinese)
[9] COSTA M,CODREANU M,EPHREMIDES A.On the age of information in status update systems with packet management[J].IEEE Transactions on Information Theory,2016,62(4):1897-1910.
[10] MOLTAFET M,LEINONEN M,CODREANU M.On the age of information in multi-source queueing models[J].IEEE Transactions on Communications,2020,68(8):5003-5017.
[11] INOUE Y,MASUYAMA H,TAKINE T,et al.A general formula for the stationary distribution of the age of information and its application to single-server queues[J].IEEE Transactions on Information Theory,2019,65(12):8305-8324.
[12] YATES R D,KAUL S K.The age of information:real-time status updating by multiple sources[J].IEEE Transactions on Information Theory,2019,65(3):1807-1827.
[13] YATES R D.The age of information in networks:moments,distributions,and sampling[J].IEEE Transactions on Information Theory,2020,66(9):5712-5728.
[14] 魏哲敏,贾向东,赵玉华,等.短包传输下缓冲区辅助的无线传感器状态更新系统的信息新鲜度研究[J/OL].信号处理:1711-1718[2022-03-21].https://kns.cnki.net/KCMS/detail/detail.aspx?filename=XXCN20220317001&dbname=CJFD&dbcode=CJFQ.WEI Z M,JIA X D,ZHAO Y H,et al.Research on information freshness of buffer-aided wireless sensor status update system with short packet transmission[J/OL].Journal of Signal Processing:1711-1718[2022-03-21].https://kns.cnki.net/KCMS/detail/detail.aspx?filename=XXCN20220317001&dbname=CJFD&dbcode=CJFQ.(in Chinese)
[15] MOLTAFET M,LEINONEN M,CODREANU M.Average AoI in multi-source systems with source-aware packet management[J].IEEE Transactions on Communications,2021,69(2):1121-1133.
[16] TALAK R,KARAMAN S,MODIANO E.Optimizing information freshness in wireless networks under general interference constraints[J].IEEE/ACM Transactions on Networking,2020,28(1):15-28.
[17] KOSTA A,PAPPAS N,EPHREMIDES A,et al.Queue management for age sensitive status updates[C]//Proceedings of 2019 IEEE International Symposium on Information Theory.Washington D.C.,USA:IEEE Press,2019:330-334.
[18] TRIPATHI V,TALAK R,MODIANO E.Age of information for discrete time queues[EB/OL].[2022-03-10].https://arxiv.org/abs/1901.10463.
[19] KOSTA A,PAPPAS N,EPHREMIDES A,et al.The age of information in a discrete time queue:stationary distribution and non-linear age mean analysis[J].IEEE Journal on Selected Areas in Communications,2021,39(5):1352-1364.
[20] 吴大正.信号与线性系统分析[M].4版.北京:高等教育出版社,2005.WU D Z.Analysis of signals and linear systems[M].4th ed.Beijing:Higher Education Press,2005.(in Chinese)
[21] AKAR N,DOĞAN O,ATAY E U.Finding the exact distribution of (peak) age of information for queues of PH/PH/1/1 and M/PH/1/2 type[J].IEEE Transactions on Communications,2020,68(9):5661-5672.
[22] AKAR N,DOGAN O.Discrete-time queueing model of age of information with multiple information sources[J].IEEE Internet of Things Journal,2021,8(19):14531-14542.
[23] HESPANHA J P.Modelling and analysis of stochastic hybrid systems[J].IEEE Proceedings-Control Theory and Applications,2006,153(5):520-535.
[24] ZHANG Z S,CHAI X M,LONG K P,et al.Full duplex techniques for 5G networks:self-interference cancellation,protocol design,and relay selection[J].IEEE Communications Magazine,2015,53(5):128-137.
[25] ZHENG D S,YANG Y L,WEI L,et al.Decode-and-forward short-packet relaying in the internet of things:timely status updates[J].IEEE Transactions on Wireless Communications,2021,20(12):8423-8437.
[26] ZHANG J X,XU Y F.On age of information for discrete time status updating system with Ber/G/1/1 queues[EB/OL].[2022-03-10].https://arxiv.org/abs/2109.00246.

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