Non-linear Age of Information in a Discrete Time Queue: Stationary Distribution and Average Performance Analysis

This paper considers a status update communication system consisting of a source-destination link with timeliness requirements. First, we study the properties of a sample path of the age of information (AoI) process at the destination. Under the assumption of ergodicity, we obtain a general formula of the stationary distribution of the AoI. We relate this result to a discrete time queueing system and provide a general expression of the generating function of AoI in relation with the system time and the peak age of information (PAoI). Furthermore, we consider the first-come-first-served (FCFS) Geo/Geo/1 queue and we obtain closed-form expressions of the generating functions and the stationary distributions of the AoI and the PAoI. We built upon these results to provide a methodology for analyzing general non-linear age functions for this type of systems.

[1]  S. Stidham,et al.  Sample-Path Analysis of Queueing Systems , 1998 .

[2]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[3]  Roy D. Yates,et al.  Status updates through queues , 2012, 2012 46th Annual Conference on Information Sciences and Systems (CISS).

[4]  Roy D. Yates,et al.  Age of information in a network of preemptive servers , 2018, IEEE INFOCOM 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).

[5]  Roy D. Yates,et al.  The Age of Information in Networks: Moments, Distributions, and Sampling , 2018, IEEE Transactions on Information Theory.

[6]  Eytan Modiano,et al.  Age of Information for Discrete Time Queues , 2019, ArXiv.

[7]  Tetsuya Takine,et al.  A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues , 2018, IEEE Transactions on Information Theory.

[8]  Yin Sun,et al.  Sampling for data freshness optimization: Non-linear age functions , 2018, Journal of Communications and Networks.

[9]  Sennur Ulukus,et al.  Age of Information in G/G/1/1 Systems: Age Expressions, Bounds, Special Cases, and Optimization , 2019, IEEE Transactions on Information Theory.

[10]  Osvaldo Simeone,et al.  Reliable Transmission of Short Packets Through Queues and Noisy Channels Under Latency and Peak-Age Violation Guarantees , 2018, IEEE Journal on Selected Areas in Communications.

[11]  Emre Telatar,et al.  Status updates in a multi-stream M/G/1/1 preemptive queue , 2018, IEEE INFOCOM 2018 - IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS).

[12]  Yin Sun,et al.  Information Aging Through Queues: A Mutual Information Perspective , 2018, 2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).

[13]  Roy D. Yates,et al.  Real-time status: How often should one update? , 2012, 2012 Proceedings IEEE INFOCOM.

[14]  S. Wittevrongel,et al.  Queueing Systems , 2019, Introduction to Stochastic Processes and Simulation.

[15]  Anthony Ephremides,et al.  Effect of Message Transmission Path Diversity on Status Age , 2016, IEEE Transactions on Information Theory.

[16]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[17]  Vangelis Angelakis,et al.  Age of Information: A New Concept, Metric, and Tool , 2018, Found. Trends Netw..

[18]  Anthony Ephremides,et al.  Age and value of information: Non-linear age case , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[19]  Anthony Ephremides,et al.  Queue Management for Age Sensitive Status Updates , 2019, 2019 IEEE International Symposium on Information Theory (ISIT).

[20]  George Kesidis,et al.  The distribution of age-of-information performance measures for message processing systems , 2019, Queueing Syst. Theory Appl..

[21]  Eytan Modiano,et al.  Can Determinacy Minimize Age of Information? , 2018, ArXiv.

[22]  James Gross,et al.  On the Distribution of AoI for the GI/GI/1/1 and GI/GI/1/2* Systems: Exact Expressions and Bounds , 2019, IEEE INFOCOM 2019 - IEEE Conference on Computer Communications.

[23]  Roy D. Yates,et al.  Update or wait: How to keep your data fresh , 2016, IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications.

[24]  Yin Sun,et al.  Sampling of the Wiener Process for Remote Estimation Over a Channel With Random Delay , 2017, IEEE Transactions on Information Theory.

[25]  Yin Sun,et al.  Sampling for Remote Estimation through Queues: Age of Information and Beyond , 2019, 2019 International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOPT).

[26]  Rajai Nasser,et al.  Age of information: The gamma awakening , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[27]  Marian Codreanu,et al.  On the Age of Information in Status Update Systems With Packet Management , 2015, IEEE Transactions on Information Theory.

[28]  Ness B. Shroff,et al.  Optimizing data freshness, throughput, and delay in multi-server information-update systems , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[29]  Randolph D. Nelson,et al.  Probability, stochastic processes, and queueing theory - the mathematics of computer performance modeling , 1995 .