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Foundations and Trends R in Networking Age of Information: A New Concept, Metric, and Tool Suggested Citation: Antzela Kosta, Nikolaos Pappas and Vangelis Angelakis (2017), “Age of Information: A New Concept, Metric, and Tool”, Foundations and Trends R in Networking: Vol. 12, No. 3, pp 162–259. DOI: 10.1561/1300000060. Antzela Kosta Dept. of Science and Technology Linköping University, Sweden antzela.kosta@liu.se Nikolaos Pappas Dept. of Science and Technology Linköping University, Sweden nikolaos.pappas@liu.se Vangelis Angelakis Dept. of Science and Technology Linköping University, Sweden vangelis.angelakis@liu.se This article may be used only for the purpose of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without ex- plicit Publisher approval. Boston — Delft

Contents 1 Introduction 163 2 The Introduction of the Concept 166 2.1 Age of Information . . . . . . . . . . . . . . . . . . . . . 166 2.2 First Queue-theoretic System Abstractions . . . . . . . . . 171 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 3 The Early Works 177 . . . 178 3.1 Sharing the System Among Multiple Traﬃc Streams 3.2 Basic Scheduling Through Queues . . . . . . . . . . . . . 182 3.3 Peak Age of Information . . . . . . . . . . . . . . . . . . 188 3.4 Availability of Resources . . . . . . . . . . . . . . . . . . . 191 3.5 Packet Management . . . . . . . . . . . . . . . . . . . . . 201 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 4 Subsequent Works and Extensions 216 4.1 Rate Control Optimization . . . . . . . . . . . . . . . . . 217 4.2 Packet Deadlines . . . . . . . . . . . . . . . . . . . . . . 222 4.3 Optimizing Age, Throughput, and Delay . . . . . . . . . . 227 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

5 Age as a Tool 230 5.1 Channel State Information . . . . . . . . . . . . . . . . . 230 5.2 Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . 233 5.3 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . 236 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 239 6 Latest Contributions 6.1 Eﬀect of Errors . . . . . . . . . . . . . . . . . . . . . . . 239 6.2 Beyond Single-hop Communication . . . . . . . . . . . . . 241 6.3 Other Topics . . . . . . . . . . . . . . . . . . . . . . . . . 242 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 7 Future Directions and Open Questions 246 7.1 Connection with Information Theory . . . . . . . . . . . . 247 7.2 Connection with Signal Processing . . . . . . . . . . . . . 248 7.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . 250 7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Acknowledgements References 252 253

Age of Information: A New Concept, Metric, and Tool Antzela Kosta1, Nikolaos Pappas2 and Vangelis Angelakis3 1Dept. of Science and Technology, Linköping University, Sweden; antzela.kosta@liu.se 2Dept. of Science and Technology, Linköping University, Sweden; nikolaos.pappas@liu.se 3Dept. of Science and Technology, Linköping University, Sweden; vangelis.angelakis@liu.se ABSTRACT Age of information (AoI) was introduced in the early 2010s as a notion to characterize the freshness of the knowledge a system has about a process observed remotely. AoI was shown to be a fundamentally novel metric of timeliness, signiﬁcantly diﬀerent, to existing ones such as delay and latency. The importance of such a tool is paramount, espe- cially in contexts other than transport of information, since communication takes place also to control, or to compute, or to infer, and not just to reproduce messages of a source. This volume comes to present and discuss the ﬁrst body of works on AoI and discuss future directions that could yield more challenging and interesting research. Antzela Kosta, Nikolaos Pappas and Vangelis Angelakis (2017), “Age of Information: A New Concept, Metric, and Tool”, Foundations and Trends R in Networking: Vol. 12, No. 3, pp 162–259. DOI: 10.1561/1300000060.

1 Introduction The concept of Age of Information (AoI) was introduced in 2011 in [31] to quantify the freshness of the knowledge we have about the status of a remote system. More speciﬁcally, AoI is the time elapsed since the generation of the last successfully received message containing update information about its source system. Utilizing a simple communication system model, in a series of papers ([32], [33], [30], and [58]), the ﬁrst group of characterizations of the Age of Information metric had appeared by 2012. Since then, AoI has attracted a vivid interest, with over 50 publications, in the last six years 1. The attention AoI has been receiving is due to two factors. The ﬁrst is the sheer novelty brought by AoI in characterizing the freshness of information versus for example that of the metrics of delay or latency. Second, the need and importance of characterizing the freshness of such information is paramount in a wide range of information, communication, and control systems. By now, age has been studied with considerable diversity of systems, being as a concept, a performance metric, and a tool. 1In this volume we take into consideration works that have been published no later than June 2017. 163

164 Introduction The purpose of this volume is to present a critical summary of this ﬁrst body of works performed on AoI and discuss future research directions. Already at this early point we need to put down our ﬁrst disclaimer: we have chosen to treat the early works with signiﬁcantly more detail, going deeper in the derivations and presenting more results and insights from them than we do with more recent works. The reason for this is to achieve a tutorial nature in the volume, which can provide a solid ground of the AoI as a concept. Moreover, the ﬁrst works, which we chose to present in more detail than the rest, aim to provide funda- mentally new knowledge in the premise of maintaining information fresh in a system. This basic goal opens up a wide range of communication contexts that span from estimation and prediction, to applications such as vehicular networks and information caching, to name a few. With this in mind, we begin this volume presenting the AoI concept as it was originally introduced. For this, we discuss the original models of Kaul, Gruteser and Yates of [33], considering a system where a source is transmitting packets containing status updates to a destination. The analysis presented is based on a simple queueing model. Already in that work the minimization of AoI was shown to be non-trivial for the source sampling methods studied. However, it had already become clear that timely updating a destination about a remote system is neither the same as maximizing the utilization of the communication system, nor of ensuring that generated status updates are received with minimum delay. This is because utilization can be maximized by making the source send updates as fast as possible which would lead to the destination receiving delayed statuses because messages are backlogged in the communication system studied. In this case, delay suﬀered by the stream of status updates can be reduced by decreasing the rate of updates. Alternatively, decreasing the update rate can also lead to the destination having unnecessarily outdated status information because of lack of updates. AoI has spawned relevant performance metrics that are more tractable such as the Peak Age of Information or the Cost of Update Delay, open- ing even more research opportunities. Under the timely update context, the relevant timeliness performance metrics should be kept at values

165 that ensure high freshness of information. Already the ﬁrst AoI lower bound had appeared in [33] and we discuss it in Section 2. We then con- tinue the discussion on the early works of AoI as a performance metric in Section 3, where we present the case of AoI for multiple sources, its use in scheduling, and demonstrate packet management techniques that have been employed. Section 4 treats AoI as a metric for rate control, addresses the case of packets with deadlines, and presents an optimal policy for optimizing age, throughput, and delay. Keeping the AoI metrics low is of high interest when AoI is being treated as a tool to facilitate the timely update of information that will eventually improve performance metrics in diﬀerent contexts. Con- sider for example remote estimation; if the process under observation consists of highly correlated data, then the frequency of generation and transmission of updates can be signiﬁcantly reduced without aﬀecting the timeliness of the information at a remote receiver. In Section 5, we discuss three domains in which AoI has been treated as a tool: Channel State Information (CSI) estimation, energy harvesting, and scheduling. Recent works that have appeared in the time of writing of this volume have been categorized and treated in Section 6. Finally, in Section 7, we provide a brief discussion of indicative future topics on which the AoI can contribute. The topics we cover there are not a complete list, as there is an immense wealth of possible problems associated with the notion of timeliness as captured by age, in the form of either a tool, a performance metric, or even a concept.

2 The Introduction of the Concept With the introduction of Age of Information (AoI) in [31] and the subsequent works of Kaul, Yates, and Gruteser, it became clear that this new concept is novel compared to, at that time, existing measures of information timeliness. Based on the seminal work of [33], in this section we give to the reader the fundamentals of AoI for a status update system under the queueing models assumed therein. As we already noted in the introduction, we provide a good level of detail, for this ﬁrst work. This is to give solid insight and background to the reader and also to reﬂect the value of the contribution to the topic of information timeliness. 2.1 Age of Information Consider a system comprising two nodes. A stochastic process X(t) is observed by the source node, that extracts samples. These are assumed to carry information about the status of the process at the source node. Assuming this status information is needed at the other node, each collected sample needs to be transmitted over a communication link to that destination. At the transmitter of the source node there is a buﬀer which stores the samples in the form of packets containing (i) the value 166

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