信息新鲜度新指标：Age of Information (AOI) 深入解析

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"Age of Information: A New Metric for Information Freshness" 本文是关于通信网络领域新兴的Age of Information (AOI) 指标的详细论述，由Yin Sun、Igor Kadota、Rajat Talak和Eytan Modiano等专家撰写。AOI是一种评估信息新鲜程度的新方法，它在当前的文献中尚未得到充分探讨，因此这份资料对理解AOI的概念和技术具有重要意义。 Age of Information（AOI）是一个度量信息在系统中的老化速度或信息更新频率的指标。在现代通信网络中，实时性成为许多应用的关键要求，例如物联网(IoT)中的传感器数据、自动驾驶车辆的导航信息等。AOI的引入旨在解决这些问题，通过量化信息的“新鲜度”，帮助优化网络性能，确保关键信息的及时性和准确性。 AOI的计算通常涉及从信息产生到接收的时间差，包括传输延迟、处理延迟以及等待新信息到来的时间等。一个较低的AOI值意味着信息更接近实时状态，而较高的AOI则表示信息可能已经过时。因此，AOI在设计高效的信息传输策略和协议时起着至关重要的作用。这篇合成讲座系列的目的是提供通信网络设计、实现和管理领域的深度分析，涵盖了从算法到硬件实现的广泛主题，包括安全问题、多址接入协议等。AOI作为其中的一个专题，旨在帮助工程师和高级学生跟踪快速发展的技术，同时也便于教学课程的开发。在实际应用中，AOI的概念可以应用于各种场景，例如无线传感器网络的监控系统，通过最小化AOI来优化数据收集的效率；或者在自适应光学网络中，通过调整更新策略来保持信息的新鲜度。多臂博弈(Multi-Armed Bandit)理论也可能被用来研究如何在多个信息源之间进行最优选择，以降低整体的AOI。 "Age of Information: A New Metric for Information Freshness"深入探讨了AOI作为衡量信息新鲜度的新标准，为通信网络的研究和优化提供了新的视角和工具。通过理解和应用AOI，我们可以更好地设计和管理网络系统，确保信息的实时性和有效性，从而提升系统的整体性能。

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5.10 Average age penalty of an exponential penalty function

exp

..t// D e

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 1 vs. the coeﬃcient  of discretized log-normal

service time distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

5.11 Signal variations during time intervals of length T . . . . . . . . . . . . . . . . . . . . . 176

5.12 A signal sampling and estimation system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

xix

Preface

In recent years, the number of studies on Age of Information (AoI) has grown exponentially,

such that providing a detailed and comprehensive treatment of the ﬁeld is beyond the scope of a

single book. In this book, we attempt to provide an overview of some fundamental works on the

topic. In Chapter 2, we will consider the problem of AoI minimization in queueing networks and

design age-optimal scheduling policies. In Chapter 3, we will consider the problem of AoI min-

imization in broadcast wireless networks, and in Chapter 4, we will consider wireless networks

under general interference constraints. Finally, in Chapter 5, we will consider the relationship

between AoI and sampling and then develop optimal sampling strategies for minimizing AoI

and estimation error.

AoI in Queueing Networks: In Chapter 2, we consider AoI minimizing in queueing net-

works. We use a sample-path method to prove that a Last-Generated, First-Served (LGFS)

scheduling policy and its variations can achieve (near) optimal age performance in several types

of queueing networks with multiple servers, multiple hops, and/or multiple sources. If the service

times are exponentially distributed, we show that the preemptive LGFS policy is age-optimal

in a stochastic ordering sense, among all causal scheduling policies. If the service times satisfy

a New-Better-than-Used (NBU) distributional property, the non-preemptive LGFS policy is

shown to be within a constant gap from the optimum age performance. ese age-optimality

results are quite general: (i) they hold for quite general packet generation times and arrival

times (including out-of-order packet arrivals); (ii) they hold for minimizing not only the time-

average age and average peak age, but also for minimizing the age stochastic process and any

non-decreasing functional of the age stochastic process; and (iii) they hold for several types of

queueing networks. In single-hop queueing systems, if the packets arrive at the queue in the

same order of their generation times, the LGFS policies reduce to the Last-Come, First-Served

(LCFS) policies. Hence, the age optimality results of LCFS-type policies are also established.

AoI in Broadcast Wireless Networks: In Chapter 3, we turn our attention to optimizing

AoI in wireless networks. In particular, we address the problem of minimizing AoI in broadcast

wireless networks. We consider a single-hop wireless network with a base station and a number

of nodes sharing time-sensitive information through unreliable wireless links. We formulate

a discrete-time decision problem and develop transmission scheduling policies that attempt to

minimize AoI in the network. We evaluate the performance of those policies using analytical and

numerical results. First, we consider a network in which sources can generate packets with fresh

information on demand. is assumption isolates the link scheduling problem from the eﬀects of

packet generation and queueing, allowing us to extract valuable insight from the problem. Later

in the chapter we also consider the case where the source generates packets at random, which are

xx PREFACE

queued for transmission, as well as situations where diﬀerent nodes have minimum throughput

requirements that must be satisﬁed. In all cases we develop a number of scheduling policies

with provable performance guarantees. Our scheduling policies are derived from a stochastic

optimization framework and include both index policies as well as max-weight-type policies

that schedule transmissions based on the current age at the destination.

AoI in General Wireless Networks: In Chapter 4, we design scheduling policies to min-

imize age in wireless network under general interference constraints and time-varying links.

e wireless network consists of a set of source-destination pairs, connected by a wireless link.

Each source generates information updates, which are to be sent to its destination. We will

ﬁrst consider the case in which the scheduler does not have access to the current channel state

information and describe a simple randomized link activation policy that is peak-age optimal

and within a factor of two of the optimal time-average age. We will also describe a simple, yet

broad, class of distributed scheduling policies, in which each link attempts transmission with a

certain probability. We then turn our attention to the case where the scheduler can observe the

channel state and show that age can be improved signiﬁcantly by utilizing the current channel

state information.

AoI and Sampling: In Chapter 5, we consider how to take samples at a source for im-

proving the freshness of received samples at a remote receiver. We use nonlinear functions of

AoI to measure information freshness and provide a survey on nonlinear age functions and their

applications. e sampler design problem is studied to optimize these information freshness

measures, even when there is a sampling rate constraint. is sampling problem is formulated

as a constrained Markov decision process (MDP) with a possibly uncountable state space. We

present a complete characterization of the optimal solution to this MDP: e optimal sampling

policy is a deterministic or randomized threshold policy, where the threshold and the random-

ization probabilities are characterized based on the optimal objective value of the MDP and the

sampling rate constraint. We show that the optimal signal-aware sampler is a threshold policy

on instantaneous estimation error and the optimal signal-ignorant sampler is a threshold policy

on expected estimation error. In addition, the optimal threshold is obtained for both cases. In-

teresting connections between the AoI concept and information theory, signal processing, and

control theory, which are worth of future investigation, are also discussed in this chapter.

Yin Sun, Igor Kadota, Rajat Talak, and Eytan Modiano

October 2019

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