entropy-logo

Journal Browser

Journal Browser

Age of Information: Concept, Metric and Tool for Network Control

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (9 October 2022) | Viewed by 35947

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors


E-Mail Website
Guest Editor
ECE Department, University of Maryland, College Park, MD 20742, USA
Interests: information theory; communication theory; multi-user systems; communication networks; satellite systems; systems theory; stochastic systems; optimization; signal processing; wireless communications; age of information

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering, Auburn University, Auburn, AL 36849-5201, USA
Interests: age of information; information freshness; wireless networks; remote estimation; machine learning

Special Issue Information

Dear Colleagues,

The concept of information freshness has developed over the last few years into an active and rapidly growing area of research. It has become known as the Age of Information (AoI). After its initial formal introduction, it became clear that it was very relevant (if not crucial) for numerous applications, ranging from autonomous vehicle systems, internet of things, real-time computing to database access, caching, and wireless communications. More importantly, the combination of transmission delay and sampling rate that are involved in the formulation of the AoI concept made it clear that there are far-reaching consequences in the relationship between signal processing, information theory, and control theory at a fundamental level. 

In this Special Issue, we aim at attracting contributions that span the full range of applications and theoretical foundations of the AoI concept, which, in fact, is also a performance metric and an analysis tool. Of special interest is the role of AoI in bridging different disciplines and the use of AoI in the analysis and optimization involved in important applications.

Prof. Anthony Ephremides
Prof. Yin Sun
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (16 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

32 pages, 717 KiB  
Article
Distribution of the Age of Gossip in Networks
by Mohamed A. Abd-Elmagid and Harpreet S. Dhillon
Entropy 2023, 25(2), 364; https://doi.org/10.3390/e25020364 - 16 Feb 2023
Cited by 11 | Viewed by 1782
Abstract
We study a general setting of gossip networks in which a source node forwards its measurements (in the form of status updates) about some observed physical process to a set of monitoring nodes according to independent Poisson processes. Furthermore, each monitoring node sends [...] Read more.
We study a general setting of gossip networks in which a source node forwards its measurements (in the form of status updates) about some observed physical process to a set of monitoring nodes according to independent Poisson processes. Furthermore, each monitoring node sends status updates about its information status (about the process observed by the source) to the other monitoring nodes according to independent Poisson processes. We quantify the freshness of the information available at each monitoring node in terms of Age of Information (AoI). While this setting has been analyzed in a handful of prior works, the focus has been on characterizing the average (i.e., marginal first moment) of each age process. In contrast, we aim to develop methods that allow the characterization of higher-order marginal or joint moments of the age processes in this setting. In particular, we first use the stochastic hybrid system (SHS) framework to develop methods that allow the characterization of the stationary marginal and joint moment generating functions (MGFs) of age processes in the network. These methods are then applied to derive the stationary marginal and joint MGFs in three different topologies of gossip networks, with which we derive closed-form expressions for marginal or joint high-order statistics of age processes, such as the variance of each age process and the correlation coefficients between all possible pairwise combinations of age processes. Our analytical results demonstrate the importance of incorporating the higher-order moments of age processes in the implementation and optimization of age-aware gossip networks rather than just relying on their average values. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

23 pages, 732 KiB  
Article
Optimizing Urgency of Information through Resource Constrained Joint Sensing and Transmission
by Zhuoxuan Ju, Parisa Rafiee and Omur Ozel
Entropy 2022, 24(11), 1624; https://doi.org/10.3390/e24111624 - 9 Nov 2022
Cited by 6 | Viewed by 1553
Abstract
Applications requiring services from modern wireless networks, such as those involving remote control and supervision, call for maintaining the timeliness of information flows. Current research and development efforts for 5G, Internet of things, and artificial intelligence technologies will benefit from new notions of [...] Read more.
Applications requiring services from modern wireless networks, such as those involving remote control and supervision, call for maintaining the timeliness of information flows. Current research and development efforts for 5G, Internet of things, and artificial intelligence technologies will benefit from new notions of timeliness in designing novel sensing, computing, and transmission strategies. The age of information (AoI) metric and a recent related urgency of information (UoI) metric enable promising frameworks in this direction. In this paper, we consider UoI optimization in an interactive point-to-point system when the updating terminal is resource constrained to send updates and receive/sense the feedback of the status information at the receiver. We first propose a new system model that involves Gaussian distributed time increments at the receiving end to design interactive transmission and feedback sensing functions and develop a new notion of UoI suitable for this system. We then formulate the UoI optimization with a new objective function involving a weighted combination of urgency levels at the transmitting and receiving ends. By using a Lyapunov optimization framework, we obtain a decision strategy under energy resource constraints at both transmission and receiving/sensing and show that it can get arbitrarily close to the optimal solution. We numerically study performance comparisons and observe significant improvements with respect to benchmarks. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

28 pages, 1532 KiB  
Article
Optimal Information Update for Energy Harvesting Sensor with Reliable Backup Energy
by Lixin Wang, Fuzhou Peng, Xiang Chen and Shidong Zhou
Entropy 2022, 24(7), 961; https://doi.org/10.3390/e24070961 - 11 Jul 2022
Cited by 1 | Viewed by 1695
Abstract
The timely delivery of status information collected from sensors is critical in many real-time applications, e.g., monitoring and control. In this paper, we consider a scenario where a wireless sensor sends updates to the destination over an erasure channel with the supply of [...] Read more.
The timely delivery of status information collected from sensors is critical in many real-time applications, e.g., monitoring and control. In this paper, we consider a scenario where a wireless sensor sends updates to the destination over an erasure channel with the supply of harvested energy and reliable backup energy. We adopt the metric age of information (AoI) to measure the timeliness of the received updates at the destination. We aim to find the optimal information updating policy that minimizes the time-average weighted sum of the AoI and the reliable backup energy cost. First, when all the environmental statistics are assumed to be known, the optimal information updating policy exists and is proved to have a threshold structure. Based on this special structure, an algorithm for efficiently computing the optimal policy is proposed. Then, for the unknown environment, a learning-based algorithm is employed to find a near-optimal policy. The simulation results verify the correctness of the theoretical derivation and the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

36 pages, 661 KiB  
Article
Age Analysis of Status Updating System with Probabilistic Packet Preemption
by Jixiang Zhang and Yinfei Xu
Entropy 2022, 24(6), 785; https://doi.org/10.3390/e24060785 - 2 Jun 2022
Cited by 5 | Viewed by 1935
Abstract
The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by [...] Read more.
The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

26 pages, 712 KiB  
Article
Using Timeliness in Tracking Infections
by Melih Bastopcu and Sennur Ulukus
Entropy 2022, 24(6), 779; https://doi.org/10.3390/e24060779 - 31 May 2022
Cited by 1 | Viewed by 1627
Abstract
We consider real-time timely tracking of infection status (e.g., COVID-19) of individuals in a population. In this work, a health care provider wants to detect both infected people and people who have recovered from the disease as quickly as possible. In order to [...] Read more.
We consider real-time timely tracking of infection status (e.g., COVID-19) of individuals in a population. In this work, a health care provider wants to detect both infected people and people who have recovered from the disease as quickly as possible. In order to measure the timeliness of the tracking process, we use the long-term average difference between the actual infection status of the people and their real-time estimate by the health care provider based on the most recent test results. We first find an analytical expression for this average difference for given test rates, infection rates and recovery rates of people. Next, we propose an alternating minimization-based algorithm to find the test rates that minimize the average difference. We observe that if the total test rate is limited, instead of testing all members of the population equally, only a portion of the population may be tested in unequal rates calculated based on their infection and recovery rates. Next, we characterize the average difference when the test measurements are erroneous (i.e., noisy). Further, we consider the case where the infection status of individuals may be dependent, which occurs when an infected person spreads the disease to another person if they are not detected and isolated by the health care provider. In addition, we consider an age of incorrect information-based error metric where the staleness metric increases linearly over time as long as the health care provider does not detect the changes in the infection status of the people. Through extensive numerical results, we observe that increasing the total test rate helps track the infection status better. In addition, an increased population size increases diversity of people with different infection and recovery rates, which may be exploited to spend testing capacity more efficiently, thereby improving the system performance. Depending on the health care provider’s preferences, test rate allocation can be adjusted to detect either the infected people or the recovered people more quickly. In order to combat any errors in the test, it may be more advantageous for the health care provider to not test everyone, and instead, apply additional tests to a selected portion of the population. In the case of people with dependent infection status, as we increase the total test rate, the health care provider detects the infected people more quickly, and thus, the average time that a person stays infected decreases. Finally, the error metric needs to be chosen carefully to meet the priorities of the health care provider, as the error metric used greatly influences who will be tested and at what test rate. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

27 pages, 1269 KiB  
Article
Implementation and Evaluation of Age-Aware Downlink Scheduling Policies in Push-Based and Pull-Based Communication
by Tahir Kerem Oğuz, Elif Tuğçe Ceran, Elif Uysal and Tolga Girici
Entropy 2022, 24(5), 673; https://doi.org/10.3390/e24050673 - 11 May 2022
Cited by 8 | Viewed by 1962
Abstract
As communication systems evolve to better cater to the needs of machine-type applications such as remote monitoring and networked control, advanced perspectives are required for the design of link layer protocols. The age of information (AoI) metric has firmly taken its place in [...] Read more.
As communication systems evolve to better cater to the needs of machine-type applications such as remote monitoring and networked control, advanced perspectives are required for the design of link layer protocols. The age of information (AoI) metric has firmly taken its place in the literature as a metric and tool to measure and control the data freshness demands of various applications. AoI measures the timeliness of transferred information from the point of view of the destination. In this study, we experimentally investigate AoI of multiple packet flows on a wireless multi-user link consisting of a transmitter (base station) and several receivers, implemented using software-defined radios (SDRs). We examine the performance of various scheduling policies under push-based and pull-based communication scenarios. For the push-based communication scenario, we implement age-aware scheduling policies from the literature and compare their performance with those of conventional scheduling methods. Then, we investigate the query age of information (QAoI) metric, an adaptation of the AoI concept for pull-based scenarios. We modify the former age-aware policies to propose variants that have a QAoI minimization objective. We share experimental results obtained in a simulation environment as well as on the SDR testbed. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

15 pages, 703 KiB  
Article
Age of Information Minimization for Radio Frequency Energy-Harvesting Cognitive Radio Networks
by Juan Sun, Shubin Zhang, Changsong Yang and Liang Huang
Entropy 2022, 24(5), 596; https://doi.org/10.3390/e24050596 - 24 Apr 2022
Cited by 5 | Viewed by 2130
Abstract
The Age of Information (AoI) measures the freshness of information and is a critic performance metric for time-sensitive applications. In this paper, we consider a radio frequency energy-harvesting cognitive radio network, where the secondary user harvests energy from the primary users’ transmissions and [...] Read more.
The Age of Information (AoI) measures the freshness of information and is a critic performance metric for time-sensitive applications. In this paper, we consider a radio frequency energy-harvesting cognitive radio network, where the secondary user harvests energy from the primary users’ transmissions and opportunistically accesses the primary users’ licensed spectrum to deliver the status-update data pack. We aim to minimize the AoI subject to the energy causality and spectrum constraints by optimizing the sensing and update decisions. We formulate the AoI minimization problem as a partially observable Markov decision process and solve it via dynamic programming. Simulation results verify that our proposed policy is significantly superior to the myopic policy under different parameter settings. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

22 pages, 496 KiB  
Article
On the Age of Information in a Two-User Multiple Access Setup
by Mehrdad Salimnejad and Nikolaos Pappas
Entropy 2022, 24(4), 542; https://doi.org/10.3390/e24040542 - 12 Apr 2022
Cited by 8 | Viewed by 2308
Abstract
This work considers a two-user multiple access channel in which both users have Age of Information (AoI)-oriented traffic with different characteristics. More specifically, the first user has external traffic and cannot control the generation of status updates, and the second user monitors a [...] Read more.
This work considers a two-user multiple access channel in which both users have Age of Information (AoI)-oriented traffic with different characteristics. More specifically, the first user has external traffic and cannot control the generation of status updates, and the second user monitors a sensor and transmits status updates to the receiver according to a generate-at-will policy. The receiver is equipped with multiple antennas and the transmitters have single antennas; the channels are subject to Rayleigh fading and path loss. We analyze the average AoI of the first user for a discrete-time first-come-first-served (FCFS) queue, last-come-first-served (LCFS) queue, and queue with packet replacement. We derive the AoI distribution and the average AoI of the second user for a threshold policy. Then, we formulate an optimization problem to minimize the average AoI of the first user for the FCFS and LCFS with preemption queue discipline to maintain the average AoI of the second user below a given level. The constraints of the optimization problem are shown to be convex. It is also shown that the objective function of the problem for the first-come-first-served queue policy is non-convex, and a suboptimal technique is introduced to effectively solve the problem using the algorithms developed for solving a convex optimization problem. Numerical results illustrate the performance of the considered optimization algorithm versus the different parameters of the system. Finally, we discuss how the analytical results of this work can be extended to capture larger setups with more than two users. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

22 pages, 559 KiB  
Article
On the Value of Information in Status Update Systems
by Peng Zou and Suresh Subramaniam
Entropy 2022, 24(4), 449; https://doi.org/10.3390/e24040449 - 24 Mar 2022
Cited by 2 | Viewed by 1757
Abstract
The age of information (AoI) is now well established as a metric that measures the freshness of information delivered to a receiver from a source that generates status updates. This paper is motivated by the inherent value of packets arising in many cyber-physical [...] Read more.
The age of information (AoI) is now well established as a metric that measures the freshness of information delivered to a receiver from a source that generates status updates. This paper is motivated by the inherent value of packets arising in many cyber-physical applications (e.g., due to precision of the information content or an alarm message). In contrast to AoI, which considers all packets are of equal importance or value, we consider status update systems with update packets carrying values as well as their generated time stamps. A status update packet has a random initial value at the source and a deterministic deadline after which its value vanishes (called ultimate staleness). In our model, the value of a packet either remains constant until the deadline or decreases in time (even after reception) starting from its generation to the deadline when it vanishes. We consider two metrics for the value of information (VoI) at the receiver: sum VoI is the sum of the current values of all packets held by the receiver, whereas packet VoI is the value of a packet at the instant it is delivered to the receiver. We investigate various queuing disciplines under potential dependence between value and service time and provide closed form expressions for both average sum VoI and packet VoI at the receiver. Numerical results illustrate the average VoI for different scenarios and relations between average sum VoI and average packet VoI. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

39 pages, 602 KiB  
Article
Scheduling to Minimize Age of Incorrect Information with Imperfect Channel State Information
by Yutao Chen and Anthony Ephremides
Entropy 2021, 23(12), 1572; https://doi.org/10.3390/e23121572 - 25 Nov 2021
Cited by 14 | Viewed by 2369
Abstract
In this paper, we study a slotted-time system where a base station needs to update multiple users at the same time. Due to the limited resources, only part of the users can be updated in each time slot. We consider the problem of [...] Read more.
In this paper, we study a slotted-time system where a base station needs to update multiple users at the same time. Due to the limited resources, only part of the users can be updated in each time slot. We consider the problem of minimizing the Age of Incorrect Information (AoII) when imperfect Channel State Information (CSI) is available. Leveraging the notion of the Markov Decision Process (MDP), we obtain the structural properties of the optimal policy. By introducing a relaxed version of the original problem, we develop the Whittle’s index policy under a simple condition. However, indexability is required to ensure the existence of Whittle’s index. To avoid indexability, we develop Indexed priority policy based on the optimal policy for the relaxed problem. Finally, numerical results are laid out to showcase the application of the derived structural properties and highlight the performance of the developed scheduling policies. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

19 pages, 465 KiB  
Article
Age of Information of Parallel Server Systems with Energy Harvesting
by Josu Doncel
Entropy 2021, 23(11), 1549; https://doi.org/10.3390/e23111549 - 21 Nov 2021
Viewed by 1554
Abstract
Motivated by current communication networks in which users can choose different transmission channels to operate and also by the recent growth of renewable energy sources, we study the average Age of Information of a status update system that is formed by two parallel [...] Read more.
Motivated by current communication networks in which users can choose different transmission channels to operate and also by the recent growth of renewable energy sources, we study the average Age of Information of a status update system that is formed by two parallel homogeneous servers and such that there is an energy source that feeds the system following a random process. An update, after getting service, is delivered to the monitor if there is energy in a battery. However, if the battery is empty, the status update is lost. We allow preemption of updates in service and we assume Poisson generation times of status updates and exponential service times. We show that the average Age of Information can be characterized by solving a system with eight linear equations. Then, we show that, when the arrival rate to both servers is large, the average Age of Information is one divided by the sum of the service rates of the servers. We also perform a numerical analysis to compare the performance of our model with that of a single server with energy harvesting and to study in detail the aforementioned convergence result. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

16 pages, 440 KiB  
Article
Age-Aware Utility Maximization in Relay-Assisted Wireless Powered Communication Networks
by Ning Luan, Ke Xiong, Zhifei Zhang, Haina Zheng, Yu Zhang, Pingyi Fan and Gang Qu
Entropy 2021, 23(9), 1177; https://doi.org/10.3390/e23091177 - 7 Sep 2021
Viewed by 1796
Abstract
This article investigates a relay-assisted wireless powered communication network (WPCN), where the access point (AP) inspires the auxiliary nodes to participate together in charging the sensor, and then the sensor uses its harvested energy to send status update packets to the AP. An [...] Read more.
This article investigates a relay-assisted wireless powered communication network (WPCN), where the access point (AP) inspires the auxiliary nodes to participate together in charging the sensor, and then the sensor uses its harvested energy to send status update packets to the AP. An incentive mechanism is designed to overcome the selfishness of the auxiliary node. In order to further improve the system performance, we establish a Stackelberg game to model the efficient cooperation between the AP–sensor pair and auxiliary node. Specifically, we formulate two utility functions for the AP–sensor pair and the auxiliary node, and then formulate two maximization problems respectively. As the former problem is non-convex, we transform it into a convex problem by introducing an extra slack variable, and then by using the Lagrangian method, we obtain the optimal solution with closed-form expressions. Numerical experiments show that the larger the transmit power of the AP, the smaller the age of information (AoI) of the AP–sensor pair and the less the influence of the location of the auxiliary node on AoI. In addition, when the distance between the AP and the sensor node exceeds a certain threshold, employing the relay can achieve better AoI performance than non-relaying systems. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

21 pages, 722 KiB  
Article
A UoI-Optimal Policy for Timely Status Updates with Resource Constraint
by Lehan Wang, Jingzhou Sun, Yuxuan Sun, Sheng Zhou and Zhisheng Niu
Entropy 2021, 23(8), 1084; https://doi.org/10.3390/e23081084 - 20 Aug 2021
Cited by 4 | Viewed by 3100
Abstract
Timely status updates are critical in remote control systems such as autonomous driving and the industrial Internet of Things, where timeliness requirements are usually context dependent. Accordingly, the Urgency of Information (UoI) has been proposed beyond the well-known Age of Information (AoI) by [...] Read more.
Timely status updates are critical in remote control systems such as autonomous driving and the industrial Internet of Things, where timeliness requirements are usually context dependent. Accordingly, the Urgency of Information (UoI) has been proposed beyond the well-known Age of Information (AoI) by further including context-aware weights which indicate whether the monitored process is in an emergency. However, the optimal updating and scheduling strategies in terms of UoI remain open. In this paper, we propose a UoI-optimal updating policy for timely status information with resource constraint. We first formulate the problem in a constrained Markov decision process and prove that the UoI-optimal policy has a threshold structure. When the context-aware weights are known, we propose a numerical method based on linear programming. When the weights are unknown, we further design a reinforcement learning (RL)-based scheduling policy. The simulation reveals that the threshold of the UoI-optimal policy increases as the resource constraint tightens. In addition, the UoI-optimal policy outperforms the AoI-optimal policy in terms of average squared estimation error, and the proposed RL-based updating policy achieves a near-optimal performance without the advanced knowledge of the system model. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

17 pages, 464 KiB  
Article
Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process
by Zijing Wang, Mihai-Alin Badiu and Justin P. Coon
Entropy 2021, 23(8), 940; https://doi.org/10.3390/e23080940 - 23 Jul 2021
Cited by 4 | Viewed by 2188
Abstract
The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information [...] Read more.
The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

19 pages, 468 KiB  
Article
Channel Quality-Based Optimal Status Update for Information Freshness in Internet of Things
by Fuzhou Peng, Xiang Chen and Xijun Wang
Entropy 2021, 23(7), 912; https://doi.org/10.3390/e23070912 - 18 Jul 2021
Cited by 1 | Viewed by 2435
Abstract
This paper investigates the status updating policy for information freshness in Internet of things (IoT) systems, where the channel quality is fed back to the sensor at the beginning of each time slot. Based on the channel quality, we aim to strike a [...] Read more.
This paper investigates the status updating policy for information freshness in Internet of things (IoT) systems, where the channel quality is fed back to the sensor at the beginning of each time slot. Based on the channel quality, we aim to strike a balance between the information freshness and the update cost by minimizing the weighted sum of the age of information (AoI) and the energy consumption. The optimal status updating problem is formulated as a Markov decision process (MDP), and the structure of the optimal updating policy is investigated. We prove that, given the channel quality, the optimal policy is of a threshold type with respect to the AoI. In particular, the sensor remains idle when the AoI is smaller than the threshold, while the sensor transmits the update packet when the AoI is greater than the threshold. Moreover, the threshold is proven to be a non-increasing function of channel state. A numerical-based algorithm for efficiently computing the optimal thresholds is proposed for a special case where the channel is quantized into two states. Simulation results show that our proposed policy performs better than two baseline policies. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

19 pages, 1746 KiB  
Article
Scheduling Strategy Design Framework for Cyber–Physical System with Non-Negligible Propagation Delay
by Zuoyu An, Shaohua Wu, Tiange Liu, Jian Jiao and Qinyu Zhang
Entropy 2021, 23(6), 714; https://doi.org/10.3390/e23060714 - 4 Jun 2021
Cited by 3 | Viewed by 2167
Abstract
Cyber–physical systems (CPS) have been widely employed as wireless control networks. There is a special type of CPS which is developed from the wireless networked control systems (WNCS). They usually include two communication links: Uplink transmission and downlink transmission. Those two links form [...] Read more.
Cyber–physical systems (CPS) have been widely employed as wireless control networks. There is a special type of CPS which is developed from the wireless networked control systems (WNCS). They usually include two communication links: Uplink transmission and downlink transmission. Those two links form a closed-loop. When such CPS are deployed for time-sensitive applications such as remote control, the uplink and downlink propagation delay are non-negligible. However, existing studies on CPS/WNCS usually ignore the propagation delay of the uplink and downlink channels. In order to achieve the best balance between uplink and downlink transmissions under such circumstances, we propose a heuristic framework to obtain the optimal scheduling strategy that can minimize the long-term average control cost. We model the optimization problem as a Markov decision process (MDP), and then give the sufficient conditions for the existence of the optimal scheduling strategy. We propose the semi-predictive framework to eliminate the impact of the coupling characteristic between the uplink and downlink data packets. Then we obtain the lookup table-based optimal offline strategy and the neural network-based suboptimal online strategy. Numerical simulation shows that the scheduling strategies obtained by this framework can bring significant performance improvements over the existing strategies. Full article
(This article belongs to the Special Issue Age of Information: Concept, Metric and Tool for Network Control)
Show Figures

Figure 1

Back to TopTop