This paper characterizes the structure of the Age of Information (AoI)-optimal policy in wireless powered communication systems while accounting for the time and energy costs of generating status updates at the source nodes. In particular, for a single source-destination pair in which a radio frequency (RF)-powered source sends status updates about some physical process to a destination node, we minimize the long-term average AoI at the destination node. The problem is modeled as an average cost Markov Decision Process (MDP) in which, the generation times of status updates at the source, the transmissions of status updates from the source to the destination, and the wireless energy transfer (WET) are jointly optimized. After proving the monotonicity property of the value function associated with the MDP, we analytically demonstrate that the AoI-optimal policy has a threshold-based structure w.r.t. the state variables. Our numerical results verify the analytical findings and reveal the impact of state variables on the structure of the AoI-optimal policy. Our results also demonstrate the impact of system design parameters on the optimal achievable average AoI as well as the superiority of our proposed joint sampling and updating policy w.r.t. the generate-at-will policy.
In this paper, for the discrete time status updating system with infinite size, we derive the explicit expression of average age of information (AoI), and the AoI's stationary distribution. Based on the discussions of difference between finite and infinite size status updating systems, we successfully characterize the random dynamics of system's AoI using a two-dimensional state vector, which simultaneously tracks the real time AoI and the age of packet currently under service. We constitute the two-dimensional age process and completely solve all the stationary probabilities. Then, as one of …
In this paper, we consider performing packet managements in discrete time status updating system, focusing on determining the stationary AoI-distribution of the system. Firstly, let the queue model be Ber/G/1/1, we obtain the AoI-distribution by introducing a two-dimensional AoI-stochastic process and solving its steady state, which describes the random evolutions of AoI and age of packet in system simultaneously. In this case, actually we analyze a more general queue called probabilistic preemption Ber/G/1/1, where the packet service is allowed to be preempted with certain probabilities. As a…
In this paper we consider the age of information (AoI) of a status updating system with a relay, where the updates are delivered to destination either from the direct line or the two-hop link via the relay. An updating packet generated at source is sent to receiver and the relay simultaneously. When the direct packet transmission fails, the relay replaces the source and retransmits the packet until it is eventually obtained at the receiver side. Assume that the propagation delay on each link is one time slot, we determine the stationary distribution of the AoI for three cases: (a) relay has no…
We examine multiple independent sources providing status updates to a monitor through simple queues. We formulate an Age of Information (AoI) timeliness metric and derive a general result for the AoI that is applicable to a wide variety of multiple source service systems. For first-come first-served and two types of last-come first-served systems with Poisson arrivals and exponential service times, we find the region of feasible average status ages for multiple updating sources. We then use these results to characterize how a service facility can be shared among multiple updating sources. A ne…
In this paper, we consider the age of information (AoI) of a discrete time status updating system, focusing on finding the stationary AoI distribution assuming that the Ber/G/1/1 queue is used. Following the standard queueing theory, we show that by invoking a two-dimensional state vector which tracks the AoI and packet age in system simultaneously, the stationary AoI distribution can be derived by analyzing the steady state of the constituted two-dimensional stochastic process. We give the general formula of the AoI distribution and calculate the explicit expression when the service time is a…
In this paper, we consider a status updating system where updates are generated at a constant rate at $K$ sources and sent to the corresponding recipients through a noise-free broadcast channel. We assume that perfect channel state information (CSI) is available at the transmitter before each transmission, and the transmitter is able to utilize the CSI information to precode the updates. Our object is to design optimal precoding schemes to minimize the summed average \emph{age of information} (AoI) at the recipients. Under various assumptions on the size of each update $B$, the number of trans…
Consider an energy harvesting (EH) sensor that continuously monitors a system and sends time-stamped status update to a destination. The sensor harvests energy from nature and uses it to power its updating operations. The destination keeps track of the system status through the successfully received updates. With the recently introduced information freshness metric "Age of Information" (AoI), our objective is to design optimal online status updating policy to minimize the long-term average AoI at the destination, subject to the energy causality constraint at the sensor. Due to the noisy channe…
The extreme or maximum age of information (AoI) is analytically studied for wireless communication systems. In particular, a wireless powered single-antenna source node and a receiver (connected to the power grid) equipped with multiple antennas are considered when operated under independent Rayleigh-faded channels. Via the extreme value theory and its corresponding statistical features, we demonstrate that the extreme AoI converges to the Gumbel distribution whereas its corresponding parameters are obtained in straightforward closed-form expressions. Capitalizing on this result, the risk of t…
Caching has been regarded as a promising technique to alleviate energy consumption of sensors in Internet of Things (IoT) networks by responding to users' requests with the data packets stored in the edge caching node (ECN). For real-time applications in caching enabled IoT networks, it is essential to develop dynamic status update strategies to strike a balance between the information freshness experienced by users and energy consumed by the sensor, which, however, is not well addressed. In this paper, we first depict the evolution of information freshness, in terms of age of information (AoI…
We propose a frame slotted ALOHA (FSA)-based protocol for a random access network where sources transmit status updates to their intended destinations. We evaluate the effect of such a protocol on the network's timeliness performance using the Age of Information (AoI) metric. Specifically, we leverage tools from stochastic geometry to model the spatial positions of the source-destination pairs and capture the entanglement amongst the nodes' spatial-temporal attributes through the interference they caused to each other. We derive analytical expressions for the average and variance of AoI over a…
This paper considers a multi-source real-time updating system in which an energy harvesting (EH)-powered transmitter node has multiple sources generating status updates about several physical processes. The status updates are then sent to a destination node where the freshness of each status update is measured in terms of Age of Information (AoI). The status updates of each source and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. Unlike most of …
We study the average Age of Information (AoI) and peak AoI (PAoI) of a dual-queue status update system that monitors a common stochastic process. Although the double queue parallel transmission is instrumental in reducing AoI, the out of order of data arrivals also imposes a significant challenge to the performance analysis. We consider two settings: the M-M system where the service time of two servers is exponentially distributed; the M-D system in which the service time of one server is exponentially distributed and that of the other is deterministic. For the two dual-queue systems, closed-f…
This paper investigates the age of information (AoI) for a radio frequency (RF) energy harvesting (EH) enabled network, where a sensor first scavenges energy from a wireless power station and then transmits the collected status update to a sink node. To capture the thirst for the fresh update becoming more and more urgent as time elapsing, urgency-aware AoI (U-AoI) is defined, which increases exponentially with time between two received updates. Due to EH, some waiting time is required at the sensor before transmitting the status update. To find the optimal transmission policy, an optimization…
We consider a system consisting of a library of time-varying files, a server that at all times observes the current version of all files, and a cache that at the beginning stores the current versions of all files but afterwards has to update %fresh versions of these files from the server. Unlike previous works, the update duration is not constant but depends on the file and its Age of Information (AoI), i.e., of the time elapsed since it was last updated. The goal of this work is to design an update policy that minimizes the average AoI of all files with respect to a given popularity distribut…
We consider a novel intermittent status updating model where an energy harvesting node with an intermittent energy source performs status updating to a receiver through non-preemptive sensing and transmission operations. Each operation costs a single energy recharge of the node and the node cannot harvest energy while in operation. The sensing time for each update is independent with a general distribution. The transmission queue has a single server receiving packets generated after sensing operation, general service time distribution and a single data buffer to save the latest arriving update…
Age of Information (AoI) is a key metric to understand data freshness in Internet of Things (IoT) devices. In this paper we analyse an intermittently-powered IoT sensor - with mixed-memory (volatile and non-volatile) architecture - that uses a Time-Dependent Checkpointing (TDC) scheme. We derive the average Peak Age of Information (PAoI) and average AoI of the system, and use these metrics to understand which device parameters most significantly influence performance. We go on to consider how the average PAoI of a mixed-memory system compares with entirely volatile or entirely non-volatile arc…
A status updating system is considered in which a source updates a destination over an erasure channel. The utility of the updates is measured through a function of their age-of-information (AoI), which assesses their freshness. Correlated with the status updates is another process that needs to be kept private from the destination. Privacy is measured through a leakage function that depends on the amount and time of the status updates received: stale updates are more private than fresh ones. Different from most of the current AoI literature, a post-sampling waiting time is introduced in order…
Age of Information (AoI) has attracted much attention recently due to its capability of characterizing the freshness of information. To improve information freshness over fading channels, efficient scheduling methods are highly desired for wireless transmissions. However, due to the channel instability and arrival randomness, optimizing AoI is very challenging. In this paper, we are interested in the AoI-optimal transmissions with rate-adaptive transmission schemes in a buffer-aware system. More specifically, we utilize a probabilistic scheduling method to minimize the AoI while satisfying an …
A status updating system is considered in which multiple data sources generate packets to be delivered to a destination through a shared energy harvesting sensor. Only one source's data, when available, can be transmitted by the sensor at a time, subject to energy availability. Transmissions are prune to erasures, and each successful transmission constitutes a status update for its corresponding source at the destination. The goal is to schedule source transmissions such that the collective long-term average age-of-information (AoI) is minimized. AoI is defined as the time elapsed since the la…
In this paper, we consider an information update system where a wireless sensor sends timely updates to the destination over an erasure channel with the supply of harvested energy and reliable backup energy. The metric Age of Information(AoI) is adopted 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 by formulating an infinite state Markov decision process(MDP). The optimal information updating policy is proved to have a thresh…
Age of information (AoI), a metric to analyse data freshness, is of interest for time-critical applications in upcoming wireless networks. Besides, wireless power transfer (WPT) is also essential to prolong lifetime of a wireless sensor network. Thus, we study a flat-fading wireless powered cooperative network, wherein a source and a relay charge their finite-sized capacitors by harvesting energy from a remote power station. For two conventional decode-and-forward (DF) and amplify-and-forward (AF) relaying, average AoI and peak AoI (PAoI) are studied to show how the randomness of the data/powe…
On the Distribution of Age of Information in Time-varying Updating Systems
School of Management, Huazhong University of Science and Technology（华中科技大学管理学院）；Department of Physics and Astronomy, University of Victoria（维多利亚大学物理与天文系）；Department of Electrical Engineering and Computer Science, Syracuse University（雪城大学电气与计算机工程系）
Consider an energy harvesting node where generation of a status update message takes non-negligible time due to sensing, computing and analytics operations performed before making update transmissions. The node has to harmonize its (re)transmission strategy with the sensing/computing. We call this general set of problems intermittent status updating. In this paper, we consider intermittent status updating through non-preemptive sensing/computing (S/C) and transmission (Tx) operations, each costing a single energy recharge of the node, through an erasure channel with (a) perfect channel feedbac…
This paper proposes a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided wireless-powered non-orthogonal multiple access (NOMA) system, which includes an access point (AP), a STAR-RIS, and two non-orthogonal users located at both sides of the STAR-RIS. In this system, the users first harvest the radio-frequency energy from the AP in the downlink, then adopt the harvested energy to transmit information to the AP in the uplink concurrently. Two policies are considered for the proposed system. The first one assumes that the time-switching protocol is used…
Age-of-Information (AoI) is an application layer metric that has been widely adopted to quantify the information freshness of each information source. However, few works address the impact of probabilistic transmission failures on satisfying the harsh AoI requirement of each source, which is of critical importance in a great number of wireless-powered real-time applications. In this paper, we investigate the transmission scheduling problem of maximizing throughput over wireless channels under different time-average AoI requirements for heterogeneous information sources. When the channel reliab…
In this paper, we aim to establish the connection between Age of Information (AoI) in network theory, information uncertainty in information theory, and detection delay in time series analysis. We consider a dynamic system whose state changes at discrete time points, and a state change won't be detected until an update generated after the change point is delivered to the destination for the first time. We introduce an information theoretic metric to measure the information freshness at the destination, and name it as generalized Age of Information (GAoI). We show that under any state-independe…
We consider an Internet-of-Things (IoT) system in which an energy harvesting powered sensor node monitors the phenomenon of interest and transmits its observations to a remote monitor over a Gaussian channel. We measure the timeliness of the signals recovered by the monitor using age of information (AoI), which could be reduced by transmitting more observations to the monitor. We evaluate the corresponding distortion with the mean-squared error (MSE) metric, which would be reduced if a larger transmit power and a larger source coding rate were used. Since the energy harvested by the sensor nod…
The effective operation of time-critical Internet of things (IoT) applications requires real-time reporting of fresh status information of underlying physical processes. In this paper, a real-time IoT monitoring system is considered, in which the IoT devices sample a physical process with a sampling cost and send the status packet to a given destination with an updating cost. This joint status sampling and updating process is designed to minimize the average age of information (AoI) at the destination node under an average energy cost constraint at each device. This is formulated as an infinit…
In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions…
This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form of status updates to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI). Unlike most of the existi…
A status updating system is considered in which data from multiple sources are sampled by an energy harvesting sensor and transmitted to a remote destination through an erasure channel. The goal is to deliver status updates of all sources in a timely manner, such that the cumulative long-term average age-of-information (AoI) is minimized. The AoI for each source is defined as the time elapsed since the generation time of the latest successful status update received at the destination from that source. Transmissions are subject to energy availability, which arrives in units according to a Poiss…
Sensor sources submit updates to a monitor through an unslotted, uncoordinated, unreliable multiple access collision channel. The channel is unreliable; a collision-free transmission is received successfully at the monitor with some transmission success probability. For an infinite-user model in which the sensors collectively transmit updates as a Poisson process and each update has an independent exponential transmission time, a stochastic hybrid system (SHS) approach is used to derive the average age of information (AoI) as a function of the offered load and the transmission success probabil…
We study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to s…
In this paper, we consider an information update system where wireless sensor sends timely updates to the destination over a random blocking terahertz channel with the supply of harvested energy and reliable energy backup. The paper aims to find the optimal information updating policy that minimize the time-average weighted sum of the Age of information(AoI) and the reliable energy costs by formulating an infinite state Markov decision process(MDP). With the derivation of the monotonicity of value function on each component, the optimal information updating policy is proved to have a threshold…
Applications like environmental sensing, and health and activity sensing, are supported by networks of devices (nodes) that send periodic packet transmissions over the wireless channel to a sink node. We look at simple abstractions that capture the following commonalities of such networks (a) the nodes send periodically sensed information that is temporal and must be delivered in a timely manner, (b) they share a multiple access channel and (c) channels between the nodes and the sink are unreliable (packets may be received in error) and differ in quality. We consider scheduled access and slott…
In Internet of Things (IoT), the freshness of status updates is crucial for mission-critical applications. In this regard, it is suggested to quantify the freshness of updates by using Age of Information (AoI) from the receiver's perspective. Specifically, the AoI measures the freshness over time. However, the freshness in the content is neglected. In this paper, we introduce an age-based utility, named as Age of Changed Information (AoCI), which captures both the passage of time and the change of information content. By modeling the underlying physical process as a discrete time Markov chain,…
The notion of timely status updating is investigated in the context of cloud computing. Measurements of a time-varying process of interest are acquired by a sensor node, and uploaded to a cloud server to undergo some required computations. These computations consume random amounts of service time that are independent and identically distributed across different uploads. After the computations are done, the results are delivered to a monitor, constituting an update. The goal is to keep the monitor continuously fed with fresh updates over time, which is assessed by an age-of-information (AoI) me…
In this paper, we examine a status updating system where updates generated by the source are sent to the monitor through an erasure channel. We assume each update consists of $k$ symbols and the symbol erasure in each time slot follows an independent and identically distributed (i.i.d.) Bernoulli process. We assume rateless coding scheme is adopted at the transmitter and an update can be successfully decoded if $k$ coded symbols are received successfully. We assume perfect feedback available at the source, so that it knows whether a transmitted symbol has been erased instantly. Then, at the be…
In this article, we provide an accessible introduction to the emerging idea of Age of Information (AoI) that quantifies freshness of information and explore its possible role in the efficient design of freshness-aware Internet of Things (IoT). We start by summarizing the concept of AoI and its variants with emphasis on the differences between AoI and other well-known performance metrics in the literature, such as throughput and delay. Building on this, we explore freshness-aware IoT design for a network in which IoT devices sense potentially different physical processes and are supposed to fre…
Timely status updating is crucial for future applications that involve remote monitoring and control, such as autonomous driving and Industrial Internet of Things (IIoT). Age of Information (AoI) has been proposed to measure the freshness of status updates. However, it is incapable of capturing critical systematic context information that indicates the time-varying importance of status information, and the dynamic evolution of status. In this paper, we propose a context-based metric, namely the Urgency of Information (UoI), to evaluate the timeliness of status updates. Compared to AoI, the new…
Age of information (AoI), a notion that measures the information freshness, is an essential performance measure for time-critical applications in Internet of Things (IoT). With the surge of computing resources at the IoT devices, it is possible to preprocess the information packets that contain the status update before sending them to the destination so as to alleviate the transmission burden. However, the additional time and energy expenditure induced by computing also make the optimal updating a non-trivial problem. In this paper, we consider a time-critical IoT system, where the IoT device …
The recent development in Internet of Things necessitates caching of dynamic contents, where new versions of contents become available around-the-clock and thus timely update is required to ensure their relevance. The age of information (AoI) is a performance metric that evaluates the freshness of contents. Existing works on AoI-optimization of cache content update algorithms focus on minimizing the long-term average AoI of all cached contents. Sometimes user requests that need to be served in the future are known in advance and can be stored in user request queues. In this paper, we propose d…
Consider an energy harvesting sensor continuously monitors a system and sends time-stamped status update to a destination. The destination keeps track of the system status through the received updates. Under the energy causality constraint at the sensor, our objective is to design an optimal online status updating policy to minimize the long-term average Age of Information (AoI) at the destination. We focus on the scenario where the the channel between the source and the destination is noisy, and each transmitted update may fail independently with a constant probability. We assume there is no …
We consider a status updating system where having timely knowledge about the information source at the destination (monitor) is of utmost importance. By utilizing the age of information (AoI) metric, the freshness of status update over an erasure channel is investigated. Due to the erasure nature of the update transmission, an error-free feedback channel from the monitor to the source is necessary for reducing AoI. Each status update contains $K$ packets which can be sent through the channel one at a time. At each channel use, one status update is available from the information source. Dependi…
