Age of Information Scaling in Large Networks with Hierarchical Cooperation

Given $n$ randomly located source-destination (S-D) pairs on a fixed area network that want to communicate with each other, we study the age of information with a particular focus on its scaling as the network size $n$ grows. We propose a three-phase transmission scheme that utilizes \textit{hierarchical cooperation} between users along with \textit{mega update packets} and show that an average age scaling of $O(n^{\alpha(h)}\log n)$ per-user is achievable where $h$ denotes the number of hierarchy levels and $\alpha(h) = \frac{1}{3\cdot2^h+1}$ which tends to $0$ as $h$ increases such that asymptotically average age scaling of the proposed scheme is $O(\log n)$. To the best of our knowledge, this is the best average age scaling result in a status update system with multiple S-D pairs

Timely Group Updating

We consider two closely related problems: anomaly detection in sensor networks and testing for infections in human populations. In both problems, we have $n$ nodes (sensors, humans), and each node exhibits an event of interest (anomaly, infection) with probability $p$. We want to keep track of the anomaly/infection status of all nodes at a central location. We develop a $group$ $updating$ scheme, akin to group testing, which updates a central location about the status of each member of the population by appropriately grouping their individual status. Unlike group testing, which uses the expected number of tests as a metric, in group updating, we use the expected age of information at the central location as a metric. We determine the optimal group size to minimize the age of information. We show that, when $p$ is small, the proposed group updating policy yields smaller age compared to a sequential updating policy

Who Should Google Scholar Update More Often?

We consider a resource-constrained updater, such as Google Scholar, which wishes to update the citation records of a group of researchers, who have different mean citation rates (and optionally, different importance coefficients), in such a way to keep the overall citation index as up to date as possible. The updater is resource-constrained and cannot update citations of all researchers all the time. In particular, it is subject to a total update rate constraint that it needs to distribute among individual researchers. We use a metric similar to the age of information: the long-term average difference between the actual citation numbers and the citation numbers according to the latest updates. We show that, in order to minimize this difference metric, the updater should allocate its total update capacity to researchers proportional to the $square$ $roots$ of their mean citation rates. That is, more prolific researchers should be updated more often, but there are diminishing returns due to the concavity of the square root function. More generally, our paper addresses the problem of optimal operation of a resource-constrained sampler that wishes to track multiple independent counting processes in a way that is as up to date as possible

Age of Information with Gilbert-Elliot Servers and Samplers

We study age of information in a status updating system that consists of a single sampler, i.e., source node, that sends time-sensitive status updates to a single monitor node through a server node. We first consider a Gilbert-Elliot service profile at the server node. In this model, service times at the server node follow a finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state $g$ where the server is faster in state $g$. We determine the time average age experienced by the monitor node and characterize the age-optimal state transition matrix $P$ with and without an average cost constraint on the service operation. Next, we consider a Gilbert-Elliot sampling profile at the source. In this model, the interarrival times follow a finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state $g$ where samples are more frequent in state $g$. We find the time average age experienced by the monitor node and characterize the age-optimal state transition matrix $P$

Freshness-Optimal Caching for Information Updating Systems with Limited Cache Storage Capacity

In this paper, we investigate a cache updating system with a server containing $N$ files, $K$ relays and $M$ users. The server keeps the freshest versions of the files which are updated with fixed rates. Each relay can download the fresh files from the server in a certain period of time. Each user can get the fresh files from any relay as long as the relay has stored the fresh versions of the requested files. Due to the limited storage capacity and updating capacity of each relay, different cache designs will lead to different average freshness of all updating files at users. In order to keep the average freshness as large as possible in the cache updating system, we formulate an average freshness-optimal cache updating problem (AFOCUP) to obtain an optimal cache scheme. However, because of the nonlinearity of the AFOCUP, it is difficult to seek out the optimal cache scheme. As a result, an linear approximate model is suggested by distributing the total update rates completely in accordance with the number of files in the relay in advance. Then we utilize the greedy algorithm to search the optimal cache scheme that is satisfied with the limited storage capacity of each relay. Finally, some numerical examples are provided to illustrate the performance of the approximate solution

Timely Distributed Computation with Stragglers

We consider a status update system in which the update packets need to be processed to extract the embedded useful information. The source node sends the acquired information to a computation unit (CU) which consists of a master node and $n$ worker nodes. The master node distributes the received computation task to the worker nodes. Upon computation, the master node aggregates the results and sends them back to the source node to keep it \emph{updated}. We investigate the age performance of uncoded and coded (repetition coded, MDS coded, and multi-message MDS (MM-MDS) coded) schemes in the presence of stragglers under i.i.d.~exponential transmission delays and i.i.d~shifted exponential computation times. We show that asymptotically MM-MDS coded scheme outperforms the other schemes. Furthermore, we characterize the optimal codes such that the average age is minimized.Comment: Submitted for publicatio

Selective Encoding Policies for Maximizing Information Freshness

An information source generates independent and identically distributed status update messages from an observed random phenomenon which takes $n$ distinct values based on a given pmf. These update packets are encoded at the transmitter node to be sent to a receiver node which wants to track the observed random variable with as little age as possible. The transmitter node implements a selective $k$ encoding policy such that rather than encoding all possible $n$ realizations, the transmitter node encodes the most probable $k$ realizations. We consider three different policies regarding the remaining $n-k$ less probable realizations: $highest$ $k$ $selective$ $encoding$ which disregards whenever a realization from the remaining $n-k$ values occurs; $randomized$ $selective$ $encoding$ which encodes and sends the remaining $n-k$ realizations with a certain probability to further inform the receiver node at the expense of longer codewords for the selected $k$ realizations; and $highest$ $k$ $selective$ $encoding$ $with$ $an$ $empty$ $symbol$ which sends a designated empty symbol when one of the remaining $n-k$ realizations occurs. For all of these three encoding schemes, we find the average age and determine the age-optimal real codeword lengths, including the codeword length for the empty symbol in the case of the latter scheme, such that the average age at the receiver node is minimized. Through numerical evaluations for arbitrary pmfs, we show that these selective encoding policies result in a lower average age than encoding every realization, and find the corresponding age-optimal $k$ values.Comment: Submitted for publication, April 2020. Some text overlap with its conference version arXiv:2001.0997

Information Freshness in Cache Updating Systems

We consider a cache updating system with a source, a cache and a user. There are $n$ files. The source keeps the freshest version of the files which are updated with known rates $\lambda_i$. The cache downloads and keeps the freshest version of the files from the source with rates $c_i$. The user gets updates from the cache with rates $u_i$. When the user gets an update, it either gets a fresh update from the cache or the file at the cache becomes outdated by a file update at the source in which case the user gets an outdated update. We find an analytical expression for the average freshness of the files at the user. Next, we generalize our setting to the case where there are multiple caches in between the source and the user, and find the average freshness at the user. We provide an alternating maximization based method to find the update rates for the cache(s), $c_i$, and for the user, $u_i$, to maximize the freshness of the files at the user. We observe that for a given set of update rates for the user (resp. for the cache), the optimal rate allocation policy for the cache (resp. for the user) is a $threshold$ $policy$, where the optimal update rates for rapidly changing files at the source may be equal to zero. Finally, we consider a system where multiple users are connected to a single cache and find update rates for the cache and the users to maximize the total freshness over all users.Comment: Submitted for publicatio

Closed-Form Whittle's Index-Enabled Random Access for Timely Status Update

We consider a star-topology wireless network for status update where a central node collects status data from a large number of distributed machine-type terminals that share a wireless medium. The Age of Information (AoI) minimization scheduling problem is formulated by the restless multi-armed bandit. A widely-proven near-optimal solution, i.e., the Whittle's index, is derived in closed-form and the corresponding indexability is established. The index is then generalized to incorporate stochastic, periodic packet arrivals and unreliable channels. Inspired by the index scheduling policies which achieve near-optimal AoI but require heavy signaling overhead, a contention-based random access scheme, namely Index-Prioritized Random Access (IPRA), is further proposed. Based on IPRA, terminals that are not urgent to update, indicated by their indices, are barred access to the wireless medium, thus improving the access timeliness. A computer-based simulation shows that IPRA's performance is close to the optimal AoI in this setting and outperforms standard random access schemes. Also, for applications with hard AoI deadlines, we provide reliable deadline guarantee analysis. Closed-form achievable AoI stationary distributions under Bernoulli packet arrivals are derived such that AoI deadline with high reliability can be ensured by calculating the maximum number of supportable terminals and allocating system resources proportionally.Comment: 30 pages, 7 figures, submitted to IEEE Transactions on Communications. arXiv admin note: substantial text overlap with arXiv:1803.0818

Age of Information: An Introduction and Survey

We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications