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  1. A source node forwards fresh status updates as a point process to a network of observer nodes. Within the network of observers, these updates are forwarded as point processes from node to node. Each node wishes its knowledge of the source to be as timely as possible. In this network, timeliness at each node is measured by an age of information metric: how old is the timestamp of the freshest received update. This work extends a method for evaluating the average age at each node in the network when nodes forward updates using a memoryless gossip protocol. This method is then demonstrated by age analysis for a simple network.
  2. A source node updates its status as a point process and also forwards its updates to a network of observer nodes. Within the network of observers, these updates are forwarded as point processes from node to node. Each node wishes its knowledge of the source to be as timely as possible. In this network, timeliness is measured by a discrete form of age of information: each status change at the source is referred to as a version and the age at a node is how many versions out of date is its most recent update from the source. This work introduces a method for evaluating the average version age at each node in the network when nodes forward updates using a memoryless gossip protocol. This method is then demonstrated by version age analysis for a collection of simple networks. For gossip on a complete graph with symmetric updating rates, it is shown that each node has average age that grows as the logarithm of the network size.
  3. We quantify, over inter-continental paths, the ageing of TCP packets, throughput and delay for different TCP congestion control algorithms containing a mix of loss-based, delay-based and hybrid congestion control algorithms. In comparing these TCP variants to ACP+, an improvement over ACP, we shed better light on the ability of ACP+ to deliver timely updates over fat pipes and long paths. ACP+ estimates the network conditions on the end-to-end path and adapts the rate of status updates to minimize age. It achieves similar average age as the best (age wise) performing TCP algorithm but at end-to-end throughputs that are two orders of magnitude smaller. We also quantify the significant improvements that ACP+ brings to age control over a shared multiaccess channel.
  4. We consider updating strategies for a local cache which downloads time-sensitive files from a remote server through a bandwidth-constrained link. The files are requested randomly from the cache by local users according to a popularity distribution which varies over time according to a Markov chain structure. We measure the freshness of the requested time-sensitive files through their Age of Information (AoI). The goal is then to minimize the average AoI of all requested files by appropriately designing the local cache’s downloading strategy. To achieve this goal, the original problem is relaxed and cast into a Constrained Markov Decision Problem (CMDP), which we solve using a Lagrangian approach and Linear Programming. Inspired by this solution for the relaxed problem, we propose a practical cache updating strategy that meets all the constraints of the original problem. Under certain assumptions, the practical updating strategy is shown to be optimal for the original problem in the asymptotic regime of a large number of files. For a finite number of files, we show the gain of our practical updating strategy over the traditional square-root-law strategy (which is optimal for fixed non time-varying file popularities) through numerical simulations.
  5. 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 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 distribution. Actually a relaxed problem, close to the original optimization problem, is solved and a practical update policy is derived. The update policy relies on the file popularity and on the functions that characterize the update durations of the files depending on their AoI. Numerical simulations show a significant improvement of this new update policy compared to the so-called square-root policy that is optimal under file-independent and constant update durations.
  6. 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 generate 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 probability. The analysis is then extended to evaluate the individual age of a selected source. When the number of sources and update transmission rate grow large in fixed proportion, the limiting asymptotic individual age is shown to provide an accurate individual age approximation, even for a small number of sources.
  7. A source provides status updates to monitors through a network with state defined by a continuous-time finite Markov chain. An age of information (AoI) metric is used to characterize timeliness by the vector of ages tracked by the monitors. Based on a stochastic hybrid systems (SHS) approach, first order linear differential equations are derived for the temporal evolution of both the moments and the moment generating function (MGF) of the age vector components. It is shown that the existence of a non-negative fixed point for the first moment is sufficient to guarantee convergence of all higher order moments as well as a region of convergence for the stationary MGF vector of the age. The stationary MGF vector is then found for the age on a line network of preemptive memoryless servers. From this MGF, it is found that the age at a node is identical in distribution to the sum of independent exponential service times. This observation is then generalized to linear status sampling networks in which each node receives samples of the update process at each preceding node according to a renewal point process. For each node in the line, the age is shown to be identical in distributionmore »to a sum of independent renewal process age random variables.« less
  8. Multiple sources submit updates to a monitor through an M/M/1 queue. A stochastic hybrid system (SHS) approach is used to derive the average age of information (AoI) for an individual source as a function of the offered load of that source and the competing update traffic offered by other sources. This work corrects an error in a prior analysis. By numerical evaluation, this error is observed to be small and qualitatively insignificant.