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Register a new userOn Age of Information for Discrete Time Status Updating System With Ber/G/1/1 Queues
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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 also geometrically distributed. The discrete and continuous AoI are compared, we depict the mean of discrete AoI and that of continuous time AoI for system with M/M/1/1 queue. Although the stationary AoI distribution of some continuous time single-server system has been determined before, in this paper, we shall prove that the standard queueing theory is still appliable to analyze the discrete AoI, which is even stronger than the proposed methods handling the continuous AoI.
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We consider a communication system in which status updates arrive at a source node, and should be transmitted through a network to the intended destination node. The status updates are samples of a random process under observation, transmitted as packets, which also contain the time stamp to identify when the sample was generated. The age of the information available to the destination node is the time elapsed since the last received update was generated. In this paper, we model the source-destination link using queuing theory, and we assume that the time it takes to successfully transmit a packet to the destination is an exponentially distributed service time. We analyze the age of information in the case that the source node has the capability to manage the arriving samples, possibly discarding packets in order to avoid wasting network resources with the transmission of stale information. In addition to characterizing the average age, we propose a new metric, called peak age, which provides information about the maximum value of the age, achieved immediately before receiving an update.
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 wont 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-independent online updating policy, if the underlying state of the system evolves according to a stationary Markov chain, the GAoI is proportional to the AoI. Besides, the accumulative GAoI and AoI are proportional to the expected accumulative detection delay of all changes points over a period of time. Thus, any (G)AoI-optimal state-independent updating policy equivalently minimizes the corresponding expected change point detection delay, which validates the fundamental role of (G)AoI in real-time status monitoring. Besides, we also investigate a Bayesian change point detection scenario where the underlying state evolution is not stationary. Although AoI is no longer related to detection delay explicitly, we show that the accumulative GAoI is still an affine function of the expected detection delay, which indicates the versatility of GAoI in capturing information freshness in dynamic systems.
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 caches 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.
We address the problem of how to optimally schedule data packets over an unreliable channel in order to minimize the estimation error of a simple-to-implement remote linear estimator using a constant Kalman gain to track the state of a Gauss Markov process. The remote estimator receives time-stamped data packets which contain noisy observations of the process. Additionally, they also contain the information about the quality of the sensor source, i.e., the variance of the observation noise that was used to generate the packet. In order to minimize the estimation error, the scheduler needs to use both while prioritizing packet transmissions. It is shown that a simple index rule that calculates the value of information (VoI) of each packet, and then schedules the packet with the largest current value of VoI, is optimal. The VoI of a packet decreases with its age, and increases with the precision of the source. Thus, we conclude that, for constant filter gains, a policy which minimizes the age of information does not necessarily maximize the estimator performance.
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 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 for a small number of sources.
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