In this paper, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information , or simply age , which is defined as how old the freshest received update is, since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semi-Markov decision problem with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if: 1) the age penalty function grows quickly with respect to the age; 2) the packet transmission times over the channel are positively correlated over time; or 3) the packet transmission times are highly random (e.g., following a heavy-tail distribution).

Update or Wait: How to Keep Your Data Fresh

THE theory of Fourier integrals arises out of the elegant pair of reciprocal formulae The Laplace Transform By David Vernon Widder. (Princeton Mathematical Series.) Pp. x + 406. (Princeton: Princeton University Press; London: Oxford University Press, 1941.) 36s. net.

The Laplace Transform

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 new simplified technique for evaluating the AoI in finite-state continuous-time queuing systems is also derived. Based on stochastic hybrid systems, this method makes AoI evaluation to be comparable in complexity to finding the stationary distribution of a finite-state Markov chain.

The Age of Information: Real-Time Status Updating by Multiple Sources

Recent emphasis on green communications has generated great interest in the investigations of energy harvesting communications and networking. Energy harvesting from ambient energy sources can potentially reduce the dependence on the supply of grid or battery energy, providing many attractive benefits to the environment and deployment. However, unlike the conventional stable energy, the intermittent and random nature of the renewable energy makes it challenging in the realization of energy harvesting transmission schemes. Extensive research studies have been carried out in recent years to address this inherent challenge from several aspects: energy sources and models, energy harvesting and usage protocols, energy scheduling and optimization, implementation of energy harvesting in cooperative, cognitive radio, multiuser and cellular networks, etc. However, there has not been a comprehensive survey to lay out the complete picture of recent advances and future directions. To fill such a gap, in this paper, we present an overview of the past and recent developments in these areas and highlight a number of possible future research avenues.

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Advances in Energy Harvesting Communications: Past, Present, and Future Challenges

Age of information (AoI) was introduced in the early 2010s as a notion to characterize the freshness of the knowledge a system has about a process observed remotely. AoI was shown to be a fundament ...

/pdf/age-of-information-a-new-concept-metric-and-tool-5exabo4n56.pdf

Age of Information: A New Concept, Metric, and Tool

We consider managing the freshness of status updates sent from a source (such as a sensor) to a monitoring node. The time-varying availability of energy at the sender limits the rate of update packet transmissions. At any time, the age of information is defined as the amount of time since the most recent update was successfully received. An offline solution that minimizes not only the time average age, but also the peak age for an arbitrary energy replenishment profile is derived. The related decision problem under stochastic energy arrivals at the sender is studied through a discrete time dynamic programming formulation, and the structure of the optimal policy that minimizes the expected age is shown. It is found that tracking the expected value of the current age (which is a linear operation), together with the knowledge of the current energy level at the sender side is sufficient for generating an optimal threshold policy. An effective online heuristic, Balance Updating (BU), that achieves performance close to an omniscient (offline) policy is proposed. Simulations of the policies indicate that they can significantly improve the age over greedy approaches. An extension of the formulation to stochastically formed updates is considered.

Age of information under energy replenishment constraints

Age of Information is a measure of the freshness of status updates in monitoring applications and update-based systems. We study a real-time sensing scenario with a sensor which is restricted by time-varying energy constraints and battery limitations. The sensor sends updates over a packet erasure channel with no feedback. The problem of finding an age-optimal threshold policy, with the transmission threshold being a function of the energy state and the estimated current age, is formulated. The average age is analyzed for the unit battery scenario under a memoryless energy arrival process. Somewhat surprisingly, for any finite arrival rate of energy, there is a positive age threshold for transmission, which corresponding to transmitting at a rate lower than that dictated by the rate of energy arrivals. A lower bound on the average age is obtained for general battery size.

Scheduling status updates to minimize age of information with an energy harvesting sensor

We study the problem of minimizing the time-average expected Age of Information for status updates sent by an energy-harvesting source with a finite-capacity battery. In prior literature, optimal policies were observed to have a threshold structure under Poisson energy arrivals, for the special case of a unit-capacity battery. In this paper, we generalize this result to any (integer) battery capacity, and explicitly characterize the threshold structure. We provide the expressions relating the threshold values on the age to the average age. One of these results, that we derive from these expressions, is the unexpected equivalence of the minimum average AoI and the optimal threshold for the highest energy state.

Achieving the Age-Energy Tradeoff with a Finite-Battery Energy Harvesting Source

We consider an energy harvesting source equipped with a finite battery, which needs to send timely status updates to a remote destination The timeliness of status updates is measured by a non-decreasing penalty function of the age of information (AoI) The problem is to find a policy for generating updates that achieves the lowest possible time-average expected age penalty among all online policies We prove that one optimal solution of this problem is a monotone threshold policy, which satisfies (i) each new update is sent out only when the age is higher than a threshold and (ii) the threshold is a non-increasing function of the instantaneous battery level Let τB denote the optimal threshold corresponding to the full battery level B, and p(·) denote the age-penalty function, then we can show that p(τB) is equal to the optimum objective value, ie, the minimum achievable time-average expected age penalty These structural properties are used to develop an algorithm to compute the optimal thresholds Our numerical analysis indicates that the improvement in average age with added battery capacity is largest at small battery sizes; specifically, more than half the total possible reduction in age is attained when battery storage increases from one transmission's worth of energy to two This encourages further study of status update policies for sensors with small battery storage

Optimal status updating with a finite-battery energy harvesting source

We study the problem of minimizing the time-average expected Age of Information for status updates sent by an energy-harvesting source with a finite-capacity battery. In prior literature, optimal policies were observed to have a threshold structure under Poisson energy arrivals, for the special case of a unit-capacity battery. In this paper, we generalize this result to any (integer) battery capacity, and explicitly characterize the threshold structure. We obtain tools to derive the optimal policy for arbitrary energy buffer (i.e. battery) size. One of these results is the unexpected equivalence of the minimum average AoI and the optimal threshold for the highest energy state.

Baran Tan Bacinoglu

Papers

Age of information under energy replenishment constraints

Scheduling status updates to minimize age of information with an energy harvesting sensor

Achieving the Age-Energy Tradeoff with a Finite-Battery Energy Harvesting Source

Optimal status updating with a finite-battery energy harvesting source

Achieving the Age-Energy Tradeoff with a Finite-Battery Energy Harvesting Source