Source-linked AI summary
Scheduling Status Updates to Minimize Age of Information with an Energy Harvesting Sensor
Baran Tan Bacinoglu, Elif Uysal-Biyikoglu
TL;DR
This paper asks how to minimize the freshness age of updates from an energy-constrained sensor with finite battery storage and no channel feedback. It formulates an age-minimizing threshold policy and analyzes its average age under Poisson energy arrivals. Even at finite arrival rates, a positive transmission threshold can outperform zero-wait, and the policy sends updates more slowly than the energy-arrival rate would permit.
Problem
The paper studies how to minimize status-update age when a sensor has time-varying energy constraints, limited battery capacity, and a packet-erasure channel without feedback.
Source: §I · p. 1Method
It formulates threshold-based update scheduling as a function of energy state and estimated age, and analyzes average age for a unit-energy buffer under Poisson arrivals.
Source: §I · p. 1, §III · p. 2Results
For every finite energy arrival rate, a positive transmission-age threshold can achieve lower average age than zero-wait, with mean inter-update duration about 1.307 times the mean energy inter-arrival duration.
Source: §I · p. 1Takeaways & Limitations
The age-optimal threshold policy sends updates more slowly than the upper bound on update rate imposed by energy arrivals.
Source: §I · p. 1The average-age analysis is given for a unit-energy buffer with Poisson energy arrivals, while the general-battery result is a lower bound.
Source: §I · p. 1, A. Poisson Arrivals · p. 5
Abstract
from arXiv · showhide
Age of Information is a measure of the freshness of status updates in monitoring applications and update-based systems. We study a real-time remote 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.
I. INTRODUCTION
Prior work shows that age-optimal scheduling can differ from delay- or throughput-optimal scheduling. This paper analyzes threshold policies with finite energy storage over an infinite horizon, finding that positive waiting can improve average age even when energy is available.
I. INTRODUCTION
- Earlier studies found that age minimization differs from delay or throughput optimization,, –[11], and that delay- or throughput-optimal policies can be suboptimal for age.Energy-harvesting studies considered negligible or deterministic transmission delay and random service times under an average-power constraint.Source: §I · p. 1
- A threshold policy was previously used for optimal transmission of a discrete Markov source observed by an energy-harvesting sensor.That work is distinct from the age-minimization settings discussed here.Source: §I · p. 1
- Unlike, this work considers finite energy storage, where unused energy packets can be wasted, and an infinite horizon rather than a finite time window.It considers threshold-type policies for stationary energy harvesting processes, following the framework in.Source: §I · p. 1
- For any finite energy arrival rate, a positive transmission-age threshold can achieve lower average age than zero-wait, with mean inter-update duration about 1.307 times the mean energy inter-arrival duration.The threshold policy also sends updates more slowly than the upper bound imposed by energy arrivals.Source: §I · p. 1
- The paper analyzes long-term average age for threshold policies over a packet-erasure channel and gives a lower bound based on the lossless channel.For unit energy storage, it derives average age for Poisson energy arrivals on the lossless channel.Source: §I · p. 1
II. SYSTEM DESCRIPTION
The system has an energy-harvesting transmitter that sends status updates to a destination over a channel without feedback. A scheduler and sampler track the transmitter’s energy buffer and the monitored system’s status to control update timing.
II. SYSTEM DESCRIPTION
- The destination’s age is measured from the generation time of its most recently received update, while the sampler can estimate age from the update history despite receiving no destination feedback.The sampler tracks the expected age using prior transmitted updates.Source: §II · p. 2
- Each update consumes one energy unit, the battery holds B units, and each transmitted update succeeds with probability p.Energy arrivals come in unit-energy chunks; these may also represent transmission tokens or opportunities.Source: §II · p. 2
- The model tracks cumulative updates and energy harvests over time, with the battery state representing stored unit-energy arrivals.The passage introduces the battery-state dynamics and the update counting process.Source: §II · p. 2
III. MINIMIZING AVERAGE AGE
The paper minimizes average age over threshold-type update policies, with the threshold depending on the battery state. It characterizes average age through inter-update durations and cumulative age between updates.
III. MINIMIZING AVERAGE AGE
- An optimal threshold policy obeys the threshold-policy constraint and minimizes the average-age objective.The policy cannot transmit with an empty battery; with arbitrarily large stored energy, its threshold tends to zero.Source: §III · p. 2
- A zero-wait policy sets the transmission threshold to zero whenever the battery has at least one energy unit, while the empty-battery threshold remains infinite.The policy is a special case of the threshold rule.Source: §III · p. 2
- For policies and energy-arrival processes where the relevant limits exist, average age equals the limiting expected cumulative age between updates divided by the limiting inter-update duration.The analysis uses the inter-update duration and expected cumulative age between successive updates.Source: §III · pp. 2–3
A. Poisson Arrivals
For Poisson energy arrivals, the paper analyzes age-minimizing threshold policies and derives results for lossless and erasure channels. It establishes a unit-buffer comparison with zero-wait transmission and lower bounds for broader buffer settings.
A. Poisson Arrivals
- A threshold policy has finite average age under Poisson energy arrivals, and bounds on inter-update durations and their second moments support the analysis.The policies considered are oblivious to the history of energy arrivals.Source: A. Poisson Arrivals · p. 3
- For Poisson arrivals, the minimum average age with an erasure channel is lower-bounded by the lossless-channel minimum for the same buffer limit.For p = 1, age resets after each update and inter-update durations depend on energy states rather than age.Source: A. Poisson Arrivals · p. 4
- Up to 10% lower average age is achieved by a threshold policy than by zero-wait transmission when B = 1 and p = 1.The reported ratio is 2W(1/2) ≈ 0.901.Source: A. Poisson Arrivals · pp. 3, 5, Figure 2 · p. 5
- A lower bound on minimum average age is derived for Poisson arrivals for any buffer limit B and success probability p.The theorem statement is supplied without the bound's full expression.Source: A. Poisson Arrivals · p. 5
- With an infinite buffer and p = 1, thresholds τ_m = 1/μH + ε for m > 0 achieve the lower limit as ε becomes arbitrarily small.The result concerns Poisson energy arrivals with rate μH.Source: A. Poisson Arrivals · pp. 5–6