Source-linked AI summary
Semantic Freshness Optimal Sampling and Transmission for Gossiping Receivers
Irtiza Hasan, Ahmed Arafa
TL;DR
The paper asks how to jointly sample and transmit source information to two gossiping receivers while minimizing VAoI and communication costs. It formulates an average-cost MDP and uses Relative Value Iteration to characterize the optimal policy. The policy has threshold and ordering structure, while receiver imbalance and link reliability determine whether transmission or idling is favored.
Problem
The paper studies joint sampling and transmission for two receivers that share information through gossiping while tracking source freshness under VAoI and communication costs.
Method
The authors formulate an infinite-horizon average-cost MDP and use Relative Value Iteration to characterize the optimal stationary policy.
Results
Sampling has a transmitter-VAoI threshold, direct transmissions serve the older receiver, and transmit-versus-idle structure depends on receiver imbalance and link reliabilities.
Takeaways & Limitations
Jointly adapting sampling, transmission, and gossip yields a policy whose decisions respond to freshness imbalance and communication reliability.
Abstract
from arXiv · showhide
We study the optimal joint sampling and transmission policy for a transmitter communicating with two gossiping receivers that share information with each other, with the objective of tracking a source under the Version Age of Information (VAoI) metric. The transmitter can observe source-version changes, but it has to pay a sampling cost to get the current source information content. Similarly, it can communicate with a receiver by paying a transmission cost. Gossiping enables local information exchange and is able to reduce costly direct transmissions. With imperfect communication links, we formulate an infinite-horizon average-cost Markov Decision Process (MDP) to jointly minimize receiver VAoI, sampling cost, and transmission cost. Using Relative Value Iteration (RVI), we evaluate the optimal policy and establish several properties of its structure. We prove that sampling has a threshold structure in the transmitter VAoI. Among direct transmissions, it is optimal to serve the older receiver. We further characterize the transmit or idle decision through the receiver VAoI difference. Our analysis shows that link reliability and receiver VAoI imbalance have a significant effect on the optimal policy structure. Numerical results verify the structural properties and demonstrate the performance gains of the optimal policy over multiple baselines.
I. INTRODUCTION
The paper motivates semantic freshness in networks where receivers can exchange information locally, then studies joint sampling and transmission for two gossiping receivers. It formulates structural questions around when to sample, whom to transmit to, and when gossip can replace direct communication.
- Information freshness matters in sensor, vehicle, IoT, and wireless edge systems supporting control, estimation, and decisionmaking.
- Gossiping lets receivers exchange updates locally, reducing the need for every update to pass through the central transmitter.
- The system jointly considers source sampling, direct transmission, receiver gossip, and idling under sampling and transmission costs.
- The study formulates an average-cost MDP and establishes threshold and ordering properties for sampling and direct-transmission decisions.
II. SYSTEM MODEL AND MDP FORMULATION
The model is a time-slotted finite-state system with one source, one transmitter, and two receivers whose version ages evolve through source changes, direct transmissions, sampling, and gossip. An average-cost MDP assigns receiver VAoI and action costs to stationary policies and is solved using Relative Value Iteration.
- The system contains one source, one transmitter, and two receivers, with transmitter and receiver version ages tracked through acknowledgments.
- VAoI measures how many source versions each node lags behind the current source version.
- VAoIs are truncated at Vmax, producing a finite state space for the MDP.
- Actions are idling, transmitting to RX1, transmitting to RX2, or sampling the source; direct links and gossip links have separate success probabilities.
- Direct transmission updates its targeted receiver upon success, whereas idling and sampling allow receivers to gossip using their available versions.
- The one-step cost combines receiver VAoI with direct-transmission and sampling costs, and RVI computes the optimal average cost and relative value function.
III. PROPERTIES OF THE RELATIVE VALUE FUNCTION AND STRUCTURE OF THE OPTIMAL POLICY
The paper establishes structural properties of the optimal policy: sampling follows a transmitter-VAoI threshold, direct transmission favors the older receiver, and transmit-versus-idle decisions follow receiver VAoI differences shaped by link reliability.
- Monotonicity properties: The relative value function is coordinate-wise nondecreasing in the state variables.
- Sampling policy: Sampling has a threshold structure in transmitter VAoI: once optimal at a feasible value, it remains optimal at every larger feasible value.The threshold result fixes the receiver VAoIs and varies only the transmitter VAoI.
- Direct transmission policy: Among direct transmissions, it is optimal to serve the receiver with the larger VAoI.Under symmetric links, receiver-coordinate symmetry reduces the comparison to serving either receiver, and equal immediate costs make the older receiver preferable after successful transmission.
- Transmit-versus-idle policy: For fixed transmitter VAoI and smaller receiver VAoI, the transmit-versus-idle decision has a threshold structure in the receiver VAoI difference.The decision is characterized through g(d), where d is the difference between the older and smaller receiver VAoIs.
- Transmit-versus-idle policy: When gossip is more reliable than direct transmission, the policy can switch from transmission to idling as receiver VAoI difference increases; when direct transmission is more reliable, the switch direction reverses.If pv = p, the transmit-versus-idle decision is independent of receiver VAoI difference.
- Transmit-versus-idle policy: When the transmitter and fresher receiver hold the same version, direct transmission is strictly suboptimal if gossip is at least as reliable as the direct link and transmission cost is positive.
IV. NUMERICAL ANALYSIS AND POLICY VISUALIZATION
The numerical analysis visualizes the optimal policy across VAoI states and parameter sweeps, showing how reliability and costs shape reliance on direct transmission, idling, gossip, and sampling. The optimal RVI policy achieves the lowest long-term average cost among the considered policies across the parameter sweeps.
- The optimal policy is visualized over (vtx, v1, v2), with fixed-vtx slices showing its structure over receiver VAoIs.
- When vtx = 0, direct transmission and idling occupy most of the state space because the transmitter already has the current source version.
- Increasing transmission cost Ctx makes direct transmission less attractive and increases reliance on gossip.
- As Cs increases, sampling becomes less attractive, delaying source acquisition until its freshness benefit justifies the sampling cost.
- The optimal RVI policy consistently achieves the lowest long-term average cost among the considered policies across the parameter sweeps.
V. CONCLUSION
The conclusion summarizes an average-cost MDP for joint sampling, transmission, and gossiping under VAoI. It establishes structural policy properties and reports performance gains from jointly adapting the three decisions.
- The problem is formulated as an infinite-horizon average-cost MDP for joint sampling, transmission, and gossiping under VAoI.
- The sampling decision has a threshold structure in transmitter VAoI, and direct transmissions optimally serve the older receiver.
- Increasing receiver VAoI imbalance can shift the decision between transmission and idling, depending on the relative gossip and direct-link reliabilities.
- When the transmitter and fresher receiver hold the same version and gossip is at least as reliable as the direct link, direct transmission is strictly suboptimal.
- Numerical results demonstrate performance gains from jointly adapting sampling, transmission, and gossiping decisions.