Joint Freshness and Age-Dispersion Control over Finite-State Markov Wireless Channels

RESUMO

Age of information (AoI) has become a standard design objective for timely monitoring as it measures the freshness of the latest update at a receiver. AoI alone, however, is insufficient in goal-oriented applications where decisions depend on consecutive observations. Age dispersion complements AoI by measuring the generation-time separation between consecutive updates. In this paper, we study joint freshness and dispersion control for a generate-at-will status update link modeled as a finite-state Markov wireless channel. The objective is to minimize the long-run probability that either AoI or age dispersion exceeds a prescribed threshold under an average transmission rate constraint. For channel-dependent randomized transmission policies, we derive exact matrix expressions for the stationary joint distribution of AoI and dispersion. For reversible channels, mean dispersion is lower bounded by the reciprocal of the delivery throughput, and the difference is an explicit non-negative variance term for which we establish the exact equality condition. We then formulate the adaptive joint-threshold control problem as a constrained Markov decision process and prove that it admits an exact finite-state representation whose size scales linearly with the number of channel states and the threshold levels. Simulation results show that the controller reduces joint threshold violations by 37.3% relative to adaptive AoI-only control under the same transmission budget, while increasing mean AoI by 8.3%.