Query-Based Sampling of Heterogeneous CTMCs: Modeling and Optimization with Binary Freshness

TL;DR

This paper develops a framework for optimizing query-based sampling of heterogeneous CTMC sources to maximize information freshness, providing closed-form solutions and efficient algorithms for system monitoring.

Contribution

It introduces a novel approach to optimize sampling rates for heterogeneous CTMCs using a water-filling solution under freshness constraints.

Findings

Closed-form expressions for mean information freshness under three models.

Optimal sampling policies significantly improve freshness compared to baselines.

Efficient quadratic complexity algorithm for large source sets.

Abstract

We study a remote monitoring system in which a mutually independent and heterogeneous collection of finite-state irreducible continuous time Markov chain (CTMC) based information sources is considered. In this system, a common remote monitor queries the instantaneous states of the individual CTMCs according to a Poisson process with possibly different intensities across the sources, in order to maintain accurate estimates of the original sources. \color{black}Three information freshness models are considered to quantify the accuracy of the remote estimates: fresh when equal (FWE), fresh when sampled (FWS) and fresh when close (FWC). For each of these freshness models, closed-form expressions are derived for mean information freshness for a given source. Using these expressions, optimum sampling rates for all sources are obtained so as to maximize the weighted sum freshness of the monitoring system, subject to an overall sampling rate constraint. This optimization problem leads to a water-filling solution with quadratic worst case computational complexity in the number of information sources. Numerical examples are provided to validate the effectiveness of the optimum sampling policy in comparison to several baseline sampling policies.