Real-Time Remote Monitoring of Correlated Markovian Sources

We investigate real-time tracking of two correlated stochastic processes over a shared wireless channel. The joint evolution of the processes is modeled as a two-dimensional discrete-time Markov chain. Each process is observed by a dedicated sampler and independently reconstructed at a remote monitor according to a task-specific objective. Although both processes originate from a common underlying phenomenon (e.g., distinct features of the same source), each monitor is interested only in its corresponding feature. A reconstruction error is incurred when the true and reconstructed states mismatch at one or both monitors. To address this problem, we propose an error-aware joint sampling and transmission policy, under which each sampler probabilistically generates samples only when the current process state differs from the most recently reconstructed state at its corresponding monitor. We adopt the time-averaged reconstruction error as the primary performance metric and benchmark the proposed policy against state-of-the-art joint sampling and transmission schemes. For each policy, we derive closed-form expressions for the resulting time-averaged reconstruction error. We further formulate and solve an optimization problem that minimizes the time-averaged reconstruction error subject to an average sampling cost constraint. Analytical and numerical results demonstrate that the proposed error-aware policy achieves the minimum time-averaged reconstruction error among the considered schemes while efficiently utilizing the sampling budget. The performance gains are particularly pronounced in regimes with strong inter-process correlation and stringent tracking requirements, where frequent sampling by both samplers is necessary.