Ismail Cosandal

Ismail Cosandal, Sennur Ulukus

The groundbreaking metric age of information (AoI) has been introduced to measure information freshness in communication networks. As transformational as it is, AoI metric falls short in some applications, such as remote monitoring, since it is a semantic-agnostic metric which does not consider the dynamics of the random process. There is a need to quantify the performance of a remote estimator via a metric that combines freshness and semantic aspects. To this end, in this paper, we introduce a novel metric coined age of staleness (AoS) that measures when the last time that the current estimation was correct. First, we analyze a simple scenario where an $n$-ary symmetric Markov source is observed by a monitor via a constant sampling rate, obtain a closed-form expression for the AoS, and show that it is a monotonically decreasing function of the sampling rate. Next, we consider multiple distinct Markov sources, and formulate an optimization problem, where the remote monitor allocates the total sampling rate to tracking the sources. Although the optimization problem is non-convex, its structure is suitable for obtaining a near-optimal solution using the polyblock algorithm, which leverages the monotonicity of the objective function. While the new AoS metric could be applicable in many scenarios, we believe it is particularly well-suited for a digital twin network (DTN) where multiple physical objects (POs) are monitored with a total sampling rate constraint to maintain a digital representation of them, namely, their digital twin (DT).

Ismail Cosandal, Sennur Ulukus, Nail Akar

Age of incorrect information (AoII) is a recently proposed freshness and mismatch metric that penalizes an incorrect estimation along with its duration. Therefore, keeping track of AoII requires the knowledge of both the source and estimation processes. In this paper, we consider a time-slotted pull-based remote estimation system under a sampling rate constraint where the information source is a general discrete-time Markov chain (DTMC) process. Moreover, packet transmission times from the source to the monitor are non-zero which disallows the monitor to have perfect information on the actual AoII process at any time. Hence, for this pull-based system, we propose the monitor to maintain a sufficient statistic called {\em belief} which stands for the joint distribution of the age and source processes to be obtained from the history of all observations. Using belief, we first propose a maximum a posteriori (MAP) estimator to be used at the monitor as opposed to existing martingale estimators in the literature. Second, we obtain the optimality equations from the belief-MDP (Markov decision process) formulation. Finally, we propose two belief-dependent policies one of which is based on deep reinforcement learning, and the other one is a threshold-based policy based on the instantaneous expected AoII.