Open-loop scheduling for minimizing polynomial functions of age of information

Abstract

Age of Information (AoI) is a metric that quantifies freshness of information in a status update system, making it crucial for applications where timely updates are essential, such as real-time monitoring systems, IoT networks, and mission-critical communication systems. This thesis explores age-agnostic cyclic scheduling in multi-source, single-server Generate-At-Will (GAW) status update systems, where the goal is to minimize the expected value of a non-linear polynomial function of AoI in a discrete-time setting. In the literature, approaches that aim to minimize the weighted sum of average AoI often rely solely on the first two moments of packet service times. However, the use of non-linear functions of age as the information freshness metric, requires an analytical model to obtain the distribution of AoI which also uses the distributions of packet service times as input to the model. In this work, given a cyclic transmission pattern, we use the theory of discrete-time absorbing Markov chains to obtain the distribution of the AoI of each user, which then allows us to find the expected value of any nonlinear function of individual ages, referred to as the Value of Information (VoI) in this work. Subsequently, using the proposed analytical method, we propose a metaheuristic based space-search algorithm, specifically leveraging the Simulated Annealing (SA) technique, to obtain a cyclic schedule with the goal of minimizing a polynomial cost function of age. Numerical results are presented to validate the proposed approach.