Analysis of an Age-Dependent Stochastic Hybrid System

In this paper, we provide an analysis of a status update system modeled through the Stochastic Hybrid Systems (SHSs) tool. Contrary to previous works, which assumed constant transition rates, we allow the system’s transition dynamics to be functions of the Age of Information (AoI). This dependence allows us to encapsulate many applications and opens the door for more sophisticated systems to be studied. However, this same dependence on the AoI engenders technical and analytical difficulties. Our paper provides a first step in addressing these difficulties. Specifically, we first showcase the regularity and other critical characteristics of the age process in our system of interest. Then, we provide a framework to establish the Lagrange stability and positive recurrence of the process. Building on these results, we provide an approach, dubbed as the moment closure technique, to compute the m-th moment of the age process for any m≥1. Interestingly, this technique allows us to approximate the average age of various systems by solving a simple set of linear equations.