Discrete Time Markov Chain in Age of Information analysis for URLLC services in DECT-2020 New Radio

This paper presents an analytical study of the Age of Information (AoI) for Ultra-Reliable Low-Latency Communication (URLLC) services in DECT-2020 New Radio (NR) using a Discrete-Time Markov Chain (DTMC) model. The focus is on the Random Access (RA) phase, when nodes in a clustered network topology compete for resources. The DTMC constructed to describe the node's state transitions during the RA phase takes into account the idle, back-off, listen-before-talk, update, and time-out states. Analytical expressions for stationary probabilities of DTMC states for given distributions of time spent in each state allow to calculate the time characteristics of the model corresponding to the key performance metrics of DECT-2020 network, i.e. average packet delay and average Peak Age of Information (PAoI). The expressions for the worst metric make it possible to estimate the ranges of system parameters' values in which the average PAoI remains within the limits determined for the URLLC services. The numerical experiment demonstrates the impact of the number of nodes in a cluster on the average delay, revealing a direct correlation between increased nodes density and longer session durations.