Age of Information in a Multisource Ber/Geo/1/1 Preemptive Queueing System

TL;DR

This paper analyzes the age of information in a multi-source preemptive queueing system with heterogeneous service times, providing a detailed Markovian framework to derive the distribution and average AoI for each source.

Contribution

It introduces a novel Markov two-dimensional age process to fully characterize per-source AoI in a multi-source preemptive queueing system with heterogeneous service times.

Findings

Analytical expressions for per-source AoI distribution and average are derived.

Numerical results confirm the accuracy of the theoretical models.

Abstract

This work studies the information freshness of the vehicle-to-infrastructure status updating in Internet of vehicles, which is modeled as a multi-source Ber/Geo/1/1 preemptive queueing system with heterogeneous service time. We pay attention to both the distribution and average of AoI. To fully track the per-source AoI evolution, a Markov two-dimensional (2D) age process is introduced. The first element of the 2D age process stands for the instantaneous per-source AoI, while the second represents whether an update of the concerned source is being served and its current age. A complete framework and detailed analyses on the per-source AoI are presented based on the Markovity of the 2D age process. By studying the state transition probabilities, stationary equations, and stationary distribution of the 2D age process, analytical expressions of the probability mass function and average of per-source AoI are derived. Numerical results validate the accuracy of the theoretical analyses.