The Multi-Source Preemptive M/PH/1/1 Queue with Packet Errors: Exact Distribution of the Age of Information and Its Peak

TL;DR

This paper develops an exact analytical model for the Age of Information and Peak AoI in a multi-source, preemptive, bufferless queueing system with packet errors, using matrix-analytical methods.

Contribution

It introduces a general queueing model with multiple sources, distinct service distributions, and preemption probabilities, providing exact AoI and PAoI distributions unlike previous average-based models.

Findings

Exact AoI and PAoI distributions derived for complex queueing system.

Preemption probabilities significantly affect information freshness metrics.

Model validated with numerical examples demonstrating practical insights.

Abstract

Age of Information (AoI) and Peak AoI (PAoI) and their analytical models have recently drawn substantial amount of attention in information theory and wireless communications disciplines, in the context of qualitative assessment of information freshness in status update systems. We take a queueing-theoretic approach and study a probabilistically preemptive bufferless $M/PH/1/1$ queueing system with arrivals stemming from $N$ separate information sources, with the aim of modeling a generic status update system. In this model, a new information packet arrival from source $m$ is allowed to preempt a packet from source $n$ in service, with a probability depending on $n$ and $m$. To make the model even more general than the existing ones, for each of the information sources, we assume a distinct PH-type service time distribution and a distinct packet error probability. Subsequently, we obtain the exact distributions of the AoI and PAoI for each of the information sources using matrix-analytical algorithms and in particular the theory of Markov fluid queues and sample path arguments. This is in contrast with existing methods that rely on Stochastic Hybrid Systems (SHS) which obtain only the average values and in less general settings. Numerical examples are provided to validate the proposed approach as well as to give engineering insight on the impact of preemption probabilities on certain AoI and PAoI performance figures.