# Peak Age of Information in Priority Queueing Systems

## TL;DR

This paper analyzes the Peak Age of Information in a priority queueing system with multiple classes, deriving exact and approximate formulas for different buffer sizes and service disciplines, and explores how priority ordering affects information freshness.

## Contribution

It provides new exact and approximate formulas for PAoI in priority queues with various buffer sizes and service disciplines, including large k scenarios.

## Key findings

- Exact PAoI for buffer size one with exponential service time.
- Closed-form PAoI expressions for infinite buffer with FCFS and LCFS.
- Priority and discipline significantly impact information freshness.

## Abstract

We consider a priority queueing system where a single processor serves k classes of packets that are generated randomly following Poisson processes. Our objective is to compute the expected Peak Age of Information (PAoI) under various scenarios. In particular, we consider two situations where the buffer size at each queue is one and infinite, and in the infinite buffer size case we consider First Come First Serve (FCFS) and Last Come First Serve (LCFS) as service disciplines. For the system with buffer size one at each queue, we derive PAoI exactly for the case of exponential service time and bounds (which are excellent approximations) for the case of general service time, with small k. For the system with infinite buffer size, we provide closed-form expressions of PAoI for both FCFS and LCFS where service time is general and k could be large. Using those results we investigated the effect of ordering of priorities and service disciplines for the various scenarios. We perform extensive numerical studies to validate our results and develop insights.