Age of Information for Small Buffer Systems

TL;DR

This paper analyzes the age of information in small buffer systems with a LIFO policy, providing analytical expressions for AoI distribution in steady-state, demonstrated through the case of buffer size three.

Contribution

It offers the first detailed analysis of AoI for P_m systems with small buffers operating under LIFO without preemption, including analytical expressions derived with computer algebra.

Findings

Analytical expressions for AoI in P_m systems are obtainable.

Steady-state AoI distribution can be characterized for small buffer sizes.

The analysis is exemplified for buffer size m=3.

Abstract

Consider a message processing system whose objective is to produce the most current information as measured by the quantity known as "age of information". We have argued in previous papers that if we are allowed to design the message processing policy ad libitum, we should keep a small buffer and operate according to a LIFO policy. In this small note we provide an analysis for the AoI of the P_m system which uses a buffer of size m, a single server, operating without service preemption and in a LIFO manner for stored messages. Analytical expressions for the mean (or even distribution) of the AoI in steady-state are possible but with the aid computer algebra. We explain the the analysis for m=3.