# Age-Delay Tradeoffs in Single Server Systems

## TL;DR

This paper investigates the fundamental tradeoff between information freshness, measured by Age of Information, and communication latency, measured by packet delay, in a single server system with controllable service order and distribution.

## Contribution

It establishes a strong age-delay tradeoff, showing that minimizing average age leads to unbounded delay and variance, and characterizes the necessary service time distribution.

## Key findings

- Strong age-delay tradeoff proven
- Minimizing average age requires unbounded second moment in service time
- Delay and variance approach infinity as age approaches minimum

## Abstract

Information freshness and low latency communication is important to many emerging applications. While Age of Information (AoI) serves as a metric of information freshness, packet delay is a traditional metric of communication latency. We prove that there is a natural tradeoff between the AoI and packet delay. We consider a single server system, in which at most one update packet can be serviced at a time. The system designer controls the order in which the packets get serviced and the service time distribution, with a given service rate. We analyze two tradeoff problems that minimize packet delay and the variance in packet delay, respectively, subject to an average age constraint. We prove a strong age-delay and age-delay variance tradeoff, wherein, as the average age approaches its minimum, the delay and its variance approach infinity. We show that the service time distribution that mininizes average age, must necessarily have an unbounded-second moment.