# Status updates through M/G/1/1 queues with HARQ

## TL;DR

This paper analyzes the age of information in a single-server queue with Poisson arrivals and general service times, comparing preemptive and non-preemptive policies, and evaluates HARQ schemes for update transmission.

## Contribution

It provides the first analysis of age in M/G/1/1 queues with HARQ, showing non-preemption is optimal and IIR HARQ outperforms FR HARQ in age minimization.

## Key findings

- Non-preemptive policy is optimal for age.
- IIR HARQ yields lower age than FR HARQ.
- Optimal update rate depends on service time distribution.

## Abstract

We consider a system where randomly generated updates are to be transmitted to a monitor, but only a single update can be in the transmission service at a time. Therefore, the source has to prioritize between the two possible transmission policies: preempting the current update or discarding the new one. We consider Poisson arrivals and general service time, and refer to this system as the M/G/1/1 queue. We start by studying the average status update age and the optimal update arrival rate for these two schemes under general service time distribution. We then apply these results on two practical scenarios in which updates are sent through an erasure channel using (a) an infinite incremental redundancy (IIR) HARQ system and (b) a fixed redundancy (FR) HARQ system. We show that in both schemes the best strategy would be not to preempt. Moreover, we also prove that, from an age point of view, IIR is better than FR.