# Workload of Queueing Systems with Autocorrelated Service Times

## TL;DR

This paper analyzes queueing systems where service times are autocorrelated, deriving new formulas for workload-related metrics and showing that average workload can be unexpectedly large.

## Contribution

New formulas for workload probability density, tail, average, and entropy in autocorrelated service time queueing systems are derived.

## Key findings

- The average workload can exceed several times the product of average queue size and average service time.
- Formulas for workload metrics are derived for both time-dependent and steady-state cases.
- Numerical examples illustrate the behavior of the derived workload formulas.

## Abstract

The queuing model with autocorrelated service times is studied with respect to workload, i.e., the time needed to serve all the customers in the queue. Specifically, new formulas for the probability density of workload, its tail, the average value, and entropy are derived and illustrated using numerical examples. Both time-dependent and steady-state cases are covered. It is also demonstrated that the average workload may reach surprisingly large values, exceeding several times the product of the average queue size and the average service time.