# Strong Embeddings for Transitory Queueing Models

## TL;DR

This paper develops strong embedding theorems for nonstationary, non-Markovian transitory queueing models, enabling accurate diffusion approximations of their performance metrics despite inherent complexity.

## Contribution

It introduces strong embedding results in the Komlos-Major-Tusnady framework for complex queueing models, facilitating precise sample path approximations.

## Key findings

- Established strong embedding theorems for transitory queueing models
- Provided error bounds for diffusion process approximations
- Enhanced understanding of performance metrics in nonstationary queues

## Abstract

In this paper we establish strong embedding theorems, in the sense of the Komlos-Major-Tusnady framework, for the performance metrics of a general class of transitory queueing models of nonstationary queueing systems. The nonstationary and non-Markovian nature of these models makes the computation of performance metrics hard. The strong embeddings yield error bounds on sample path approximations by diffusion processes, in the form of functional strong approximation theorems.