Flow level convergence and insensitivity for multi-class queueing networks

TL;DR

This paper proves the weak convergence of multi-class queueing networks to document transfer processes, establishing insensitivity results and enabling comparison across various document size distributions.

Contribution

It introduces a stochastic model for document transfer, proving convergence and insensitivity results that extend understanding of queueing network behavior.

Findings

Weak convergence of queueing process to document transfer process

Insensitivity results for the limit queueing process

Comparison framework for general document size distributions

Abstract

We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochastic model as a model document transfer in a communication network where the documents transferred have a general distribution. We prove the weak convergence of the multi-class queueing process to the document transfer process. Our convergence result allows the comparison of general document size distributions, and consequently, we prove general insensitivity results for the limit queueing process.