Abstract

We model a multi-class queueing network as a simple model of document transfer across a packet switching network. We assume the size of documents is large and also that packets are processed through the network. A natural limit to take is one where the size of documents tends to infinity, where the rate packets are processes through the network tends to infinity and where also the time until documents are fully transfered stays positive and finite. The queueing system resulting from this limit is one studied by Bonald and Proutiere because it satisfies a certain insensitivity property. That is to say that the stationary distribution of the resulting queueing system depends on the distribution of document sizes only through their mean document size.

By formally proving the convergence of a series of multi-class queueing networks to this insensitive queueing systems we are able to directly prove quite general insensitivity results for these queueing systems.