Random matrices, phase transitions and queuing theory

Abstract: There are often unexpected and deep connections between
mathematics and the applied sciences. We tell one such story here
which starts with the engineering problem of latency analysis in
queuing networks. By exploiting a remarkable connection between
queuing theory and non-intersecting random walks, we obtain simple
answers for a basic model of this problem, which connects the latency
distribution with that of the largest eigenvalue of a random matrix.
Using random matrix theory to flesh out this connection reveals the
existence of phase transitions in the behavior of the queuing system.
With random matrix theory as a new tool, we are able to analyze more
complex models for the queuing system and make contact with
computational intractability related aspects of scheduling theory and
the travelling salesman problem.

This abstract borrowed heavily from one David Tse's abstracts (see
www.eecs.berkeley.edu/~dtse/free.pdf).