Stationary distributions via first passage times

This article gives a survey of how to express the stationary distribution of a queueing system in terms of first passage time (ruin) probabilities for an associated process and how to solve the corresponding ruin problem. Special attention is given to Siegmund duality (with extensions to Markov-modulated models and stochastic recursions), finite buffer problems, fluid ATM models and Markov-modulated M/G/1 qeueus. The solution of the ruin problem is in some cases based upon some stopping time identities generalizing the classical work of Wald.