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Fluid limit techniques have become a central tool to analyze queueingnetworks over the last decade, with applications to performance analysis,simulation and optimization. In this paper, some of these techniques areextended to a general class of skip-free Markov chains. As in the case ofqueueing models, a fluid approximation is obtained by scaling time, space andthe initial condition by a large constant. The resulting fluid limit is thesolution of an ordinary differential equation (ODE) in ``most'' of the statespace. Stability and finer ergodic properties for the stochastic model thenfollow from stability of the set of fluid limits. Moreover, similarly to thequeueing context where fluid models are routinely used to design controlpolicies, the structure of the limiting ODE in this general setting provides anunderstanding of the dynamics of the Markov chain. These results areillustrated through application to Markov chain Monte Carlo methods.

The ODE method for stability of skip-free Markov chains with applications to MCMC