Stochastic discretization is a technique of representing a
continuous random variable as a random sum of i.i.d. exponential
random variables. In this article, we apply this technique to
study the limiting behavior of a stochastic fluid model.
Specifically, we consider an infinite-capacity fluid buffer,
where the net input of fluid is regulated by a finite-state
irreducible continuous-time Markov chain. Most long-run performance
characteristics for such a fluid system can be expressed as
the long-run average reward for a suitably chosen reward structure.
In this article, we use stochastic discretization of the fluid
content process to efficiently determine the long-run average
reward. This method transforms the continuous-state Markov process
describing the fluid model into a discrete-state
quasi-birth–death process. Hence, standard tools, such
as the matrix-geometric approach, become available for the analysis
of the fluid buffer. To demonstrate this approach, we analyze
the output of a buffer processing fluid from K sources
on a first-come first-served basis.