## Transient Analysis of Fluid Flow Models via Stochastic Coupling to a Queue

**Abstract :**
Markovian fluid flow models are used extensively in performance analysis of
communication networks. They are also instances of Markov reward models that
find applications in several areas like storage theory, insurance risk and
financial models, and inventory control. This paper deals with the transient
analysis of such models. Given a Markovian fluid flow, we construct on the same
probability space a sequence of queues that are stochastically coupled to the
fluid flow in the sense that at certain selected random epochs the distribution
of the fluid level and the phase (the state of the modulating Markov chain) is
identical to that of the work in the queue and the phase. The fluid flow is
realized as a stochastic process limit of the processes of work in the system
for the queues, and the latter are analyzed using the matrix-geometric method.
These in turn provide the needed characterization of transient results for the
fluid model.