On the generalized reward generator for stochastic fluid models: a new equation for Ψ

We construct a generalized reward matrix Z(s) which is an extension of the fluid generator Q(s) of a stochastic fluid model (SFM). We consider the generators that are projections of Z(s) including the generator Q(s), and discuss the application of the resulting generators in different contexts.

One such projection, Z⁺(s), is used to define a matrix M, which records the expected number of crossings of level 0. We use the elements of M and its physical interpretation to derive an explicit equation for the matrix Ψ, which is a key building block to many other performance measures. Work on algorithmic techniques to efficiently compute M are in progress.