The majority of computational methods applied for the analysis of homogeneous Markov
reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By
the nature of inhomogeneous models, only forward differential equations can be used
to describe the model behaviour.
In this paper we provide forward partial differential equations describing the distribution
of reward measures of inhomogeneous MRMs. Based on this descriptions, we introduce
the set of ordinary differential equations that describes the behaviour of the moments
of reward measures when it is possible. This description of moments allows the effective
numerical analysis of rather large inhomogeneous MRMs.
A numerical example demonstrates the application of inhomogeneous MRMs in practice
and the numerical behaviour of the introduced analysis technique.
