The problem considered in the paper can not be solved by the tradition
al technique available for the analysis of Markov Regenerative Process
es (MRGP). The widely used description of MRGPs, i.e. by the local and
the global kernels, do not contain sufficient information on the proc
ess to evaluate the distribution of reward measures. A new analytical
approach is proposed and studied to utilize better the Markov regenera
tive property for the analysis of Markov Regenerative Reward Models (M
RRM). The distribution of the accumulated reward and the completion ti
me of MRRMs is provided in transform domain, as well as considerations
about the time domain numerical evaluation of these measures. As a si
mple application example the performance of a finite queueing system i
s analyzed.