  The need to model a Markov renewal on-off process with multiple off-states
arise in many applications such as economics, physics, and engineering.
Characterization of the occupation time of one specific off-state marginally or
two off-states jointly is crucial to understanding such processes. We derive
the exact marginal and joint distributions of the off-state occupation times.
The theoretical results are confirmed numerically in a simulation study. A
special case when all holding times have Levy distribution is considered for
the possibility of simplification of the formulas.
