Today, mobile robot systems are designed for open public environments and can benefit from modeling uncertainties in their decision processes. For this reason, approaches based on Markov Decision Processes (MDP) are proposed to control autonomous robots since few decades. Optimally solving an MDP based model to coordinate a fleet of robots can rapidly become intractable. This paper focuses on the distributive property of Multi-agent Markov Decision Processes (MMDP) and identify an MMDP model as "Completly Distributable", "Partially Distributable" or "Distributable with Coordination". Based on those definitions, the classical multi-mobile-robot problems addressed in the literature are classified and discussed accordingly regarding the potential to compute an optimal solution in a distributive way.