On the hierarchy of functioning rules in distributed computing

In previous papers, we used a Markovian model to determine the optimal functioning rules of a distributed system in various settings. Searching optimal functioning rules amounts to solve an optimization problem under constraints. The hierarchy of solutions arising from the above problem is called the ‘first order hierarchy’, and may possibly yield equivalent solutions. The present paper emphasizes a specific technique for deciding between two equivalent solutions, which establishes the ‘second order hierarchy’.