Priority as extremal probability

We extend the stratified model of probabilistic processes to obtain a very general notion of process priority. The main idea is to allow probability guards of value 0 to be associated with alternatives of a probabilistic summation expression. Such alternatives can be chosen only if the non-zero alternatives are precluded by contextual constraints. We refer to this model as one of "extremal probability" and to its signature as PCCS_ζ. We provide PCCS_ζ with a structural operational semantics and a notion of probabilistic bisimulation, which is shown to be a congruence. Of particular interest is the abstraction PCCS_π of PCCS_ζ in which all non-zero probability guards are identified. PCCS_π represents a customized framework for reasoning about priority, and covers all features of process algebras proposed for reasoning about priority that we know of.