An algebraic structure for duration automata

Algebraic structures such as group, lattice and fuzzy algebra play an important role in the field of information technology, especially in modelling systems. The previous researches [1, 2, 3, 4] have introduced a formal tool named duration automata, by which we modelled systems and developed algorithms to solve problems on scheduling jobs for a cluster computer, routing on priority network or dealing with uncertain processing time jobs. Here we introduce a new weak semigroup with the aim to combine duration automata together with algebraic structures to solve some optimization problems.