Using timed automata and model-checking to simulate material flow in agricultural production systems—Application to animal waste management

Due to intensification and specialisation of animal production and the increasing pressure of environmental regulations, the careful management of animal wastes becomes a key point for the sustainability of livestock farming. This paper addresses the dynamic representation of a network composed by a set of production units (i.e., livestock farms) that need to transfer their wastes to a set of consumption units (i.e., crops onto which wastes may be spread over). The dynamics of stocks (taken as continuous fluxes with imprecise parameters) is combined with management decisions or actions (taken as discrete events). Various temporal constraints determine the possibilities of waste transfers. For each production or consumption unit, these constraints are modelled as a timed automaton. Possible allocation of wastes is then analysed using model-checking techniques applied to the global timed automaton resulting from the product of all the elementary timed automata. To this end, the Kronos software based on the Timed Computational Tree Logic (TCTL) is used. Our approach is illustrated through the analysis of a typical farming system made of livestock and crop enterprises in the context of the Reunion Island. Using the computer tool implementing this approach, we show how an initial waste management policy can be improved by simulation to find a better waste allocation to crops.