Abstract. Following TER nets, an approach to the modelling of time in high-level Petri nets, we propose a model of time within (attributed) graph transformation systems where logical clocks are represented as distinguished node attributes. Corresponding axioms for the time model in TER nets are generalised to graph transformation systems and semantic variations are discussed. They are summarised by a general theorem ensuring the consistency of temporal order and casual dependencies.The resulting notions of typed graph transformation with time specialise the algebraic doublepushout (DPO) approach to typed graph transformation. In particular, the concurrency theory of the DPO approach can be used in the transfer of the basic theory of TER nets.

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Resource allocation and scheduling optimization problems are core problems in the field of IT systems. However, such problems frequently underlay several additional constraints and the formalization of a reál life problem requires a well-defined mathematical and modeling approach providing an integrated verification and optimization. We propose such methods adapting Process Network Synthesis algorithms to the Petri net model: