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Stochastic Graph Transformation Systems

100%

Heckel R. , Lajios G. , Menge S.

2006

tom Vol. 74, nr 1

63-84

In distributed and mobile systems with volatile bandwidth and fragile connectivity, non-functional aspects like performance and reliability become more and more important. To formalize, measure, and predict such properties, stochastic methods are required. At the same time such systems are characterized by a high degree of architectural reconfiguration. Viewing the architecture of a distributed system as a graph, this is naturally modeled by graph transformations. To combine these two views, in this paper we introduce stochastic graph transformation systems associating with each rule its application rate-the rate of the exponential distribution governing the delay of its application. Beside the basic definitions and a motivating example, we derive continuous time Markov chains, establish a link with continuous stochastic logic, deal with the problem of abstraction through graph isomorphisms, and discuss the analysis of properties by means of an experimental tool chain.

Graph Transformation with Time

100%

Gyapay S. , Varró D. , Heckel R.

2003

tom Vol. 58, nr 1

1--22

Following TER nets, an approach to the modeling 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 generalized to graph transformation systems and semantic variations are discussed. They are summarized by a general theorem ensuring the consistency of temporal order and casual dependencies. The resulting notions of typed graph transformation with time specialize the algebraic double-pushout (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.