Optimization in Graph Transformation Systems with Time Using Petri Net Based Techniques

Abstract

Extra–functional properties of IT systems have to be analyzed and subsequently optimized carefully during the design phase in order to assure a proper quality of service and decrease operational costs. Several verification and validation methods are known to check the correctness of the system services, while optimization may serve to reach boundaries thus minimizing costs or duration of operating the system. However, the combination of the best practices of the two fields according to the purpose of the analysis is a challenging question. In a previous paper, we showed how such a problem can be formalized and solved when the evolution of the system is captured by graph transformation systems (GTS) with cost parameters attached to each graph transformation rule denoting the cost of firing the rule.

This technique is adapted in the current paper to deliver a time–optimal trajectory in a GTS with time. While the cost of a GT rule sequence always equals to the sum of the cost of the involved GT rules, the concurrent application of GT rules may reduce the minimal duration of a GT rule sequence, which is a major conceptual difference concerning optimization.