Data Structures and Algorithms for Extended State Space and Structural Level Reduction of the GSPN Model

This paper extends the applicability of exact analysis of the GSPN model by providing methods to improve the time and space complexity of both state space and structural level reduction. For state space level reduction, we maximize the concurrent firing of immediate transitions. For structural level reduction, we minimize the number of generated replicas for timed transitions by using branch and bound techniques to create concurrent replicas that simulate the firing of the timed transition followed by the simultaneously firing of multiple immediate transitions. 1 I n t r o d u c t i o n State space level reduction techniques eliminate vanishing markings by concurrently firing multiple immediate transitions in a single state space transition [1, 4]. Structural level reduction techniques eliminate immediate transitions, the source of vanishing markings, by iteratively creating replicas of a timed transition to simulate the firing of the timed transition followed by the firing of an immediate transition [2, 6]. This paper provides data structures and algorithms to extend the applicabili ty and to efficiently implement both state space and structural level reduction of the GSPN model. With respect to state state space level reduction, we rely on knowledge of the given marking, as well as the GSPN structure, to maximize the concurrent firing of immediate transitions. In addition, we develop efficient algorithms to generate the concurrent transition firing combinations and their corresponding firing probabilities. With respect to structural level reduction, we avoid the generation of redundant replicas by applying state space level reduction techniques at the structural level to generate concurrent replicas which simulate the firing of a timed transition followed by the concurrent firing of multiple immediate transitions. In addition, we use branch and bound techniques to both This work was sponsored by the Advanced Research Projects Agency of the U.S. Department of Defense under Contract MDA 972-91=J-1011, Advanced Networking and Distributed Systems.