Solution of Large GSPN Models
Gianfranco Ciardo, Kishor Shridharbhai Trivedi · 2021
Generalized stochastic Petri nets (GSPNs) can be effectively used to represent many systems in a compact way. Efficient algorithms for the translation of a GSPN into its underlying continuous-time Markov chain (CTMC) are known and have been implemented in a number of software packages. While GSPNs relieve the modeler from the cumbersome and error-prone task of building and inputting the CTMC by hand, their analytical tractability is still limited by the combinatorial growth of the underlying CTMC. In order to avoid construction and solution of a large CTMC, we propose decomposing the GSPN into a set of subnets and separately solving individual subnets. Dependence among the subnets requires that, after solving each 566 subnet, certain quantities be exported to other subnets. A fixed-point iteration is then used over the exported quantities. We discuss ways of decomposing a net into subnets, the type of quantities that need to be exchanged between subnets, and the convergence of the fixed-point iterative schemes.