Transient analysis of deterministic and stochastic Petri nets by the method of supplementary variables

The paper addresses the transient analysis of stochastic Petri nets with deterministic and exponentially distributed firing times. Using the method of supplementary variables, general state equations are derived which are valid under certain structural conditions. A numerical technique for the iterative solution of the state equations is proposed. Furthermore, a special case is identified, for which an efficient and easy to implement solution is possible. This technique can be also used for the approximate solution in more general cases. Numerical examples demonstrate the use of the different algorithms