Modeling discrete event systems with state-dependent deterministic service times

In this paper extensions to the numerical solution method of deterministic and stochastic Petri nets (DSPNs) are introduced in order to cope with deterministic transitions with marking-dependent firing delays. The basic idea lies in scaling each row of the generator matrix of the Markov chain subordinated to a deterministic transition with marking-dependent firing delay by the delay value corresponding to this marking. Computational formulas of this solution method are implemented in the software package DSPNexpress which completely automates the solution process of DSPNs. The extended modeling power of DSPNs is illustrated by a single-server queuing system with Poisson arrivals, degradable deterministic service requirements, and finite capacity. Christoph Lindemann was supported by the Federal Ministry for Research and Technology of Germany (BMFT) and by the German Research Council (DFG) under grants ITR9003 and Ho 1257/2-1, respectively. Reinhard German was supported by Siemens Corporate Research and Development and by a doctoral fellowship from the German Research Council (DFG) under grant Ho 1257/1-2.