In: 92: Berlin, Techn. univ., Diss. 2. 1992.
Abstract: Deterministic and Stochastic Petri Nets (DSPNs) have been introduced as an analytical modeling tool which allows the representation of exponentially distributed as well as deterministic delays. DSPN models are of particular interest to the quantitative evaluation of computer systems and communication networks because numerous activities in such systems can be exactly represented by a constant duration by means of this modeling method. Previously, the applicability of DSPNs has been restricted to simple systems due to the high computational effort required by the numerical solution algorithm. In this dissertation a substantially more efficient numerical algorithm for calculating the steady-state solutions of DSPNs is developed. This numerical algorithm has been implemented in a software package. Two application examples show the performance of the method developed in this thesis. First, a DSPN model of a real-time local area network which operates under a CSMA/CD protocol with deterministic collision resolution has been developed. As a second application we consider a multiprocessor system in which Distributed Shared Memory is implemented by sequential consistency with a write-invalidate protocol. Due to the complexity of these DSPN models their solutions can only be calculated in practise by the numerical algorithm developed in this dissertation.