The performance analysis of parallel algorithms and systems is considered. For these, numerical solutions methods quickly show their limits because of the enormous state-space growth. The proposed methodology and software tool, list-manipulation parallel-modeling package (LISPACK) uses string manipulation, lumping, and recursive elimination to define the large Markovian process, its restructuring, and efficient solution. The analysis of a typical parallel system and algorithm model is developed as a case study, to discuss the features of the method. The paper has two contributions. The first is the symbolic-approach methodology proposed for the performance analysis of parallel algorithms and systems. The second is a tool that exploits the capabilities of the symbolic approach in the solution of parallel models, where the numerical techniques reveal their limits.>

This paper presents the symbolic and inductive techniques adopted by LISA, a system for the symbolic computation related to the analysis and resolution of complex systems modelled through Markov Chains.The package is especially useful to model systems and algorithms with internal concurrency.Because of the high complexity of these systems, due to the enormous state-apace growth, the numerical solution methods quickly show their limits; the symbolic approach overcomes most of the problems and leads to an efficient method to define and solve the systems.Some major advantages introduced by using the package relate to the possibility of modeling and handling queueing systems whose apace state depends on task position in the system, A new methodology for an inductive-based solution is presented, Some system configurations have been effectually resolved.