Modeling the software architecture of a prototype parallel machine
SIGMETRICS '87 Proceedings of the 1987 ACM SIGMETRICS conference on Measurement and modeling of computer systems
muMath: a microcomputer algebra system
muMath: a microcomputer algebra system
Modeling and analysis of computer system availability
IBM Journal of Research and Development
Approximate Analysis of Fork/Join Synchronization in Parallel Queues
IEEE Transactions on Computers
Performance Analysis of Parallel Processing Systems
IEEE Transactions on Software Engineering
A performance evaluation of a general parallel processing model
SIGMETRICS '90 Proceedings of the 1990 ACM SIGMETRICS conference on Measurement and modeling of computer systems
Communications of the ACM - Special issue on LISP
Computable Error Bounds for Aggregated Markov Chains
Journal of the ACM (JACM)
Data Structures and Algorithms
Data Structures and Algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Aggregation Methods for Large Markov Chains
Proceedings of the International Workshop on Computer Performance and Reliability
Colored GSPN Models and Automatic Symmetry Detection
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Aggregation of States in Colored Stochastic Petri Nets: Application to a Multiprocessor Architecture
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
Performance Analysis of Parallel Search Algorithms on Multiprocessors
Performance '90 Proceedings of the 14th IFIP WG 7.3 International Symposium on Computer Performance Modelling, Measurement and Evaluation
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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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.