The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Hierarchical Markovian models: symmetries and reduction
Performance Evaluation - Special issue: 6th international conference on modelling techniques and tools for computer performance evaluation
Iterative aggregation/disaggregation techniques for nearly uncoupled markov chains
Journal of the ACM (JACM)
A Passage-Time Preserving Equivalence for Semi-Markov Processes
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
WOSP '04 Proceedings of the 4th international workshop on Software and performance
Iterative convergence of passage-time densities in semi-Markov performance models
Performance Evaluation - Performance modelling and evaluation of high-performance parallel and distributed systems
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High-level semi-Markov modelling paradigms such as semi-Markov stochastic Petri nets and process algebras are used to capture realistic performance models of computer and communication systems but often have the drawback of generating huge underlying semi-Markov processes. Extraction of performance measures such as steady-state probabilities and passage-time distributions therefore relies on sparse matrix-vector operations involving very large transition matrices. Previous studies have shown that exact state-by-state aggregation of semi-Markov processes can be applied to reduce the number of states. This can, however, lead to a dramatic increase in matrix density caused by the creation of additional transitions between remaining states. Our paper addresses this issue by presenting the concept of state space partitioning for aggregation. We present a new deterministic partitioning method which we term barrier partitioning. We show that barrier partitioning is capable of splitting very large semi-Markov models into a number of partitions such that first passage-time analysis can be performed more quickly and using up to 99% less memory than existing algorithms.