Passage-time computation and aggregation strategies for large semi-Markov processes

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. Aggregation of partitions can be done in one of two ways. The first is to use exact state-by-state aggregation to aggregate each individual state w...

• Type: Journal
• Year: 2011
• Where: PE
• Authors: Marcel C. Guenther, Nicholas J. Dingle, Jeremy T. Bradley, William J. Knottenbelt
• Keywords: Atomic Partition Aggregation, Exact State-by-state Aggregation, Optimization, Passage-time Analysis, PE 2011