Passage time distributions in large Markov chains

Probability distributions of response times are important in the design and analysis of transaction processing systems and computercommunication systems. We present a general technique for deriving such distributions from high-level modelling formalisms whose state spaces can be mapped onto finite Markov chains. We use a load-balanced, distributed implementation to find the Laplace transform of the first passage time density and its derivatives at arbitrary values of the transform parameter s. Setting s = 0 yields moments while the full passage time distribution is obtained using a novel distributed Laplace transform inverter based on the Laguerre method. We validate our method against a variety of simple densities, cycle time densities in certain overtake-free (tree-like) queueing networks and a simulated Petri net model. Our implementation is thereby rigorously validated and has already been applied to substantial Markov chains with over 1 million states. Corresponding theoretical r...

• Type: Journal
• Year: 2002
• Where: SIGMETRICS
• Authors: Peter G. Harrison, William J. Knottenbelt
• Keywords: Hardware, Markov Chains, Passage Time, Passage Time Density, SIGMETRICS 2002