In: Lecture Notes in Computer Science, Vol. 977: Quantitative Evaluation of Computing and Communication Systems, pages 194-208. Springer Verlag, 1995.
Abstract: Continuous-time Markov chains describing the behavior of closed queueing networks are considered in this paper. An algorithm is presented which enables the reduction of storage requirements for generator matrices of Markov chains. Applying this algorithm in the area of iterative numerical solution methods, it can be shown that neither the generator matrix nor `parts' of of it must be generated and stored. Models with up to 107 states and 109 matrix entries can be analyzed. Further, this algorithm can be integrated easily into tools which contain iterative numerical solution methods.
Keywords: Markovian queueing networks, iterative numerical solutions, stochastic Petri nets.