A new iterative numerical solution algorithm for Markovian queueing networks

Abstract

Continuous time Markov chains describing the behaviour of closed queueing networks are considered. We present an algorithm which enables the reduction of storage requirements for generator matrices of Markov chains. Applying this algorithm in the area of iterative numerical solution methods, we can show that neither the generator matrix nor ”parts” of them must be generated and stored. We will consider models with up to 107 states and 109 matrix entries and we will demonstrate that these models can be analysed. Further, this algorithm can be integrated easily in tools which contain iterative numerical solution methods.