06070929

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06070929 Br\'azdil, Tom\'{a}\v{s} Kiefer, Stefan Stabilization of branching queueing networks. D\"urr, Christoph (ed.) et al., STACS 2012. 29th international symposium on theoretical aspects of computer science, Paris, France, February 29th -- March 3rd, 2012. Wadern: Schloss Dagstuhl -- Leibniz Zentrum f\"ur Informatik (ISBN 978-3-939897-35-4). LIPICS -- Leibniz International Proceedings in Informatics 14, 507-518, electronic only (2012). 2012 Wadern: Schloss Dagstuhl -- Leibniz Zentrum f\"ur Informatik EN continuous-time Markov decision processes infinite-state systems performance analysis

doi:10.4230/LIPIcs.STACS.2012.507

Summary: Queueing networks are gaining attraction for the performance analysis of parallel computer systems. A Jackson network is a set of interconnected servers, where the completion of a job at server $i$ may result in the creation of a new job for server $j$. We propose to extend Jackson networks by``branching" and by ``control" features. Both extensions are new and substantially expand the modelling power of Jackson networks. On the other hand, the extensions raise computational questions, particularly concerning the stability of the networks, i.e, the ergodicity of the underlying Markov chain. We show for our extended model that it is decidable in polynomial time if there exists a controller that achieves stability. Moreover, if such a controller exists, one can efficiently compute a static randomized controller which stabilizes the network in a very strong sense; in particular, all moments of the queue sizes are finite.