Stabilization of Branching Queueing Networks

Authors Tomáš Brázdil, Stefan Kiefer

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Tomáš Brázdil
Stefan Kiefer

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Tomáš Brázdil and Stefan Kiefer. Stabilization of Branching Queueing Networks. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 507-518, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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.
  • continuous-time Markov decision processes
  • infinite-state systems
  • performance analysis


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