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      Kronecker-based infinite level-dependent QBD processes

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      Author
      Dayar, T.
      Orhan, M. C.
      Date
      2012
      Source Title
      Journal of Applied Probability
      Print ISSN
      0021-9002
      Publisher
      Applied Probability Trust
      Volume
      49
      Issue
      4
      Pages
      1166 - 1187
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably infinite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, even though more memory is consumed, there are many cases where a matrix-analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation. © Applied Probability Trust 2012.
      Keywords
      Biology
      Markov process
      Numerical analysis
      Queues: theory
      Simulation
      Permalink
      http://hdl.handle.net/11693/21198
      Published Version (Please cite this version)
      http://dx.doi.org/10.1239/jap/1354716665
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