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      • Theses - Department of Computer Engineering
      • Dept. of Computer Engineering - Master's degree
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      Kronecker-based infinite level-dependent QBDS : matrix analytic solution versus simulation

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      Author
      Orhan, Muhsin Can
      Advisor
      Dayar, Tuğrul
      Date
      2011
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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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 in- finite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death (LDQBD) 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, albeit more memory consuming, 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.
      Keywords
      Markov processes
      Numerical analysis
      Simulation
      Biology
      Queues theory
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      http://hdl.handle.net/11693/15256
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      • Dept. of Computer Engineering - Master's degree 511
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