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1 results

  • Kronecker-Based Infinite Level-Dependent QBD Processes

  • Part of
  • TuǦrul Dayar, M. Can Orhan
  • Journal:
    Journal of Applied Probability / Volume 49 / Issue 4 / December 2012
    Published online by Cambridge University Press:
    30 January 2018, pp. 1166-1187
    Print publication:
    December 2012
    • Article
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  • 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.