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Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes

Author

Listed:
  • Winfried K. Grassmann

    (University of Saskatchewan)

  • Steve Drekic

    (University of Waterloo)

Abstract

A number of authors have recently suggested solving quasi birth-and-death (QBD) processes through the use of eigenvalue-based methods. These methods take on a special form when there are multiple eigenvalues present. We investigate this problem in a general setting as well as in the context of a specific preemptive priority queueing model.

Suggested Citation

  • Winfried K. Grassmann & Steve Drekic, 2008. "Multiple Eigenvalues in Spectral Analysis for Solving QBD Processes," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 73-83, March.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:1:d:10.1007_s11009-007-9036-4
    DOI: 10.1007/s11009-007-9036-4
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    References listed on IDEAS

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    1. Winfried K. Grassmann, 2003. "The Use of Eigenvalues for Finding Equilibrium Probabilities of Certain Markovian Two-Dimensional Queueing Problems," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 412-421, November.
    2. Douglas R. Miller, 1981. "Computation of Steady-State Probabilities for M / M /1 Priority Queues," Operations Research, INFORMS, vol. 29(5), pages 945-958, October.
    3. Drekic, Steve & Woolford, Douglas G., 2005. "A preemptive priority queue with balking," European Journal of Operational Research, Elsevier, vol. 164(2), pages 387-401, July.
    4. Steve Drekic & Winfried Grassmann, 2002. "An Eigenvalue Approach to Analyzing a Finite Source Priority Queueing Model," Annals of Operations Research, Springer, vol. 112(1), pages 139-152, April.
    Full references (including those not matched with items on IDEAS)

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