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An Eigenvalue Approach to Analyzing a Finite Source Priority Queueing Model

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  • Steve Drekic
  • Winfried Grassmann

Abstract

In this paper, we present a novel approach to determining the steady-state distribution for the number of jobs present in a 2-class, single server preemptive priority queueing model where the low priority source population is finite. Arrivals are assumed to be Poisson with exponential service times. The system investigated is a quasi birth and death process, and the joint distribution is derived via the method of generalized eigenvalues. Using this approach, we are able to obtain all eigenvalues and corresponding eigenvectors explicitly. Furthermore, we link this method to the matrix analytic approach by obtaining an explicit solution for the rate matrix R. Two numerical examples are given to illustrate the procedure and highlight some important computational features. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:112:y:2002:i:1:p:139-152:10.1023/a:1020933122382
    DOI: 10.1023/A:1020933122382
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    Citations

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    Cited by:

    1. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.
    2. Velika I. Dragieva, 2016. "Steady state analysis of the M/G/1//N queue with orbit of blocked customers," Annals of Operations Research, Springer, vol. 247(1), pages 121-140, December.
    3. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    4. 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.
    5. Doroudi, Sherwin & Avgerinos, Thanassis & Harchol-Balter, Mor, 2021. "To clean or not to clean: Malware removal strategies for servers under load," European Journal of Operational Research, Elsevier, vol. 292(2), pages 596-609.
    6. 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.
    7. 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.

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