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Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks

Author

Listed:
  • J. George Shanthikumar

    (University of California, Berkeley, California)

  • David D. Yao

    (Harvard University, Cambridge, Massachusetts)

Abstract

We study a Gordon-Newell type of closed queueing network that frequently arises in modeling manufacturing and computer systems. We are concerned with the transient and equilibrium behavior of the joint and individual queue lengths in the network when the job population increases. We show that increasing the job population will stochastically increase the queue-length vector process, provided that all stations have nondecreasing service rates. Single and multivariate likelihood ratio orderings are also established for the joint queue lengths in equilibrium. Our results extend the applicability of previously known results in the literature.

Suggested Citation

  • J. George Shanthikumar & David D. Yao, 1987. "Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks," Operations Research, INFORMS, vol. 35(4), pages 583-588, August.
    • Handle: RePEc:inm:oropre:v:35:y:1987:i:4:p:583-588
    DOI: 10.1287/opre.35.4.583
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    Citations

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    Cited by:

    1. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    2. Dijk, N.M. van, 1989. "Simple performance estimates and error bounds for slotted ALOHA loss systems," Serie Research Memoranda 0013, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    3. Dijk, N.M. van, 1988. "Truncation of Markov chains with applications to queueing," Serie Research Memoranda 0053, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. Dijk, N.M. van, 1989. "The importance of bias-terms for error bounds and comparison results," Serie Research Memoranda 0036, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    5. Saumard, Adrien & Wellner, Jon A., 2018. "Efron’s monotonicity property for measures on R2," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 212-224.
    6. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    7. Dijk, N.M. van, 1989. "A simple performability estimate for Jackson networks with an unreliable output channel," Serie Research Memoranda 0032, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

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