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A Concept of Monotonicity and Its Characterization for Closed Queueing Networks

Author

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  • Rajan Suri

    (Harvard University, Cambridge, Massachusetts)

Abstract

We define a qualitative property, called monotonicity, for a closed queueing network. This property is defined both for a station in the network and for the network as a whole. Several results in this paper relate monotonic behavior to the known parameters of a network and allow us to state a priori, for many practical systems, whether the monotonicity property will apply for a network or a station. Monotonicity thus ensures that the system is well-behaved with respect to a number of parameters. We present diverse examples that demonstrate how knowledge of this property can be useful in network design and performance evaluation.

Suggested Citation

  • Rajan Suri, 1985. "A Concept of Monotonicity and Its Characterization for Closed Queueing Networks," Operations Research, INFORMS, vol. 33(3), pages 606-624, June.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:3:p:606-624
    DOI: 10.1287/opre.33.3.606
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    Cited by:

    1. Waal, P.R. & Dijk, N.M. van, 1988. "Monotonicity of performance measures in a processor sharing queue," Serie Research Memoranda 0051, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Dijk, N.M. van, 1989. "Sensitivity error bounds for non-exponental stochastic networks," Serie Research Memoranda 0093, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    3. 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.
    4. 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.
    5. van Dijk, Nico M., 2008. "Error bounds for state space truncation of finite Jackson networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 164-181, April.
    6. Gordon H. Lewis & Ashok Srinivasan & Eswaran Subrahmanian, 1998. "Staffing and Allocation of Workers in an Administrative Office," Management Science, INFORMS, vol. 44(4), pages 548-570, April.

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