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Continuity and monotonicity of solutions to a greedy maximization problem

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  • Łukasz Kruk

    (Maria Curie-Skłodowska University)

Abstract

Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in $${\mathbb {R}}^n$$ R n , with the admissible set indexed by the time parameter. The structure of the constraints depends on the underlying network topology. We investigate continuity and monotonicity of the resulting maximizers with respect to time. Our results have important consequences for fluid models of the corresponding networks which are optimal, in the appropriate sense, with respect to handling real-time transmission requests.

Suggested Citation

  • Łukasz Kruk, 2020. "Continuity and monotonicity of solutions to a greedy maximization problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(1), pages 33-76, August.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:1:d:10.1007_s00186-020-00705-x
    DOI: 10.1007/s00186-020-00705-x
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    References listed on IDEAS

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    1. Samuli Aalto & Urtzi Ayesta, 2009. "SRPT applied to bandwidth-sharing networks," Annals of Operations Research, Springer, vol. 170(1), pages 3-19, September.
    2. Luss, Hanan, 1992. "Minimax resource allocation problems: Optimization and parametric analysis," European Journal of Operational Research, Elsevier, vol. 60(1), pages 76-86, July.
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    4. Łukasz Kruk, 2017. "Edge minimality of EDF resource sharing networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 331-366, October.
    5. Łukasz Kruk & Ewa Sokołowska, 2016. "Fluid Limits for Multiple-Input Shortest Remaining Processing Time Queues," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1055-1092, August.
    6. Łukasz Kruk, 2016. "Minimality of EDF networks with resource sharing," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 259-283, October.
    7. Douglas G. Down & H. Christian Gromoll & Amber L. Puha, 2009. "Fluid Limits for Shortest Remaining Processing Time Queues," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 880-911, November.
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