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Narrowing the Search for Optimal Call-Admission Policies Via a Nonlinear Stochastic Knapsack Model

Journal of Optimization Theory and Applications volume 164, pages 819–841 (2015)Cite this article

Abstract

Call admission control with two classes of users is investigated via a nonlinear stochastic knapsack model. The feasibility region represents the subset of the call space, where given constraints on the quality of service have to be satisfied. Admissible strategies are searched for within the class of coordinate-convex policies. Structural properties that the optimal policies belonging to such a class have to satisfy are derived. They are exploited to narrow the search for the optimal solution to the nonlinear stochastic knapsack problem that models call admission control. To illustrate the role played by these properties, the numbers of coordinate-convex policies by which they are satisfied are estimated. A graph-based algorithm to generate all such policies is presented.

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Notes

  1. This is different from the generalized stochastic knapsack problem considered in [6, Chapter 3].

  2. The notation used here is slightly different from the one of [1], where a distinction among “type-\(1\) corner points,” “type-\(2\) corner points,” and “corner points” is made.

  3. Not every combination of points in the grid is a feasible choice as a corner points. Indeed, by Definition 3.1 and the coordinate-convexity of \(\Omega \), no two corner points can be on the same vertical or horizontal lines.

  4. Recall that a monotonic path (see also [20]) is a path that starts in the upper-left corner, finishes in the lower-right corner, and consists entirely of edges pointing rightward or downward.

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Acknowledgments

G. Gnecco and M. Sanguineti were supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilitàe le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). M. Sanguineti was also supported by the Progetto di Ricerca di Ateneo 2013, granted by the University of Genoa.

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Authors and Affiliations

  1. Department of Telecommunications, Electronic, Electric, and Naval Engineering (DITEN), University of Genoa, Via Opera Pia, 11-16145 , Genova, Italy

    Marco Cello & Mario Marchese

  2. Institute for Advanced Studies (IMT), Piazza S. Ponziano, 6-55100 , Lucca, Italy

    Giorgio Gnecco

  3. Department of Computer Science, Bioengineering, Robotics, and Systems Engineering (DIBRIS), University of Genoa, Via Opera Pia, 13-16145 , Genova, Italy

    Giorgio Gnecco & Marcello Sanguineti

Authors
  1. Marco Cello
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  2. Giorgio Gnecco
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  3. Mario Marchese
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  4. Marcello Sanguineti
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Correspondence to Marcello Sanguineti.

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Cello, M., Gnecco, G., Marchese, M. et al. Narrowing the Search for Optimal Call-Admission Policies Via a Nonlinear Stochastic Knapsack Model. J Optim Theory Appl 164, 819–841 (2015). https://doi.org/10.1007/s10957-014-0570-2

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  • DOI: https://doi.org/10.1007/s10957-014-0570-2

Keywords

  • Stochastic knapsack
  • Nonlinear constraints
  • Call admission control
  • Coordinate-convex policies
  • Structural properties

Mathematics Subject Classification (2000)

  • 90B15
  • 90B18
  • 90C10
  • 90C27
  • 68M10