Narrowing the Search for Optimal Call-Admission Policies Via a Nonlinear Stochastic Knapsack Model
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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.
KeywordsStochastic knapsack Nonlinear constraints Call admission control Coordinate-convex policies Structural properties
Mathematics Subject Classification (2000)90B15 90B18 90C10 90C27 68M10
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.
- 4.Keller, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin Heidelberg (2004)Google Scholar
- 6.Ross, K.W.: Multiservice Loss Models for Broadband Telecommunication Networks. Springer, New York (1995)Google Scholar
- 11.Cello, M., Gnecco, G., Marchese, M., Sanguineti, M.: Structural properties of optimal coordinate-convex policies for CAC with nonlinearly-constrained feasibility regions. In: Proceedings of IEEE INFOCOM’11 Mini-Conf., pp. 466–470 (2011)Google Scholar
- 13.Dasylva, A., Srikant, R.: Bounds on the performance of admission control and routing policies for general topology networks with multiple call classes. In: Proceedings of IEEE INFOCOM’99, vol. 2, pp. 505–512 (1999)Google Scholar
- 15.Hörmander, L.: Notions of Convexity. Birkäuser, Boston (2007)Google Scholar
- 16.Likhanov, N., Mazumdar, R.R., Theberge, F.: Providing QoS in large networks: Statistical multiplexing and admission control. In: Boukas, E., Malhame, R. (eds.) Analysis, Control and Optimization of Complex Dynamic Systems, pp. 137–167. Kluwer (2005)Google Scholar
- 17.Barnhart, C., Wieselthier, J., Ephremides, A.: An approach to voice admission control in multihop wireless networks. In: Proceedings of IEEE INFOCOM’93, vol. 1, pp. 246–255 (1993)Google Scholar
- 20.Stanley, R.P.: Enumerative Combinatorics, vol. 2. Cambridge University Press, Cambridge (1999)Google Scholar
- 21.Comtet, L.: Advanced Combinatorics: the Art of Finite and Infinite Expansions. Kluwer, Amsterdam (1974)Google Scholar