Stochastic and semidefinite optimization for scheduling in orthogonal frequency division multiple access networks

• Published in: Journal of scheduling Vol. 17; no. 5; pp. 445 - 469
• Main Authors: Adasme, Pablo, Lisser, Abdel
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.10.2014; Springer Nature B.V; Springer Verlag
• Subjects: Artificial Intelligence; Bandwidths; Business and Management; Calculus of Variations and Optimal Control; Optimization; Computer Science; Frequency division multiple access; Linear programming; Lower bounds; Mathematical models; Mathematics; Networks; Operations Research; Operations Research/Decision Theory; Optimization; Optimization and Control; Optimization techniques; Power; Probability; Probability theory; Quadratic programming; Random variables; Scheduling; Stochasticity; Studies; Supply Chain Management; Wave division multiplexing; Wireless networks; Semidefinite programming; Resource allocation in OFDMA; Quadratic programming; Stochastic programming
• ISSN: 1094-6136; 1099-1425
• DOI: 10.1007/s10951-013-0333-1

In this paper, we propose stochastic binary quadratic programs for the scheduling resource allocation process of a wireless orthogonal frequency division multiple access network. More precisely, we formulate a two-stage stochastic model, then we further extend the two-stage model by introducing a knapsack probabilistic constrained approach, and finally we propose a multi-stage stochastic program for this problem. The models are aimed at minimizing the total power consumption of the network at each time slot of the scheduling process subject to user bit rates, sub-carrier and modulation linear constraints. In order to compute lower bounds, we derive linear and semidefinite programming relaxations for each of the proposed models. The bounds are also compared with a basic variable neighborhood search metaheuristic approach. Numerical results show tight lower bounds for the semidefinite relaxations when compared to the linear ones and with the metaheuristic. Moreover, near optimal solutions are found with the semidefinite relaxations for the two-stage model without using probabilistic constraints and for the multi-stage program as well.