Robust resource reservation in virtual wireless networks

In this paper, we study resource reservation in virtual wireless networks with the aim of minimizing the operational cost. With this regard, the main constraint facing the operator is that only limited information about future traffic demand is typically available to the operator. To address this issue, we investigate reservation policies that are robust to the worst-case traffic demand which fits the available information i.e., the policies that minimize the worst-case expected operational cost. The problem is formulated for several resource reservation options that are commonly offered in practice. For each case, convexity of the problem is discussed and the its dual form is presented as a semidefinite program. While, semidefinite programs can be solved in polynomial time, the optimal closed-form reservation policies are obtained for several practical cases. Moreover, the worst-case cost of these policies are analytically compared to the expected cost of the algorithm that has full knowledge of the future demand. The theoretical analysis is supplemented with numerical results to demonstrate the behavior of our algorithms in terms of cost in some example traffic scenarios.