Mobile ad-hoc networks : a new stochastic second-order cone programming approach

We study the semidefinite stochastic location-aided routing (SLAR) model described in Ariyawansa and Zhu (2006) [2] and in Zhu, Zhang, and Patel (2007) [16]. We propose a modification of their model to exploit the stochasticity inherent in the destination node movements. We formulate the problem as a two-stage stochastic second-order cone programming (SSOCP), see Alizadeh and Goldfarb (2003) [1], where the first-stage decision variables include both the position of the destination node and its distance from the sender node. Destination node movements are represented by ellipsoid scenarios defined in a neighborhood of the starting position and generated by uniform and normal disturbances. The MOSEK solver (under GAMS environment) allows to solve problems with a large number of scenarios (say 20250) versus the DSDP (under MATLAB framework) solver, see Benson, Ye and Zhang (2000) [4], adapted to stochastic programming framework with 500 scenarios. Stability results for the optimal first-stage solutions and for the optimal function value are obtained.