Resource allocation in satellite networks: certainty equivalent approaches versus sensitivity estimation algorithms

In this paper, we consider a resource allocation problem for a satellite network, where variations of fading conditions are added to those of traffic load. Since the capacity of the system is finite and divided in finite discrete portions, the resource allocation problem reveals to be a discrete stochastic programming one, which is typically NP-hard. We propose a new approach based on the minimization over a discrete constraint set using an estimation of the gradient, obtained through a 'relaxed continuous extension' of the performance measure. The computation of the gradient estimation is based on the infinitesimal perturbation analysis technique, applied on a stochastic fluid model of the network. No closed-forms of the performance measure, nor additional feedback concerning the state of the system, and very mild assumptions on the probabilistic properties about the statistical processes involved in the problem are requested. Such optimization approach is compared with a dynamic programming algorithm that maintains a perfect knowledge about the state of the satellite network (traffic load statistics and fading levels). The comparison shows that the sensitivity estimation capability of the proposed algorithm allows to maintain the optimal resource allocation in dynamic conditions and it is able to provide even better performance than the one reached by employing the dynamic programming approach.