Price Control for Computational Offloading Services with Chaotic Data

Recently, price control has gained attention as method to influence costumers behaviors through the services price regulation. This paper focuses on the analysis of the dynamic price control problem, from the provider perspective, in supplying computational offloading within a fog network, considering different classes of services, and without the knowledge about the equation state. The goal is to maximize the service provider profit, by controlling the prices associated to each class of service. In this regards, a monopoly condition has been considered, and we supposed that prices variations impact the services demand. The system states are represented by realistic big data that exhibit a chaotic behavior, confirmed by a preliminary study about the dynamical features of the time series. Since the formulated optimal control problem lacks in knowledge about the analytical state equations, optimal control with partial information has been used. Therefore, the state equation has been approximated by an affine nonlinear function, so that a neural network approach recently proposed in literature has been employed to overcome the system uncertainty. Finally, the numerical results confirm the validity of the approach contextualized to the proposed discrete-time nonlinear optimal control, by providing the effectiveness of the proposed analysis.