Rate allocation for satellite systems with correlated channels based on a Stackelberg game

In this paper, we consider the problem of capacity allocation for fixed broadband (Ka band) satellite networks with a large coverage and correlated atmospheric channel conditions both in time and space. The transmitted bit rate adapts to the channel by varying the coding rate and the constellation. The network is operated by a single service provider. The model of interest is the downlink where the provider allocates capacity to users with Quality of Service (QoS) guarantees. We first analyze the optimal single-objective optimum allocation by which users' utilities are maximized. We find a closed form for both the proportionally fair and opportunistic allocations. However, these allocations do not show any clear benefit for a profit-seeking service provider because both the efficiency of the network and the user satisfaction with the service cannot be controlled as it mostly depends on the random nature of the correlation properties of the channel. We then propose a Stackelberg game which provides an equilibrium that allows us to prove that 1) the proportionally fair allocation corresponds to a flat-rate pricing model (as used in today's satellite systems) and 2) Pareto improving policies can be obtained by using differential pricing. From the simulation results, we show that the bit rate allocation based on the Stackelberg formulation yields a network efficiency which is in between the one achieved by the proportionally fair and the opportunistic allocations (as expected from the Pareto improvement), with the advantage that now the efficiency is under full control of the system designer. We also show that the higher the differential pricing the higher the network efficiency. As a general conclusion, both the efficiency of the network and the satisfaction of the users improve with our proposed scheme compared to current designs and therefore a differentiated pricing should be a design goal for this type of systems.