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In this paper we focus on the provision of proportional class-based service differentiation to transmission control protocol (TCP) flows in the context of bandwidth on demand (BoD) split-TCP geostationary (GEO) satellite networks. Our approach involves the joint configuration of TCP-Performance Enhancing Proxy (TCP-PEP) agents at the transport layer and the scheduling algorithm controlling the resource allocation at the Medium Access Control (MAC) layer. We show that the two differentiation mechanisms exhibit complementary behavior in achieving the desired differentiation throughout the traffic load space: the TCP-PEPs control differentiation at low and medium system utilization, whereas the MAC scheduler becomes the dominant differentiation factor under high traffic load. The main challenge for the satellite operator is to appropriately configure those two mechanisms to achieve a specific differentiation target for the different classes of TCP flows. To this end, we propose a fixed-point framework to analytically approximate the achieved differentiated TCP performance. We validate the predictive capacity of our analytical method via simulations and show that our approximations closely match the performance of different classes of TCP flows under various scenarios for the network traffic load and configuration of the MAC scheduler and TCP-PEP agent. Satellite network operators could use our approximations as an analytical tool to tune their networks.