In this paper we present a multi-parent adaptive video streaming system (MAVSS). MAVSS is a cooperative video streaming system, based on the Peer-to-Peer (P2P) content distribution concept, to simultaneously adapt and stream video contents to heterogeneous users. In order to ensure video codec independence, we emphasize on structured metadata-based adaptation. Therefore, MPEG-21 generic Bitstream Syntax Description (gBSD) is selected to describe the parts of the video contents selected for adaptation operations. Additionally, without an optimal solution, it is hard to judge the efficiency of such systems. Therefore, in this paper, we first present the fundamental properties of a multi-parent adaptive video streaming system. We then present a mathematical model of the adaptive streaming system, where we define efficient streaming as an optimization of a cost function that can be solved as an Integer Linear Programming problem. The model illustrates the relation among all the parameters that affect the resource contribution, resource utilization, load balancing, and service fairness. We use this model to analyze the trade-offs that exist between service fairness and system efficiency.