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We analyze the stability properties of an end-to-end congestion control scheme under fixed heterogeneous delays, and for general network topologies. The scheme analyzed is based on the congestion control game, with the starting point being the unique Nash equilibrium of that game. We prove global stability of this solution (and hence of the congestion control algorithm) under a mild symmetricity condition. We further demonstrate the stability of the algorithm numerically for various delays, user numbers, and topologies.