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We analyze the optimization framework for the rate allocation problem proposed by Kelly and investigate the stability of the system with arbitrary fixed communication delays between network elements. We show that there is an underlying discrete time system arising from a natural market structure. The stability of this market equilibrium is directly related to the stability of the rate control system. We first present general stability conditions of the system with arbitrary delays, and then apply these results to establish the stability of the system with a family of popular utility and resource price functions of interest to us.