This paper introduces the procedure for an analytical derivation of the drop probability function for the Random Early Detection queue management mechanism. The procedure is based on a model of the TCP window system and the establishment for a criterion for system stability with methods of control theory. The term stability refers to the oscillation amplitude of the steady state queue size. The outcome is a polynomial function of the queue size, which can be approximated with a power function of the queue size. Besides the goal of achieving low oscillations for the whole load range, this derived function shows yet other advantages. There are no parameters to adjust, which extends the applicability of RED to a wide range of load situations applying the derived function. Additionally, the under-utilization at low loads, as often experienced with the original RED function, is avoided automatically. Simulations show clear evidence that the derived function outperforms the original linear RED function.