A method for estimating the relative speed factor parameter for a variable speed pump in a hydraulic network sufficient to maintain a fixed pressure at a control node is provided. A desired operating characteristic is determined and this is inserted into a matrix of equations describing the hydraulic system. The largely symmetrical matrix includes certain aspects of the system representing the variable speed pumps which are non-symmetrical. Non-symmetrical portions of the matrix are separated out and solved using an LU factorization technique. Non-sparse, non symmetric matrices are generated and the difference in head correction is solved for to compute the updated nodal head vector and ultimately determine the variable pump speed parameter. The invention allows estimation of the variable speed factor for a variable speed pump drive sufficient to maintain a fixed pressure at a control node. The system fully integrates variable pump speed operation with the status and control capabilities of known hydraulic network solvers.