When applied to a network as a whole, Equations 1-3 represent a coupled set of differential/algebraic equations with time-varying coefficients that must be solved for Ci in each pipe i and Cs in each storage facility s. This solution is subject to the following set of externally imposed conditions:

• Initial conditions that specify Ci for all x in each pipe i and Cs in each storage facility s at time 0
• Boundary conditions that specify values for Ck,ext and Qk,ext for all time t at each node k which has external mass inputs
• Hydraulic conditions which specify the volume Vs in each storage facility s and the flow Qi in each link i at all times t