The FastSATME method and system estimate source-to-destination traffic matrices using a simulated annealing algorithm, the traffic matrix estimation being represented as a probability distribution over the set of all possible matrices that satisfy a set of given constraints. The constraints explicitly encode information that the user knows about the network traffic as components of an objective function (a fitness function), that is then minimized using simulated annealing. With the method according to the invention, arbitrary constraints of any form can be included. FastSATME works over a series of time steps. At the first time step FastSATME acts the same as SATME but in subsequent time steps, the estimate of the traffic matrix at time t is based on the estimate at t-1.