In recent years several multi-body, circumbinary planets have been proposed to orbit short-period eclipsing binaries. In light of the recent discoveries based on the Kepler data, the existence of such systems seems plausible. However, performing a detailed dynamical analysis reveals that the majority of the proposed planetary systems follow highly unstable orbits. In order to solve the origin of this problem, we have started to model synthetic light-travel time signals of stable planetary systems. In particular, we aim to study the response of the model in various circumstances (e.g red/white noise level, various sampling frequencies, in-homogeneous data sets, baseline dependency.) This work will significantly increase the confidence with which model work is carried out for future systems and help towards an understaning when models break down (e.g resulting in unstable systems).