Analysis of feedback to obtain steady-state solutions in four-step modelling

The four-step travel demand model with feedback has been widely applied in developed cities; in contrast, its applications in developing countries are still very limited. When applying the model with feedback, it is important to figure out what kinds of feedback solutions should be used to obtain the uniquely converged outputs in an efficient way. Therefore, in this study, using the person-trip data collected in Jabodetabek metropolitan area of Indonesia in 2002, a newly developed four-step feedback model has been applied to compare the performances of different feedback solutions. Two major methods, i.e. the Constant Weights (CW) method and the Method of Successive Averages (MSA), are dealt with, where the CW method includes the conventionally applied Direct Feedback (DF) method as a special case. An empirical analysis result reveals that the application of the new feedback model based on the DF method converges most efficiently. It is further found that when using the CW method, the weight on the new matrix should be at least not less than 0.50 to make the feedback procedure converge quickly. Moreover, it is numerically confirmed that the trip matrices from different feedback solutions for one certain feedback process will lead to a unique convergence; in addition, the successive travel impedance matrices from any certain one of the feedback solutions could also converge finally.