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ABSTRACT:Car following models as well-known moving objects trajectory problems have been used for more than half a century in all traffic simulation software for describing driving behaviour in traffic flows. However, previous empirical studies and modeling about car following behavior had some important limitations. One of the main and clear defects of the introduced models was the very large number of parameters that made their calibration very time-consuming and costly. Also, any change in these parameters, even slight ones, severely disrupted the output. In this study, an artificial neural network approximator was used to introduce a trajectory model for vehicle movements. In this regard, the Levenberg-Marquardt back propagation function and the hyperbolic tangent sigmoid function were employed as the training and the transfer functions, respectively. One of the important aspects in identifying driver behavior is the reaction time. This parameter shows the period between the time the driver recognizes a stimulus and the time a suitable response is shown to that stimulus. In this paper, the actual data on car following from the NGSIM project was used to determine the performance of the proposed model. This dataset was used for the purpose of expanding behavioral algorithm in micro simulation. Sixty percent of the data was entered into the designed artificial neural network approximator as the training data, twenty percent as the testing data, and twenty percent as the evaluation data. A statistical and a micro simulation method were employed to show the accuracy of the proposed model. Moreover, the two popular Gipps and Helly models were implemented. Finally, it was shown that the accuracy of the proposed model was much higher -and its computational costs were lower -than those of other models when calibration operations were not performed on these models. Therefore, the proposed model can be used for displaying and predicting trajectories of moving objects being followed.