Several microscopic traffic flow models were tested with a publicly available data set. The task was to predict the travel times between several observers along a one-lane rural road, given as boundary conditions the flow into this road and the flow out of it. By using nonlinear optimization, the best matching set of parameters for each of the models was estimated. For this particular data set, the models that performed best were the ones with the smallest number of parameters. The average error rate of the best models is about 16%; however, this value is not very reliable: the error rate fluctuates between 2.5% and 25% for different parts of the data set.