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The standard simple rate equation model gives a qualitative description of semiconductor laser diodes. We have compared it to detailed measurements of the modulation response of a number of commercially available (AlGa)As laser diodes. For some of the diodes, the model was clearly inadequate for even a qualitative description; for others, it explained all the qualitative features of our observations. In the latter case, with the proper choice of values for the adjustable parameters, we also find remarkable quantitative agreement between the model and experiments, considering the simplicity of the model. Relaxation oscillations in general and picosecond pulse emission under RF modulation are well described by the model. However, the model parameter values that give the best fit to the experiments are different from parameter values deduced from properties of the laser material. The model represents a simple and compact parametrization of the transient modulation response of well-behaved semiconductor laser diodes.