This paper contributes to the vehicle-level analysis of two macroscopic features of the road traffic: capacity variability and capacity drop. This paper focuses only on car-following (CF) behavior and leaves the part related to lane-change maneuvers for future research. In particular, a simplistic CF model (Newell’s with bounded acceleration) for a single-lane scenario is studied. In this work, by introducing a speed limitation across a zone, a bottleneck with variable nominal capacity has been created. A continuous event-based numerical resolution method is used. Consequently, it is possible to vary the three Newell’s model parameters: maximal acceleration, minimal distance, and reaction time. It has been shown that the variability of those CF parameters (e.g., reaction time, minimal distance, and maximal acceleration) has a strong impact on pre-breakdown capacity variation and also on queue discharge flow. It has been concluded that this parameters variability does affect the drop (provided that the maximal acceleration has a relatively high mean value). Various distribution shapes (uniform, truncated Gaussian, and Gamma) have been explored. It has been realized that this does not have any significant impact on the capacity distribution. Concerning the amplitude of the capacity distribution, it is demonstrated that reaction time is the parameter with the highest impact followed by minimal distance. If all parameters vary with an amplitude of 30%, it is shown that the capacity standard deviation, in this scenario without lane changes, is about half the experimental values reported in the literature.