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