When traffic congestion forms on a road, the flow downstream of the congestion is generally lower than the pre-queue capacity. This phenomenon is called the capacity drop. Recent empirical observations show a positive relationship between the speed in congestion and the queue discharge rate. In literature, this relation is also observed in the absence of lane changing. These findings help in understanding the microscopic mechanism behind the capacity drop. Literature indicates that variations in driver behaviors can account for the capacity drop. However, there is no solid understanding of what and how this variation in driver behaviors lead to the capacity drop, especially without lane changing. Hence, a parsimonious car-following model is extended by incorporating the empirically observed desired acceleration stochasticity. The extended parsimonious car-following model shows different capacity drop magnitudes in different traffic situations, consistent with empirical observations. Data collected from a car-following experiment is applied to validate the model, which shows the new model can catch most of the properties of longitudinal behaviors. All results indicate that the stochasticity of desired accelerations is a significant reason for the capacity drop. The new insights can be used to develop and test new control measures. Our findings show newer vehicle technologies and conventional road side traffic control measures (e.g., speed limit) should be beneficial for reducing or maybe even eliminating capacity drop.