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• Formalizing heterogeneity of the vehicle-driver system. • Free-flow term of a CF model leads to the formation and propagation of oscillations. • Simulations reproduce periodical oscillations with variable amplitudes and periods. • The concave growth pattern of the standard deviation of the speed is observed. • Validation was performed on three real-world car-following datasets. • The proposed approach provides accurate fuel consumption estimations. Road traffic congestion is the result of various phenomena often of random nature and not directly observable with empirical experiments. This makes it difficult to clearly understand the empirically observed traffic instabilities. The vehicles' acceleration/deceleration patterns are known to trigger instabilities in the traffic flow under congestion. It has been empirically observed that free-flow pockets or voids may arise when there is a difference in the speeds and the spacing between the follower and the leader increases. During these moments, the trajectory is dictated mainly by the characteristics of the vehicle and the behaviour of the driver and not by the interactions with the leader. Voids have been identified as triggers for instabilities in both macro and micro level, which influence traffic externalities such as fuel consumption and emissions. In the literature, such behaviour is usually reproduced by injecting noise to the results of car-following models in order to create fluctuations in the instantaneous vehicles' acceleration. This paper proposes a novel car-following approach that takes as input the driver and the vehicle characteristics and explicitly reproduces the impact of the vehicle dynamics and the driver's behaviour by adopting the Microsimulation Free-flow aCceleration (MFC) model. The congested part of the model corresponds to the Lagrangian discretization of the LWR model and guarantees a full consistency at the macroscopic scale with congested waves propagating accordingly to the first-order traffic flow theory. By introducing naturalistic variation in the driving styles (timid and aggressive drivers) and the vehicle characteristics (specification from different vehicle models), the proposed model can reproduce realistic traffic flow oscillations, similar to those observed empirically. An advantage of the proposed model is that it does not require the injection of any noise in the instantaneous vehicle accelerations. The proposed methodology has been tested by studying a) the traffic flow oscillations produced by the model in a one-lane road uphill simulation scenario, b) the ability of the model to reproduce car-following instabilities observed in three car-following trajectory datasets and c) the ability of the model to produce realistic fuel consumption estimates. The results prove the robustness of the proposed model and the ability to describe traffic flow oscillations as a consequence of the combination of driving style and vehicle's technical specifications. [ABSTRACT FROM AUTHOR]