The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller

This paper focuses on two fundamental issues in traffic flow modelling: string stability of car following (CF), and oscillation of traffic flow. Its aim is to explore the complementary use of CF instability analysis and oscillation analysis to compress and ease traffic congestion in a connected environment. Each of these topics has been extensively investigated in the literature. However, each topic has been investigated separately and, despite the inherent conceptual and empirical closeness of the two concepts, little effort has been devoted to untangling their relationship. To address this failing, we first define four types of oscillation – amplitude-decay oscillation, amplitude-ceiling oscillation, speed-deviation ceiling oscillation, and speed-deviation growth oscillation – and reveal their similarities and dissimilarities to CF instability. Based on the stability criterion, we then develop oscillation criteria to identify different types of oscillation by relaxing two unrealistic assumptions used in CF stability analysis (i.e., infinitely-long platoon and long-wavelength perturbation). Finally, to demonstrate how CF instability analysis and oscillation analysis can be combined to influence individual vehicle stability and improve traffic oscillations in a connected environment, a platoon of vehicles that experience an oscillation in the NGSIM data is used in a case study. In this case study, different control factors are used for different vehicle types: connected (but human-driven) vehicles, and automated vehicles. Our analysis shows that a higher stability of some individual vehicles can alleviate the oscillation severity for the platoon. It also shows that desired time gap and maximum acceleration are two promising parameters that can be used to both improve individual vehicle stability and significantly smooth the oscillation of the platoon in a connected and/or automated environment. Of particular note, when considering all of the factors explored in our analysis, adjustment of the desired time gap is the most effective factor in smoothing traffic oscillations