Figure 1

(a) A sketch of three vehicles following each other on a ring road. Orange and purple arrows show the direction of information propagation through V2V communication with delays marked on each link. (b) Delay distributions (14) with support (22) for modes $k=1,2$. Dashed-dotted blue lines with circles and solid red lines with crosses correspond to the distributions calculated analytically for modes 1 and 2, respectively. Numerical approximations are shown as solid gray curves. (c) Stability chart with the stable domain shaded. Dashed-dotted blue, solid red, and dashed green curves correspond to the first, second, and third modes, respectively. When crossing thin curves stability changes through a pair of complex conjugate characteristic roots while thick lines correspond to a stability change with zero characteristic root. (d) Comparing the leading characteristic roots obtained from (18) (black circles) and (21) (blue plus, red cross, green star for modes 1,2,3) for $K=6$. Parameters correspond to the point marked by a dot on (c).Reuse & Permissions

Figure 2

Stability charts with different delay values as indicated on each panel. The same notation is used as in Fig. 1c.Reuse & Permissions