Betweenness centrality can inform stability and delay margin in a large-scale connected vehicle system

Delays in information transmission and human reactions act as one main factor of instability in connected vehicle networks (CVN). This study reveals that a relationship exists between the delay margin (DM) of a class of CVN and betweenness centrality (BC) associated with the network graph of this CVN. Two dynamic models are considered, one only uses velocity information of vehicles while the other considers velocity and headway to regulate vehicles' motions. We randomize vehicle orders in multiple trials to generate platoon samples. DM and BC values are computed in each platoon and the respective statistical models between them are obtained. The results show that the mean and variance of BC have a negative correlation with DM. We complete the study with a string stability analysis, which demonstrates the diffusion of oscillations in a platoon where there is no explicit leader. In summary, the work bridges DM with BC in a CVN and provides insights toward designing platoons with larger DM. These rules also enable means to rapidly estimate DM from statistical models. Lastly, we report that, to achieve string stability, large human -driven vehicle clusters are not recommended.