Stabilizing mixed cooperative adaptive cruise control traffic flow to balance capacity using car-following model

String stability is important for understanding traffic flow dynamics, while its analytical study for mixed traffic is deficient. We focus on an analytical framework on string stability of mixed traffic consisting of cooperative adaptive cruise control (CACC), adaptive cruise control (ACC), and human vehicles. The analytical framework was conducted based on generalized car-following model formulations of the three vehicular types. Then string stability criterions of one-class traffic flow, mixed traffic flow, and local CACC/ACC platoons were derived. Taking into account the mixed flow with partial degenerations of CACC and three concrete car-following models, an example application was studied. The example application analyzed the string stability from the perspectives of the homogeneous flow, the mixed traffic flow, and the local CACC/ACC platoon, respectively. The example application also studied balance between stability and capacity for the mixed traffic with CACC vehicles. Results show the usefulness of the proposed analytical framework, in term of not only analyzing string stability but also providing suggestions for dynamic regulations of CACC/ACC management strategy to balance string stability and traffic capacity for the mixed CACC-human flow.