Probabilistically robust string stability of mixed traffic with Markovian vehicle distribution

The string stability of mixed traffic flow depends not only on the penetration rate of connected and automated vehicles (CAVs), but also on their spatial distribution and the uncertainty of microscopic interaction parameters. To characterize this coupled effect, this study develops a probabilistically robust string stability framework for mixed traffic composed of CAVs and human-driven vehicles (HDVs). A two-state Markov chain is introduced to describe the vehicle-type sequence, and a divergence measure is defined to quantify the degree of interleaving between CAVs and HDVs under a prescribed penetration rate. Based on the steady-state proportions of adjacent vehicle pairs, a unified string stability function is constructed by aggregating the linear stability measures of different car-following modes. By combining Lipschitz continuity with velocity-region discretization, a computable sufficient condition is derived for string stability over a continuous velocity region. The deterministic criterion is then extended to a chance-constrained formulation, and a zero-violation scenario approach is employed to establish probabilistically robust stability guarantees under uncertainty. Numerical results show that the stable region expands significantly as the CAV penetration rate increases and the divergence decreases. The resulting phase diagrams further reveal a transition from instability to robust operation, while time-domain simulations confirm the corresponding disturbance propagation patterns. These results highlight that mixed-traffic stability is governed jointly by composition, spatial organization, and uncertainty, and provide a probabilistic perspective for analyzing collective traffic dynamics.