Phase transitions in a multi-phase lattice hydrodynamic area occupancy model in mixed disorder traffic considering connected and human-driven vehicles

Recent developments in transportation systems have significantly accelerated the emergence of connected vehicles (CVs) within the V2V environment, coexisting with human-driven vehicles (HDVs). Understanding the traffic dynamics in the mixed environment of CVs and HDVs in disordered traffic where the vehicles do not follow lane discipline becomes excessively complex. In this context, a lattice hydrodynamic model is proposed that incorporates the area occupancy effect for the mixed traffic environment. Further, a multi-phase optimal velocity function is considered to portray the traffic flow characteristics more realistically as it considers the discontinuous accelerations occurring in real traffic. The traffic flow behavior is investigated through linear stability analysis, which depicts that the stability region narrows down as the fraction of CVs increases. Moreover, the mKdV equation is attained to study the slowly varying behavior of density waves near the critical point. It is observed that with an increase in the fraction of CVs, traffic flow stability increases significantly with increasing sensitivity. Notably, the theoretical results are validated through numerical simulation on unidirectional multi-phase traffic flow.