A mixed traffic capacity analysis and lane management model for connected automated vehicles: A Markov chain method

The projected rapid growth of the market penetration of connected and autonomous vehicle technologies (CAV) highlights the need for preparing sufficient highway capacity for a mixed traffic environment where a portion of vehicles are CAVs and the remaining are human-driven vehicles (HVs). This study proposes an analytical capacity model for highway mixed traffic based on a Markov chain representation of spatial distribution of heterogeneous and stochastic headways. This model captures not only the full spectrum of CAV market penetration rates but also all possible values of CAV platooning intensities that largely affect the spatial distribution of different headway types. Numerical experiments verify that this analytical model accurately quantifies the corresponding mixed traffic capacity at various settings. This analytical model allows for examination of the impact of different CAV technology scenarios on mixed traffic capacity. We identify sufficient and necessary conditions for the mixed traffic capacity to increase (or decrease) with CAV market penetration rate and platooning intensity. These theoretical results caution scholars not to take CAVs as a sure means of increasing highway capacity for granted but rather to quantitatively analyze the actual headway settings before drawing any qualitative conclusion. This analytical framework further enables us to build a compact lane management model to efficiently determine the optimal number of dedicated CAV lanes to maximize mixed traffic throughput of a multi-lane highway segment. This optimization model addresses varying demand levels, market penetration rates, platooning intensities and technology scenarios. The model structure is examined from a theoretical perspective and an analytical approach is identified to solve the optimal CAV lane number at certain common headway settings. Numerical analyses illustrate the application of this lane management model and draw insights into how the key parameters affect the optimal CAV lane solution and the corresponding optimal capacity. This model can serve as a useful and simple decision tool for near future CAV lane management.