Random capacity for a single lane with mixed autonomous and human-driven vehicles: Bounds, mean gaps and probability distributions

In this study, we concentrate on the random capacity of a single lane in the context of mixed traffic flow with both autonomous vehicles (AVs) and human-driven vehicles (HVs). We first revisit and enrich the bound estimation of the random lane capacity. We proceed to rigorously investigate the non-negligible gap between two widely-used approximate mean capacity functions and their generalized function. The analysis results show that the improper use of approximate mean capacity functions in AV-HV traffic assignment and road network planning could lead to biased and even misleading decisions. Lastly, we explore the probability distribution of the random lane capacity using simulation and distribution fitting techniques, where both fixed and random headway scenarios with different AV shares are addressed. Six suitable probability distributions for the random lane capacity are identified, and the top three are Log-Pearson 3, Log-Gamma, and Lognormal distributions.