Behavior-rule dependence of capacity gains in autonomous/human mixed cellular-automaton traffic, and the absence of a penetration threshold for slow-to-start hysteresis suppression

Abstract

The dependence of capacity gains on the choice of autonomous-vehicle (AV) behavior rule is investigated using a Nagel-Schreckenberg-type cellular-automaton model of mixed AV and human-driven vehicle (HV) traffic. Four AV following rules (a naive deterministic rule, the Intelligent Driver Model, adaptive cruise control, and cooperative adaptive cruise control) are implemented under a common collision-safety architecture, in which each vehicle computes a desired speed from its own rule and is then subject to the same hard safety floor. Slow-to-start dynamics are retained for the human-driven vehicles so that metastability and hysteresis are present, and the hysteresis loop width is measured as a function of AV penetration rate on a fine penetration grid at four ring sizes. The framework is validated against an exact two-species disordered exclusion-process solution at unit maximum velocity, with agreement to within 0.53 percent. The capacity gain from AV penetration is found to be highly sensitive to the calibration of the AV following rule rather than being an intrinsic property of the rule itself: under human-calibrated Intelligent Driver Model parameters, capacity is not monotonic in penetration but falls below the human-only baseline at intermediate penetration and recovers above it at full penetration, so that a mixture of the two populations carries less flow than either population alone, whereas doubling the acceleration and deceleration capability removes the deficit. Cooperative adaptive cruise control, in contrast, saturates the common safety floor and becomes indistinguishable from the naive rule at high penetration, while adaptive cruise control remains distinct owing to its longer effective headway. The suppression of slow-to-start hysteresis, by contrast, is shown to be a continuous crossover rather than a threshold effect: the loop width decreases monotonically within uncertainty across the penetration range, the decline accelerates above roughly seventy percent penetration, and the curves for ring sizes spanning a factor of eight collapse to within a few percent, with the larger rings giving slightly smaller widths, so that the descent does not sharpen as the system is enlarged. This part of the study uses the naive deterministic AV rule alone, so it establishes the shape of the suppression and not its dependence on the behavior rule. No critical penetration rate is therefore identified. It is shown further, by direct measurement, that the AV share of standing vehicles tracks the penetration rate to within five parts in ten thousand and that standing times are indistinguishable between the two vehicle types, which excludes an explanation resting on AVs coming to dominate the standing population. We conclude that the widely assumed benefit of AV penetration for traffic flow is not a model-independent conclusion for capacity, where it depends sensitively on the behavior rule and its calibration, and that for hysteresis it accrues gradually rather than at a deployment threshold.