Recent transportation research suggests that autonomous vehicles (AVs) have the potential to improve traffic flow efficiency as they are able to maintain smaller car-following distances. Nevertheless, being a unique class of ground robots, AVs are susceptible to robotic errors, particularly in their perception module, leading to uncertainties in their movements and an increased risk of collisions. Consequently, conservative operational strategies, such as larger headway and slower speeds, are implemented to prioritize safety over traffic capacity in real-world operations. To reconcile the inconsistency, this paper proposes an analytical model framework that delineates the endogenous reciprocity between traffic safety and efficiency that arises from robotic uncertainty in AVs. Car-following scenarios are extensively examined, with uncertain headway as the key parameter for bridging the single-lane capacity and the collision probability. A Markov chain is then introduced to describe the dynamics of the lane capacity, and the resulting expected collision-inclusive capacity is adopted as the ultimate performance measure for fully autonomous traffic. With the help of this analytical model, it is possible to support the settings of critical parameters in AV operations and incorporate optimization techniques to assist traffic management strategies for autonomous traffic.
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