Projected Attainable Speed Space: A Driving Efficiency Metric Connecting Instantaneous Evaluation to Travel Time

Inefficient driving behaviors, such as overly conservative yielding, remain a key obstacle to deployment of autonomous vehicles (AVs). Instantaneous driving efficiency metrics are crucial for self-driving decision-making because they affect real-time performance evaluation and control optimization. However, commonly used indicators, including speed, relative speed, and inter-vehicle distance, are limited in capturing traffic context and in ensuring consistency between instantaneous outputs and travel-level outcomes. This study proposes the Projected Attainable Speed Space (PASS) model, a unified framework for driving efficiency assessment across instantaneous and travel-level analyses by integrating kinematic and spatial traffic information. PASS characterizes instantaneous driving efficiency with two coupled elements: potential for speed improvement (available acceleration space) and response to that potential (utilization of available acceleration space). Available acceleration space is referenced to projected attainable speed, derived from an idealized catch-up maneuver using relative speed and spacing to the leading vehicle; utilization is represented by the temporal change in available acceleration space. To ensure cross-scale consistency, time-aggregated PASS is defined as a travel-level efficiency metric. Trajectory data from a driving simulation experiment are used for parameter calibration to maximize agreement between time-aggregated PASS and observed travel times. Across 10 lane-change events, results show strong consistency, with an average coefficient of determination of 0.913, validating PASS for consistent efficiency evaluation across instantaneous and travel-level temporal scales. This study provides a unified, physically grounded framework that supports real-time decision-making and long-term performance analysis in autonomous driving.