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Objective: This paper aims to describe and test novel computational driver models, predicting drivers' brake reaction times (BRTs) to different levels of lead vehicle braking, during driving with cruise control (CC) and during silent failures of adaptive cruise control (ACC).Background: Validated computational models predicting BRTs to silent failures of automation are lacking but are important for assessing the safety benefits of automated driving.Method: Two alternative models of driver response to silent ACC failures are proposed: a looming prediction model, assuming that drivers embody a generative model of ACC, and a lower gain model, assuming that drivers' arousal decreases due to monitoring of the automated system. Predictions of BRTs issued by the models were tested using a driving simulator study.Results: The driving simulator study confirmed the predictions of the models: (a) BRTs were significantly shorter with an increase in kinematic criticality, both during driving with CC and during driving with ACC; (b) BRTs were significantly delayed when driving with ACC compared with driving with CC. However, the predicted BRTs were longer than the ones observed, entailing a fitting of the models to the data from the study.Conclusion: Both the looming prediction model and the lower gain model predict well the BRTs for the ACC driving condition. However, the looming prediction model has the advantage of being able to predict average BRTs using the exact same parameters as the model fitted to the CC driving data.Application: Knowledge resulting from this research can be helpful for assessing the safety benefits of automated driving. [ABSTRACT FROM AUTHOR]