In mixed traffic, one of the challenges for autonomous driving technology is how to safe and socially acceptable interaction with human-driven vehicles (HVs). Understanding human cognitive processes during decision-making in interactions with other road users is crucial for enhancing the smooth execution of driving tasks by autonomous vehicles (AVs). This paper proposes a cognitive model of the driver's cumulative information processing based on drift-diffusion model (DDM). By incorporating the initial decision biases, drift rate, and boundary (depending on the initial speed and gaps between ego vehicle and surrounding users) into the existing DDM, our model captures the integrated interaction between individual drivers and other road users. Classic emergency collision avoidance scenarios were constructed based on a driving simulation platform. Our cognitive model accurately described human decision-making in high-risk scenarios, identified key qualitative and quantitative input variables affecting the driver's cognitive processes, and quantified the safety thresholds of the driver's cumulative information processing. Results can support the personalized modeling of human drivers' cognition and facilitate safe and effective interactions between HVs and AVs.