The first in-depth study on the use of electrocardiogram and electrooculogram for subject-dependent classification in driver sleepiness/fatigue under realistic driving conditions is presented in this work. Since acquisitions in simulated environments may be misleading for sleepiness assessment, performing studies on road are required. For that purpose, the authors present a database resulting from a field driving study performed in the SleepEye project. Based on previous research, supervised machine learning methods are implemented and applied to 16 heart- and 25 eye-based extracted features, mostly related to heart rate variability and blink events, respectively, in order to study the influence of subject dependency in sleepiness classification, using different classifiers and dealing with imbalanced class distributions. Results showed a significantly worse performance in subject-independent classification: a decrease of similar to 40 and 20% in the detection rate of the 'sleepy' class for two and three classes, respectively. Since physiological signals are the ones that present the most individual characteristics, a subject-independent classification can be even harder to perform. Transfer learning techniques and methods for imbalanced distributions are promising approaches and need further investigation.