Despite the growing interest in the use of electroencephalogram (EEG) signals as a potential biometric for subject identification and the recent advances in the use of deep learning (DL) models to study neurological signals, such as electrocardiogram (ECG), electroencephalogram (EEG), electroretinogram (ERG), and electromyogram (EMG), there has been a lack of exploration in the use of state-of-the-art DL models for EEG-based subject identification tasks owing to the high variability in EEG features across sessions for an individual subject. In this paper, we explore the use of state-of-the-art DL models such as ResNet, Inception, and EEGNet to realize EEG-based biometrics on the BED dataset, which contains EEG recordings from 21 individuals. We obtain promising results with an accuracy of 63.21%, 70.18%, and 86.74% for Resnet, Inception, and EEGNet, respectively, while the previous best effort reported accuracy of 83.51%. We also demonstrate the capabilities of these models to perform EEG biometric tasks in real-time by developing a portable, low-cost, real-time Raspberry Pi-based system that integrates all the necessary steps of subject identification from the acquisition of the EEG signals to the prediction of identity while other existing systems incorporate only parts of the whole system.