This paper presents a distributed data analytics approach for drivers mental state monitoring using multivariate physiological signals. Drivers mental states such as cognitive distraction, sleepiness, stress, etc. can be fatal contributing factors and to prevent car crashes these factors need to be understood. Here, a cloud-based approach with heterogeneous sensor sources that generates extremely large data sets of physiological signals need to be handled and analyzed in a big data scenario. In the proposed physiological big data analytics approach, for driver state monitoring, heterogeneous data coming from multiple sources i.e., multivariate physiological signals are used, processed and analyzed to aware impaired vehicle drivers. Here, in a distributed big data environment, multi-agent case-based reasoning facilitates parallel case similarity matching and handles data that are coming from single and multiple physiological signal sources.