The growing worldwide population has increased the need for technologies, computerised software algorithms and smart devices that can monitor and assist patients anytime and anywhere and thus enable them to lead independent lives. The real-time remote monitoring of patients is an important issue in telemedicine. In the provision of healthcare services, patient prioritisation poses a significant challenge because of the complex decision-making process it involves when patients are considered 'big data'. To our knowledge, no study has highlighted the link between 'big data' characteristics and real-time remote healthcare monitoring in the patient prioritisation process, as well as the inherent challenges involved. Thus, we present comprehensive insights into the elements of big data characteristics according to the six 'Vs': volume, velocity, variety, veracity, value and variability. Each of these elements is presented and connected to a related part in the study of the connection between patient prioritisation and real-time remote healthcare monitoring systems. Then, we determine the weak points and recommend solutions as potential future work. This study makes the following contributions. (1) The link between big data characteristics and real-time remote healthcare monitoring in the patient prioritisation process is described. (2) The open issues and challenges for big data used in the patient prioritisation process are emphasised. (3) As a recommended solution, decision making using multiple criteria, such as vital signs and chief complaints, is utilised to prioritise the big data of patients with chronic diseases on the basis of the most urgent cases.