As healthcare service is a major concern world-wide therefore cloud computing-driven Internet of Medical Things(IoMT) are widely accepted technology for establishing smart healthcare frameworks in most organizations. Competition among healthcare organizations is increasing day by day to provide the utmost healthcare services for patients. Most of the IoMT-enabled healthcare services are facing technical challenges such as scalability, trust, privacy, security, and interoperability issues. Timely delivery of healthcare service for critical patients is a very crucial aspect for most healthcare organizations. To address all these challenges faced by healthcare organizations the researchers have proposed a novel Queueing assisted IoMT-Fog-Blockchain framework for the healthcare system. In this framework, the temporary data processing, storage, and filtration are done at the nearest fog node. This will reduce the overload, minimize the bandwidth requirement, reduce the traffic density and reduce the healthcare service time required by the cloud servers. A novel Queueing theory approach is proposed for better access control, providing in-time patient care service, and increasing the performance of the framework.