The Internet of Moving Things (IoMT) requires support for a data life cycle process ranging from sorting, cleaning and monitoring data streams to more complex tasks such as querying, aggregation, and analytics. Current solutions for stream data management in IoMT have been focused on partial aspects of a data life cycle process, with special emphasis on sensor networks. This paper aims to address this problem by developing streaming data life cycle process that incorporates an edge/fog/cloud architecture that is needed for handling heterogeneous, streaming and geographically-dispersed IoMT devices. We propose a 3-tier architecture to support an instant intra-layer communication that establishes a stream data flow in real-time to respond to immediate data life cycle tasks in the system. Communication and process are thus the defining factors in the design of our stream data management solution for IoMT. We describe and evaluate our prototype implementation using real-time transit data feeds. Preliminary results are showing the advantages of running data life cycle tasks for reducing the volume of data streams that are redundant and should not be transported to the cloud.