Trajectory streams consist of large volumes of time-stamped spatial data that are constantly generated from diverse and geographically distributed sources. Discovery of traveling patterns on trajectory streams such as gathering and companies needs to process each record when it arrives and correlates across multiple records near real-time. Thus techniques for handling high-speed trajectory streams should scale on distributed cluster computing. The main issues encapsulate three aspects, namely a data model to represent the continuous trajectory data, the parallelism of a discovery algorithm, and end-to-end performance improvement. In this thesis, I propose two parallel discovery methods, namely snapshot model and slot model that each consists of 1) a model of partitioning trajectories sampled on different time intervals; 2) definition on distance measurements of trajectories; and 3) a parallel discovery algorithm. I develop these methods in a stream processing workflow. I evaluate our solution with a public dataset on Amazon Web Services (AWS) cloud cluster. From parallelization point of view, I investigate system performance, scalability, stability and pinpoint principle operations that contribute most to the run-time cost of computation and data shuffling. I improve data locality with fine-tuned data partition and data aggregation techniques. I observe that both models can scale on a cluster of nodes as the intensity of trajectory data streams grows. Generally, snapshot model has higher throughput thus lower latency, while slot model produce more accurate trajectory discovery.