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ROS (Robot Operating System) is currently one of the most popular development frameworks for robotic software, which is usually subject to hard real-time constraints in safe-critical domains. Designers must formally model and analyze its timing behaviors to guarantee that real-time constraints are always honored at run-time. This paper studies real-time scheduling and analysis under a multi-threaded executor in ROS 2. We present a formal description of the scheduling model of multi-threaded executors, and develop response time analysis techniques for processing chains executing on it. Moreover, we identify a risk of increasing the response time of chains that may be caused by improper design when deploying systems on multi-threaded executors, which provides a useful guidance to designers. We conduct experiments with both randomly generated workloads and case studies on a realistic ROS 2 platform to evaluate and demonstrate our results.