Probabilistic Latency Analysis of the Data Distribution Service in ROS 2

Robot Operating System 2 (ROS 2) is now the de facto standard for robotic communication, pairing UDP transport with the Data Distribution Service (DDS) publish-subscribe middleware. DDS achieves reliability through periodic heartbeats that solicit acknowledgments for missing samples and trigger selective retransmissions. In lossy wireless networks, the tight coupling among heartbeat period, IP fragmentation, and retransmission interval obscures end to end latency behavior and leaves practitioners with little guidance on how to tune these parameters. To address these challenges, we propose a probabilistic latency analysis (PLA) that analytically models the reliable transmission process of ROS 2 DDS communication using a discrete state approach. By systematically analyzing both middleware level and transport level events, PLA computes the steady state probability distribution of unacknowledged messages and the retransmission latency. We validate our PLA across 270 scenarios, exploring variations in packet delivery ratios, message sizes, and both publishing and retransmission intervals, demonstrating a close alignment between analytical predictions and experimental results. Our findings establish a theoretical basis to systematically optimize reliability, latency, and performance in wireless industrial robotics.