Data Distribution Service (DDS) software systems are commonly used in defense, aerospace, industrial internet of things, healthcare, and automotive sectors because they provide real-time high-performance and reliable data transfer between distributed system applications. In addition to commercial DDS solutions, there are also open-source DDS software alternatives. Software reliability is critical as it directly affects the product experience of end users. In this study, we propose a learning-based method to estimate the reliability of open-source DDS software systems. For reliability estimation of DDS software, we constructed a data set that contains design, historical, and project developer metrics accessible through open-source code repositories. To categorize DDS software systems by reliability, classification models were developed by applying Logistic Regression, and Decision Tree algorithms to the obtained data set. The classification model built using Logistic Regression yielded the highest accuracy, 85%, for the case studies. Thanks to the proposed approach, users will be able to have information about the reliability of DDS software without running the software while deciding which software to choose.