Embedded systems in field-programmable gate arrays (FPGAs) can be customized and adaptive if assembled from modular components at run time. This paper examines realizing run-time system assembly by extension of platform-based design. Two major challenges are addressed in this paper. First, the design of a reconfigurable platform architecture suitable for run-time system assembly is described. Different systems are constructed by integrating the platform architecture with different modular components, which employ the communication infrastructure supplied by the platform in order to interact. Second, where on-chip communications channels use shared media, we propose techniques for modeling the intermodule communication behavior based on statistical time-division multiplexing. The proposed techniques enable system designers to guarantee that logical communication requirements between the adjunct modules can be satisfied by the infrastructure. An in-depth analysis is presented and then verified with cycle-accurate simulations for an example reconfigurable platform for real-time video applications.