AbstractWe present Jay, a software framework for offloading applications in hybrid edge clouds. Jay provides an API, services, and tools that enable mobile application developers to implement, instrument, and evaluate offloading applications using configurable cloud topologies, offloading strategies, and job types. We start by presenting Jay's job model and the concrete architecture of the framework. We then present the programming API with several examples of customization. Then, we turn to the description of the internal implementation of Jay instances and their components. Finally, we describe the Jay Workbench, a tool that allows the setup, execution, and reproduction of experiments with networks of hosts with different resource capabilities organized with specific topologies. The complete source code for the framework and workbench is provided in a GitHub repository.