Models that are created in Oracle Real-Time Integration Business Insight conform to the model lifecycle. When models are created or edited, they are in Draft state until they are Activated. Activation is the action that pushes a model definition (including milestones, indicators, mappings, etc.) out to the various runtime engines (i.e., SOA Suite and Service Bus). There are other model states as well, representing deactivation, error, and other conditions.
Models are available to add to the Home page only when they are activated. If you are expecting to be able to add a model to your Home page, but it is not listed in the model selector, then the most likely cause is that the model has not been activated. Contact the appropriate architect or an administrator and request that the model be activated.