I am facing the problem that i can't find any documentation how to add an own hosted Geoprocessing Service in ArcGIS online. I don't know wether it's possible or not, i can only find this documentation:
Tools A tool performs a function in a map or application, such as finding a place or accessing a geodatabase. Supported types of tools ArcGIS Server geocode service ArcGIS Server network analysis service ArcGIS Server geoprocessing service Geoprocessing Sample (.zip) ArcGIS Server geodata service ArcGIS geometry service Locator package (.gcpk) Geoprocessing package (.gpk)
ArcGIS Online does not currently support hosted geoprocessing services and they cannot be added to the map viewer, all of the analysis tools are built into the viewer and a configurable geoprocessing widget is not provided at this time.
The only types of services that can be hosted in the ArcGIS Online cloud are tiled map services and feature services. The documentation you mentioned references geoprocesing services as a supported item type because you can register an ArcGIS Server geoprocessing service in your content to allow users to more easily locate the service URL for use in either in ArcGIS Desktop or a web application like Flex. The actual geoprocessing service itself would still be hosted on someone's on-premise ArcGIS Server rather than being hosted in the ArcGIS Online cloud.
Esri offers free products like the ArcGIS Viewer for Flex and ArcGIS Viewer for Silverlight which provide a configurable widget to add geoprocessing services and execute them.
