We would like to reduce the amount of requests to a map service and therefore store the tiles of a specific area of interest (different for every user of the application) locally on the machine, which is comparable to a browser cache. This functionality is not (out-of-the-box) supported by the sdk, but maybe somebody does know this requirement. Any ideas or workarounds?
I think this sample "Create an offline app" will give you a head start for your task. It describes in detail about the exporting tiles from a service for an area of interest and saving it locally.
The MapView control already uses the browser cache. If the server says a tile is ok to cache, it will cache it (this could depend on server configuration). In fact on Windows if your browser already cached the tiles, your app would even reuse the cache.