OSM servers keep map data, not routing. If you want a routing service based on OSM see http://wiki.openstreetmap.org/wiki/Routing/online_routers. [online_routers][1]. For cars only YOURS and MapQuest seem to have a public API for routing. Based on the scale you plan to do this you might consider running your own server. Most of the routers mentioned on wiki is open source so you would not have to program your own routing.routing. [1]: http://wiki.openstreetmap.org/wiki/Routing/online_routers

OSM servers keep map data, not routing. If you want a routing service based on OSM see http://wiki.openstreetmap.org/wiki/Routing/online_routers. For cars only YOURS and MapQuest seem to have a public API for routing. Based on the scale you plan to do this you might consider running your own server. Most of the routers mentioned on wiki is open source so you would not have to program your own routing.