JOSM has a [routing plugin][1] option:
I have not used but it seems that you can use this on the data you have loaded in to JOSM.
JOSM.
I noticed this query that related to the plugin:
https://help.openstreetmap.org/questions/30832/how-do-i-use-the-josm-routing-plugin
[1]: https://wiki.openstreetmap.org/wiki/JOSM/Plugins/Routing
JOSM has a [routing plugin][1] option:
I have not used but it seems that you can use this on the data you have loaded in to JOSM.
[1]: https://wiki.openstreetmap.org/wiki/JOSM/Plugins/Routing