Hello
I’m planning to use OSRM router project to collect travel time and compare with some observed data in the field. You can say I want to investigate the Open Street travel time data and publish the analysis as journal article. Do I need any permission from Open Street to use or publishing this type of work?
Thanks with regard.
From your description, this does not sound like something you need special permission for. Your use case should already be allowed by our open license. 
We expect that you make it clear that you used OSM data when you publish any maps or other works based on OSM, but it sounds like this fact won’t be easily overlooked by a reader of your intended publication anyway.