My good friend Jim Mitchell of LADOTD, Louisiana Department of Transportation and Development, put a request in to the ideas site at Esri for adding LRS capabilities to ArcGIS Online. I am hoping that many of you read this and choose to support his effort to have this critical transportation functionality made part of ArcGIS Online.
ArcGIS Idea - Add Linear Referencing Support to ArcGIS Online
Click on the above link to get to the request and add your vote and opinion on adding this functionality to ArcGIS Online.