Hi,
If you are looking only to map your data (users on each segment), you can use various gradients in size and color to get your result.
If you are looking for a way to model them, unfortunately, ArcGIS network analyst does not have such capabilities (yet) no matter how detailed your network data is (in a true traffic modeling sense, remember users do not strictly use shortest path) and I would not advice you to model this in arcgis, you are better off ArcGIS.
Also, 'copy traversed source features' does not apply to OD matrix, as yet ! 🙂 and to do each route separately ... hmmm.. too much time.
[h=1]kind regards,