Where does ArcGIS Online Network Service source came from? Is there any source reference I can refer to? I tried to search on Google but I could not find anything.
Esri has collected the road datasets from various vendors, but mostly it is HERE (Nokia). For those countries where HERE doesn't have sufficiently good data, local vendor's datasets were obtained (such as with Japan, for instance). Esri's historical, live, and predictive traffic feeds come directly from HERE. This is the ArcGIS Online Network Dataset Coverage web map you can explore.
This is the list of the countries covered with respect to available routing options.
If you are interested in other data sources for road datasets, check the Esri StreetMap Premium product matrix, it has some useful insights into the data sources as well.