Is it possible to publish a map service with ArcGIS Online account (when ArcGIS for Server is not installed) perhaps based on one ESRI server clusters? Thank you so much
These should be helpful:
About hosted web layers—ArcGIS Online Help | ArcGIS
Publish hosted feature layers—ArcGIS Online Help | ArcGIS
You cant exactly publish a map service like you would do on ArcGIS Server, but you can publish your content as a feature layer on AGOL.
Retrieving data ...