Can you confirm that both of those ArcSOC.exe processes belong to that service? In 10.1, the easiest way to tell is to add the "Command Line" column to your Task Manager. This will provide the service name for each ArcSOC.exe process listed. Also, do both of those processes go away once you have stopped the service?
Jeff
Open your windows task manager and from menu select items View -> Select Columns... and then select column "Command Line" so you can see details for your two arcsoc.exe in windows task manager
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Jamal,
Your screenshot does reveal that you have 2 ArcSOC.exe instances running but it shows that only one of them is associated with the S15 map service. This is revealed by looking at the -Dservice=S15.MapServer in the Command Line for the top ArcSOC.exe process. The bottom one is not associated with any map service and was likely created with the connection from ArcMap to ArcGIS Server.