Steve Jones - SSC Editor (3/3/2014)

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I haven't typically seen connection issues taking many resources in SQL2K5+ instances. In SQL 7, it could be an issue, but usually in the 1000s of connections.

Does the app have retry logic? If so, you could kill some older, idle connections and potentially free space, but typically an idle connection isn't using much in the way of resources. The scheduler threads are re-used, and memory is minimal

http://msdn.microsoft.com/en-us/library/aa337559%28v=sql.90%29.aspx