The application probably is leaking connections. I have no idea what they mean by
The application team is telling they are using some 'Connection Pool'
for the the connection management.
But it sounds as they are trying to implement their own connection pooling system.
Generally connection leaking happens when you have calls to .open() without calling .close() on the same connection.
Since this is generally a client issue I think the only thing you can do from the database side (short of killing them every once in a while but I wouldn't suggest doing that) is use the information from sys.dm_exec_sessions to find the application leaking the connections and then talk to your developers or vendor so they can look for the offending code.
For example this query (taken from here:
select count(*) as sessions,
s.host_name,
s.host_process_id,
s.program_name,
db_name(s.database_id) as database_name
from sys.dm_exec_sessions s
where is_user_process = 1
group by host_name, host_process_id, program_name, database_id
order by count(*) desc;
will show you the number of connections per host per process. This should be enough to identify the offending application.
You could also create a job logging this information over time to chart out if the connections are really always increasing so you can "prove" to your application team there really is a leak.
