Hi,
I am developed a simple web application using servlet where it gives a response for a fixed request, but a third party application sends this request very frequently as per our project architecture, but due to this very frequent request, the tomcat server slow down after a few seconds, not only that the other application which are already deployed previously, are also slow down like starvation.

So, what to do, to remove or minimize this slow response.

Please help me.

Firstly I would suggest you check your CPU usage and Memory Usage, if your machine itself has high CPU usage (or Memory Usage lot higher than your physical memory) then irrespective of the container used your System is bound to become slow, the solution to either problems is to upgrade your hardware.
However the other thing that caught my eye was that your client application which calls the servlet sends requests a lot faster that Tomcat can finish processing a request for your servlet. Now you might be aware that Tomcat spawns a new thread for each request and there is a limit on the, maximum number of threads that it can create (specified in the server.xml file), in your case although this is just a guess, it seems like tomcat is running low on this value and hence before another request (for any webapplication in your Tomcat) it waits for a current request (for any other webapplication) to complete execution.

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