How to speed up the connection between BIG-IP LTM and web server

Because this is a very vague and ambiguous question, I'm afraid it's going to be a vague and ambiguous answers. The shortest and simplest answer is "upgrade". If you put in 40GB infrastructure, the connection between the 40GB port on your BigIP and the 40GB port on your switch will be faster than the 100MB or Gig connection you might have now.

If that is not an option (and for most it's likely not), then start by looking at your infrastructure. Do you have an old Pentium II webserver connected to the network with a 10MB Network card? Replacing that with something recent will help greatly.

I would also suggest you take a look at:

https://devcentral.f5.com/articles/stop-using-the-base-tcp-profile

https://devcentral.f5.com/articles/tuning-the-tcp-profile-part-one

https://devcentral.f5.com/articles/f5-unveils-new-built-in-tcp-profiles-25175 (version 13 only)

Reading through those should not only help you optimize your connections it should give you an idea of where else you might want to look.

Also bear in mind that we have professional services professionals who can come in and look at your infrastructure to determine where your bottlenecks and problems are.

I would also suggest just looking at your stats. Are you overloading your webserver? If so, adding another webserver may be the answer.

I hope that helps.