is BigIP connect Webserver with client?

Actually we are having website developed in asp.net,as I mentioned that our website is hosted on three server which is manged by Big-IP.Now we want to keep our webpage viewstate in session so our page performance get increased.what we are trying to understand that if we keep our viewstate in session than whether the client request will come will be handled by only one webserver or big ip will route it on another webserver, if same client in same browser put the request next time and webserver get changed than we won't be able to access the view state.