Irule for pool selection base on cookie presence

when HTTP_REQUEST {
  if {[HTTP::cookie exists {JSESSIONID}]} {
    pool mypool
  }
}

If you are looking to choose a pool juts on the presence of a cookie this should do the trick. It will require an HTTP profile. If your app is HTTPS it will also require a client SSL profile:

when HTTP_REQUEST {
    if {[HTTP::cookie exists "JSESSIONID"]}{
        pool poolA
    }
    else {
        pool poolB
    }
}