We need to know which session is yours. HTTP is stateless, so we use a cookie to keep the identifier for your session on your browser, the actual contents of the session are stored on our servers.

Our load balancer would throw a 502 (Bad Gateway) when it determined that the backends were not responsive enough. Though I like your suggestion to trap and send the user to a specific 503 error page, at the moment they would see a 'generic' (all 5xx errors) page.