When a large number of players fight in the same system, the game slows down (TIme DIlation), up to 10% of its normal speed, to avoid crashes. If the fight is particularly large (many thousands of people), the servers may take a while to respond, up to several minutes. Additionally, the large number of elements on display may make the game very laggy, lowering the FPS to single digits. This article gives some tools to help alleviate TIDI issues.
Before a large fight, make sure your graphic settings are lower to avoid low FPS. You can do so by going to Display & Graphics, Optimize Settings, Optimize for Performance, and Apply. Commonly known as potato mode.
If it is still too hard for your PC, you can go into super-potato mode by using Ctrl-Shift-F9. The binding is “Toggle 3D View” in “General” shortcuts.
Using Ctrl+Shift+Alt+M, you can activate the Engine Tools windows. You can use it to monitor different things about how well (or not) the game is running, but a particularly important one is the “Oustanding Calls” window. In it, you will see the “calls” your computer sends to the EVE servers. In normal conditions, the messages appear and disappear almost instantly, but under TIDI you will notice it can take up to several minutes before the “message is sent”. In short, don't spam your modules, just press until the message appears, and once it appears, just wait.
If your gun is on F1, press F1 until it stops blinking red. You should see a “deactivate module” in your outstanding calls window when you do it.
TBD: add pictures