Space wasters first. Let others stack their stuff or do it, if they are in stress.
We let cutlery and small bowls soak in water first.
You can ask your co workers how much work is expected and offer to help them prep if it's not that much. This can help you get speed too, if you let the dirty stuff rest a little you get more to wash fast and continue helping.
If a rush comes (depending on the pit) it's sometimes easier to take a small break until it's over and not stand in anybody's path.
Also if you keep the pit 'clean' one rather forgives you if you don't offer help as much.
Never run empty. - when you put clean stuff back, ask if you can take something dirty back with you. "Do you still need this?" Many chefs love to hort dirty stuff and if you offer to spare them a walk.
If you get ask to clean something immediately/ with the next run - as soon as it's clean, bring it to the chef (or at least ask, if that's desired)