User:The Crusader of Truth/Stuff
From this
Logistics Tutorial
Understanding bot priorities is an important part of making the logistics system work for you, and bot priorities are not something the game is very good at making clear right now. Here's a brief overview of what I've learned about their priorities:
Active provider chests - Bots make emptying active provider chests their top priority. This means they should generally only be used for chests you want to keep empty. They can be useful in very specialized roles, such as unloading trains into them, but should otherwise be avoided unless you want things moved to storage as a top priority.
Requester chests - Bots' second priority is fulfilling requests from these. They are probably the easiest chest to understand - tell it how much stuff to request, and bots will bring the stuff to it. I believe bots will take things from active provider chests to requester chests first when possible.
Passive provider chests - The bread and butter of most logistic systems. Bots will not touch things in this chest unless a requester chest needs those things. This should be your go-to chest for factory outputs or other things you want to be "available" to your logistic system without forcing it into storage.
Storage chests - Things only end up here under two circumstances. First, bots will empty active provider chests into storage if there are no requesters that need those things. Second, construction bots will take stuff that they dismantle to storage chests. Note that bots will try to keep storage "segregated" - that is, they will prefer to put iron ore in a chest that already has iron ore in it first. Failing that, they will look for an empty storage chest. Only if none of those are available will they put the iron ore in a chest with something else.
You may occasionally see inefficient or bizarre behavior with the bots that has to do with how jobs are assigned to bots. Like your example with the requester chest - even though there is a provider chest right next to it, the "job" to fill the requester chest will be given to the nearest available robot. Even if that bot is on the other end of your factory. And that bot might find it easier to grab from a provider chest that it's close to, rather than the one right next to your requester chest. Once the bot on the other side of the factory has taken the job, no other bots will take the job, because it is already being fulfilled by another bot. So it can sometimes look like bots are "ignoring" a job, when really it's just being fulfilled by a far-away bot. Sometimes compartmentalizing your logistics networks can be helpful for this reason - if you have a network for unloading trains onto belts, for example, it probably doesn't need to be connected to the main factory network.