system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Trek] How many layers deep in the holodeck can I go?

Go into the holodeck (of Voyager, say) and load up a simulation of the Voyager, go to that simulated Voyager's holodeck, and load up a simulated simulated Voyager, and so on. How many times can I do this before putting too much strain on the (real) ship's computer?
gpt
In our world, video games handle stuff like this by offloading information that isn't currently important to the simulation, essentially hibernating that portion of the program.

At a very simple level, take the original *Super Mario Bros* game; when you were in world 1-1, the computer didn't have the information for world 1-2 in-memory, but its template was available to access when needed.

Getting more complex, take the *Zelda* games where there is a Light World and a Dark World. The simulation of the Dark World isn't running when you're playing in the Light World, and vise versa. Same with the various dungeons; only one of them is actually in-memory at once. Also, if you're on Death Mountain, Kakariko Village is on hold. 

A holodeck simulation is designed to only process as much information as necessary to give you the experience you expect; it isn't a faithful representation of the world, it's the *illusion* of a faithful representation.

In order to maintain the illusion of time constantly moving forward in all of the different worlds, the computer can run a fast simulation *when you enter that world*, and update it accordingly. This doesn't have to be 100% accurate, it just needs to make a few reasonable changes. For example, if you leave the Light World in mid-day, there might be a fisherman by the pond, and a bunch of open shops. When you return, the computer fast-forwards to midnight, the fisherman is asleep, and the shops are closed.

This also brings up an interesting memory-saving technique that pertains to your question; the Light World and the Dark World are very similar, so instead of having both entire worlds as templates in memory, there's the Light World, then a list of chances necessary to make the Dark World. The Voyager holodeck would do something similar; rather than having three Voyager simulations in-memory, it would have one, and then a list of the differences.

So, the answer to your question is that the holodeck would be more limited by storage than processing capacity. Unless you had someone interacting with each layer of your simulation at once, *Inception* style, the computer would just pause the parent simulation while the child ran.