Can anyone tell me what branch of mathematics I need to study in order to better understand the factors that govern the completion times in a multi-step process, in which the thing that's traveling through the process—a product that's being built, let's say—may experience multiple delays or shortcuts of uncertain times, but estimable in type and frequency?
Let's say a team is to revise a book manuscript. The workers include copy and content editors, graphic artists, layout specialists, typographers, printers, binders, and so forth. The manuscript may go from one editor to the graphic artist to the typographer, but then back to the editor who must revise the text because of the new graphics, and then forward again through the chain, but is delayed at some points because a worker doesn't know what to do in a situation, or is continually being interrupted by another process that may also have to do with the book.
How can I begin to model something like this, including travel times and delays in a way that will reveal the weaknesses in the process, identify the culprits, and quantify the potential improvements if certain things are changed in the network or procedure?