If you have to program ANYTHING that serves requests and has a limited buffer you enter the domain of queueing theory.
Processing internet packets? Queueing theory.
Developing a distributed system? Queueing theory.
Designing software to manage a call center? Queueing theory.
Shipments? Ticketing? Payments? A myriad of other things? Queueing theory.
Fun fact, while posting this reply HN redirected my to a page "Sorry we're not able to serve your request this quickly". Guess what would have helped?
Queueing theory.