The queue management models that work for banks, grocery stores, and warehouses do not fit the highly interdependent plant operations of a coffee shop--Poisson doesn't cut it.
At any given time, there's a good deal of work contained in the "head cache" of the workers (lack of transparency) and orders are (largely) interdependent due to the limited throughput and cornucopia of wait-states of the components that process them.
For a better analog, look at the classic French "brigade de cuisine" system developed by Escoffier and watch videos of high-end restaurants during service.
Pay particular attention to the expediter and notice how there's specialization, redundancy in labor, and semaphoring to manage exceptions, wait-states, and accommodate the entirety of the workload.
None of those strategies can be utilized (at-scale) in a coffee-shop due to vastly different expectations of workload processing timeline, quality, variance, available labor, expected margin, and physical plant size.
A large fast-food restaurant is middle-ground between these extremes.