A priority channel system (PCS) is a computational model where nondeterministic finite automata communicate over a faulty network. They augment lossy channel systems with a new feature — agents can mark certain messages as more important than others so they are less likely to be dropped. Initially defined by Christopher Haase et al. in 2014, they are notable in that certain LCS-related verification problems achieve a computational complexity of \(\mathbf{F}_{\varepsilon_0}\)-complete, using a complexity class analog of the fast-growing hierarchy.