Deterministic flow lines with applications

We demonstrate that flow line models with deterministic service times and an arbitrary arrival process may be exactly decomposed into segments that each exhibit similar behavior. We call the segments channels and demonstrate that this decomposition leads to a recursion for the delay experienced by customers within the system. The consequence, in addition to clearly elucidating the manner in which customers advance, is that the state of a flow line at any time can be completely characterized by a handful of parameters per channel.