On the Mixed Monotonicity of FIFO Traffic Flow Models

At diverging junctions in vehicular traffic networks, congestion on one outgoing link may impede traffic flow to other outgoing links. This phenomenon is referred to as the first-in-first-out (FIFO) property. Traffic network models that do not include the FIFO property result in monotone dynamics for which powerful analysis techniques exist. This note shows that a large class of FIFO network models are nonetheless mixed monotone. Mixed monotone systems significantly generalize the class of monotone systems and enable similarly powerful analysis techniques. The studied class of models includes the case when the FIFO property is only partial, that is, traffic flow through diverging junctions exhibit both FIFO and non-FIFO phenomena.