The paper identifies and discusses what appears to be a central difficulty for the future development of models of dynamic traffic flows on road networks. This difficulty is due to the fact that road traffic tends to behave in a first-in-first-out (FIFO) manner: that is, traffic which embarks on a road or other facility in period t exits from that facility (‘on average’) before traffic which enters in any later time periods. The FIFO requirement does not cause a problem in static traffic assignment, but it is shown that it yields a nonconvex constraint set in dynamic assignment, especially if there are multiple destinations or commodities. Various formulations are considered, each of which yields a nonconvex optimization problem which is at present computationally tractable only for relatively small-scale examples. The above FIFO problem arises even if there is no congestion, and even if travel demands are fixed. Further the problem arises whether a system optimum or a user equilibrium is being modeled, and whether an optimization formulation or a complementarity or variational inequality formulation is used. Some suggestions are made for dealing with, or avoiding, the problem and for further research.
