Representation requirements for perfect first-in-first-out verification in continuous flow dynamic models

Dynamic models of traffic require answers for many issues. One of them is the way priorities of different traffic streams (commodities) are managed. This is particularly challenging when flows are treated as continuous. It is common to consider the First-In-First-Out (FIFO) rule as a baseline for setting priorities; but most practical continuous flow dynamic models do not satisfy FIFO perfectly. This paper examines the difficulties associated with full adherence to network-wide FIFO. We examine six different ways to represent dynamic flow solutions over a network, and for each representation we discuss whether it is sufficient for verifying FIFO, whether the verification process is finite, and whether proving FIFO can be directly implied. Throughout the evaluation eight alternative definitions of FIFO are considered, seven of them are shown to be essentially equivalent, while the last definition is not, and may therefore be considered as “weak” FIFO. The most promising representation appears to be the one denoted as “cohort bundles,” while somewhat more abstract than the other representations, supporting this representation directly shows perfect FIFO satisfaction. Further evaluation of this representation remains a subject for future research. In a nutshell, the key conclusion of this analysis is that in order to satisfy perfect network-wide FIFO the number of discretized elements of flow should probably be allowed to grow quickly and unboundedly with model duration, and it cannot be determined a-priori. These insights about the challenges of incorporating FIFO in continuous flow dynamic models, which may be relevant also for other behavior-based priority rules, can help modelers and practitioners set realistic expectations regarding the level of control over priority rules that can be achieved within finite-dimensional continuous flow dynamic models.