Consistency and Inconsistency Between the Fundamental Relationships on Which Different Traffic Assignment Models Are Based

We compare the forms and properties of different macroscopic behavioral relationships on which different static and dynamic traffic assignment models have been based, namely, travel time-flow functions, travel time-occupancy functions, and flow-occupancy functions or flow-density functions. Given any one of these three relationships we can derive the other two, so that they appear mathematically equivalent. These three behavioral relationships focus on different variables, but they are meant to be observing the same traffic and are not meant to be inconsistent or incompatible with each other. However, we see that the forms and properties usually assumed for any one of these three relationships are often inconsistent or incompatible with the forms or properties that are usually assumed for the other two, or that are considered acceptable for the other two. It might be thought that any inconsistencies between these relationships are because of modeling different phenomena, however that does not explain some...