A variety of macroscopic traffic flow models have been applied to formulate the link-based system optimal dynamic traffic assignment(SO-DTA) problem in a many-to-one network. It is expectable that SO-DTA models based on various traffic flow models usually result in different optimal link traffic evolution patterns, but whether and how traffic flow models affect the minimal system cost and the corresponding optimal arrival pattern at the destination is unclear. This paper focuses on three traffic flow models, the point-queue(P-Q), spatial-queue(S-Q), and cell-transmission models(CTM), and compare their resulted minimal system cost in many-to-one networks. We prove for three simple networks, a linear network with two sequential bottlenecks, a two-in-one-out merge network and a one-in-two-out diverge network, that the minimal system cost for the SO-DTA models based on these three traffic flow models are identical. We then show by numerical experiments that this property seems to be also held for general many-to-one networks. This interesting property may be due to the fact that all the three traffic flow models propagate the uncongested flows at the same speed and release the congested flows always at the link capacity. In SO-DTA applications where only the minimal system cost or arrival pattern at the destination is of major interest, the findings in this paper can be utilized to substantially expedite the solution procedure.
Samenvatting