Delay-function-based link models: their properties and computational issues

This paper studies the FIFO property, modelling accuracy and numerical solution of delay-function models, a class of link models widely used in the dynamic user-equilibrium (DUE) traffic assignment problem. It is found that the set of delay functions that can be used in the DUE problem is much smaller than one once expected. In particular, the paper finds that (1) the linear delay function, the only proven FIFO-consistent delay function, substantially overestimates link travel time due to the so-called double-counting effect, (2) the piece-wise linear delay function, an improvement over the linear delay function in reducing double-counting, does not always respect FIFO (i.e., not FIFO-consistent), and (3) a class of smooth, convex delay functions bounded by the linear and piece-wise linear delay functions respects FIFO for certain inflow profiles but not for others. A condition is given to identify those inflow profiles that cause FIFO violations in the delay-function model with nonlinear delay functions. Finally, the paper also provides an accurate and stable solution algorithm for delay-function models.