A note on using Davidson's function in equilibrium assignment

This paper describes the use of the Davidson congestion function in modelling network flows using equilibrium assignment. A modification to the function is given, which defines the function over all flows values, and consequently removes computational difficulties noted in earlier studies. The modification requires the inclusion of an additional model parameter, and the selection of a suitable value for this parameter is studied for two sets of data. The modified Davidson function is also compared to two alternative functions; a step-wise linear function and a quartic polynomial function, which have both been proposed as congestion functions. Comparisons are made between observed link volumes and the assigned volumes from these models. It is concluded that the modified Davidson function is useful for inclusion in an equilibrium assignment model, given its ability to reflect differences in network link type (e.g. capacity and speed) and environment through its parameters, the conceptual advantage of the function through its derivation from queueing theory, and the previous discovery of reliable methods for estimating its parameters. A value of about 0.8–0.9 is suggested for the parameter (μ, 0 < μ < 1) introduced in the modification.