Travel time functions for transport planning purposes: Davidson's function, its time dependent form and alternative travel time function

A travel time function proposed by Davidson for transport planning purposes has been subject to much discussion and efforts of calibration including some controversy over the meaning of its parameters. Modified forms of Davidson's function have been proposed to obtain finite values of travel time for flows near and above capacity. This paper presents a time-dependent form of the original Davidson function, derived by using the coordinate transformation technique. The modified form of Davidson's function proposed recently by Tisato (1991) is shown to overpredict travel times for flows near and above capacity compared with the time-dependent form. The derivation of the original Davidson function is discussed and it is concluded that the function suffers from an inconsistency in its basic parameter definitions. An alternative interpretation of the delay parameter is considered, but this leads to another inconsistency. A new travel time function is proposed as an alternative to Davidson's function to overcome the conceptual and calibration problems. In the proposed function, the delay parameter takes a meaning consistent with the formulae used for estimating intersection delays. Both the steady-state and time-dependent forms of the new function are given.