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. This paper presents a time-dependent form of the original Davidson function, derived using the coordinate transformation technique. The derivation of the original Davidson function is discussed. A new travel time function is proposed as an alternative to Davidson's function. 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. This Excel application includes calculations and graphs for various travel time functions discussed in this paper Akçelik's_Travel_Function_(for 1991 paper)_v1.xls
AKÇELIK, R. (1991). Travel Time Functions for Transport Planning Purposes: Davidson's Function, its Time-Dependent form and an Alternative Travel Time Function. Australian Road Research 21 (3), pp 49-59. (Minor revisions: December 2000).