Toward a class of link travel time functions for dynamic assignment models on signalized networks

This paper investigates time-dependent travel time functions for dynamic assignment on signalized arterial network links. Dynamic link travel times are first classified according to various applications. Subsequently, stochastic and deterministic travel time functions for longer and shorter time horizons are discussed separately, and two sets of functions are recommended for dynamic transportation network problems. The implications of those functional forms are analyzed and some modifications for dynamic network models are suggested. In addition, based on dynamic link travel time functions, we discuss how many independent variables are necessary to describe the temporal traffic flow and properly estimate the time-dependent travel time and flow propagation over an arterial link. As a result, six link flow variables and corresponding link state and flow propagation equations are proposed as the basis to formulate dynamic transportation network models.