Abstract
Daganzo (1997) proposed a kinematic wave model of a traffic system with priority vehicles and special lanes, where the priority vehicles can use both regular and special lanes, but the regular vehicles can only use the regular lanes. Further in Daganzo et al. (1997), the Incremental Transfer (IT) principle was applied to devise a Cell Transmission Model to numerically solve the model. In this paper we first derive the fundamental diagram of a traffic system with priority vehicles and special lanes based on Wardrops user equilibrium principle and then show after transforming the variables that there exist two auxiliary Lighthill-Whitham-Richards model, which can be used to define the demand and supply functions. We present a new junction flux function for the Cell Transmission Model, which is simpler than the IT principle, and more importantly, is a lane-based formulation. Comparing the proposed fluxes with the Godunov (or IT principle) ones analytically, we identify the cases that they are different. Nevertheless, with numerical experiments, we demonstrate that they are consistent in all the cases in the sense that the stationary states of both models are identical. Finally, we show numerical examples that demonstrate the IT principle is not invariant by using a non-triangular fundamental diagram. (C) 2018 The Authors. Published by Elsevier Ltd.