Efficient implementation of the shock‐fitting algorithm for the Lighthill–Whitham–Richards traffic flow model

Abstract

AbstractThis paper firstly presents the existence and uniqueness properties of the intersection time between two neighboring shocks or between a shock and a characteristic for the analytical shock‐fitting algorithm that was proposed to solve the Lighthill–Whitham–Richards (LWR) traffic flow model with a linear speed–density relationship in accordance with the monotonicity properties of density variations along a shock, which have greatly improved the robustness of the analytical shock‐fitting algorithm. Then we discuss the efficient evaluation of the measure of effectiveness (MOE) of the analytical shock‐fitting algorithm. We develop explicit expressions to calculate the MOE–which is the total travel time that is incurred by travelers, within the space‐time region that is encompassed by the shocks and/or characteristic lines. A numerical example is used to illustrate the effectiveness and efficiency of the proposed method compared with the numerical solutions that are obtained by a fifth‐order weighted essentially non‐oscillatory scheme. Copyright © 2007 John Wiley & Sons, Ltd.