Macroscopic modelling of heterogeneous, disordered road traffic flow

Abstract

The groundwork for much of the existing traffic flow theory was laid in the 1950s and 1960s by researchers from developed economies like the United States. The car-following modelling approach, which is arguably the most popular type of microscopic traffic flow models, and the kinematic wave modelling approach, which is still the basis for much of the macroscopic traffic flow theory, were first introduced during this period. Because the object of this and much of the subsequent research it has spawned is the traffic of developed economies, the classical traffic flow theory deals almost exclusively with this specific kind of traffic: lane-disciplined with relatively homogeneous passenger car traffic. However, the traffic in many developing economies have a significant share of two and three-wheeler motorized vehicles and non-motorized vehicles with different static and dynamic characteristics, resulting in a fundamentally different traffic stream. Because of the differences in sizes and manoeuvrabilities, the vehicles in this traffic stream do not follow the lane-discipline. This kind of traffic has been described in the literature as “heterogeneous, disordered (HD)” or “mixed” traffic. These developing economies, mostly from Asia and Africa, are rapidly urbanizing and the need to deal with the challenge of traffic congestion is more urgent than ever. Given that these countries are already struggling to keep pace with the rising urban population for providing the necessary road infrastructure, it may be more effective to make the most efficient use of the existing infrastructure through the use of traffic management solutions like real-time traffic monitoring and signal control. As such solutions cannot be formulated using the traditional traffic flow theory, an alternative theory that explicitly considers the characteristics of the HD traffic is urgently needed. In the present study, HD traffic is characterised by the division of its component vehicle classes into car-following and gap-filling types. Flow-density relationships are derived for each vehicle type based on first principles. A new multiclass cell transmission model (CTM) is then proposed that can accommodate these vehicle classes of these two types, and its properties are analysed. This is followed by the development of a new node-based dynamic traffic assignment (DTA) framework embedded with a single class CTM satisfying the link-level first-in-first-out principle. Both the dynamic user equilibrium (DUE) and dynamic system optimum (DSO) problems are formulated within this framework as complementarity problems with guaranteed solution existence. Algorithms are developed to efficiently compute all the relevant travel costs and marginal costs needed in the determination of the DUE and DSO solutions. This DTA framework is then combined with the CTM for HD traffic proposed previously, followed by the extension of the DUE and DSO problem formulations and all the relevant algorithms to the context of HD traffic. Other contributions of this work include a comprehensive review of the studies conducted in the context of HD traffic, the proposal of a new methodology for the con- struction of driving cycles for cities with HD traffic, and the introduction of a backpropagation technique to efficiently compute the costs needed to calculate the DTA solutions.