On node models for high-dimensional road networks

Abstract

Macroscopic traffic models are necessary for simulation and study of traffic's complex macro-scale dynamics, and are often used by practitioners for road network planning, integrated corridor management, and other applications. These models have two parts: a link model, which describes traffic flow behavior on individual roads, and a node model, which describes behavior at road junctions. As the road networks under study become larger and more complex --- nowadays often including arterial networks --- the node model becomes more important. This paper focuses on the first order node model and has two main contributions. First, we formalize the multi-commodity flow distribution at a junction as an optimization problem with all the necessary constraints. Most interesting here is the formalization of input flow priorities. Then, we discuss a very common "conservation of turning fractions" or "first-in-first-out" (FIFO) constraint, and how it often produces unrealistic spillback. This spillback occurs when, at a diverge, a queue develops for a movement that only a few lanes service, but FIFO requires that all lanes experience spillback from this queue. As we show, avoiding this unrealistic spillback while retaining FIFO in the node model requires complicated network topologies. Our second contribution is a "partial FIFO" mechanism that avoids this unrealistic spillback, and a node model and solution algorithm that incorporates this mechanism. The partial FIFO mechanism is parameterized through intervals that describe how individual movements influence each other, can be intuitively described from physical lane geometry and turning movement rules, and allows tuning to describe a link as having anything between full FIFO and no FIFO. Excepting the FIFO constraint, the present node model also fits within the well-established "general class of first-order node models" for multi-commodity flows.Comment: The abstract on this info page is slightly abbreviated, please see the paper for the full abstrac

A Dynamic-System-Based Approach to Modeling Driver Movements Across General-Purpose/Managed Lane Interfaces

“…We have suggested that our driver intentions model could be seen as an extension or component of a node model (in the traffic modeling literature, dynamics of moving between roads are captured in the node model), but analyses of node models tend to treat driver intentions (in, e.g., the form of split ratios) as exogenous (see, e.g., [17,18,26]). This assumption may be less true today than it had been in the past, as driver use of real-time traffic advisories through smartphone and in-car software have become ubiquitous.…”

“…The example discussed so far in this section is the simplest possible example, with two input links, two output links, and only one class whose split ratios are undefined (we will revisit this example in section 5.3 and use the method to be discussed in section 5 to solve it). However, it is generally required that node models be applicable to arbitrary amounts of input links, output links, and vehicle classes [17,18]. In this paper we ensure that our method for solving for driver split ratios is also generallyapplicable.…”

“…Of course, when the node is more complex and models a merge (more than one cell upstream and a single cell downstream), a diverge (a single cell upstream and more than one cell downstream), or a mergediverge (more than one cell both upstream and downstream), finding the flows across the node becomes more complex, and involves new modeling choices (i.e., choices as to which vehicles get to claim available space when multiple inflows are competing to claim that space). See [17,18] for some recent overviews and discussions of the technicalities of node models. In particular, the GP/managed lane interfaces considered in this paper take the form of a merge-diverge junction, with two cells (the GP lane and the adjacent managed lane) both entering the node and exiting the node.…”

Maximal concurrent minimal cost flow problems on extended multi-cost multi-commodity networks

“…The articles [3][4][5][6][7][8][9][10][11] the authors have studied multicommodity flows on ordinary networks. Besides, in articles [12][13][14][15][16][17][18][19][20][21][22] scientists have studied the problems of single-cost multi-commodity flow in logistics and transportation systems, economic and energy sectors, and communications and computer networks. The maximal multi-cost multicommodity flow problems presented by the authors in the work [23][24].…”

Mixed monotonicity of partial first-in-first-out traffic flow models

“…Non-FIFO models imply that, even if one of the output links is jammed, the resulting traffic spillback has no effect on those vehicles directed to the other output links, an unreasonable assumption as the FIFO effect in traffic flow networks has been observed even for multilane diverging junctions [7], [8]. On the other hand, a full FIFO model is often too restrictive [9]. To derive a class of partial S. Coogan Fig.…”