Alex A. Kurzhanskiy

Armin Askari, Daniel Albarnaz Farias, Alex A. Kurzhanskiy et al.

The paper evaluates the influence of the maximum vehicle acceleration and variable proportions of ACC/CACC vehicles on the throughput of an intersection. Two cases are studied: (1) free road downstream of the intersection; and (2) red light at some distance downstream of the intersection. Simulation of a 4-mile stretch of an arterial with 13 signalized intersections is used to evaluate the impact of (C)ACC vehicles on the mean and standard deviation of travel time as the proportion of (C)ACC vehicles is increased. The results suggest a very high urban mobility benefit of (C)ACC vehicles at little or no cost in infrastructure.

Armin Askari, Daniel Albarnaz Farias, Alex A. Kurzhanskiy et al.

To properly assess the impact of (cooperative) adaptive cruise control ACC (CACC), one has to model vehicle dynamics. First of all, one has to choose the car following model, as it determines the vehicle flow as vehicles accelerate from standstill or decelerate because of the obstacle ahead. The other factor significantly affecting the intersection throughput is the maximal vehicle acceleration rate. In this paper, we analyze three car following behaviors: Gipps model, Improved Intelligent Driver Model (IIDM) and Helly model. Gipps model exhibits rather aggressive acceleration behavior. If used for the intersection throughput estimation, this model would lead to overly optimistic results. Helly model is convenient to analyze due to its linear nature, but its deceleration behavior in the presence of obstacles ahead is unrealistically abrupt. Showing the most realistic acceleration and deceleration behavior of the three models, IIDM is suited for ACC/CACC impact evaluation better than the other two. We discuss the influence of the maximal vehicle acceleration rate and presence of different portions of ACC/CACC vehicles on intersection throughput in the context of the three car following models. The analysis is done for two cases: (1) free road downstream of the intersection; and (2) red light at some distance downstream of the intersection. Finally, we introduce the platoon model and evaluate ACC and CACC with platooning in terms of travel time ad network throughput using SUMO simulation of the 4-mile stretch of Colorado Boulevard / Huntington Drive arterial with 13 signalized intersections in Arcadia, Southern California.

Matthew A. Wright, Roberto Horowitz, Alex A. Kurzhanskiy

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transportation authorities have implemented managed lane policies, which restrict certain freeway lanes to certain types of vehicles. It was originally thought that managed lanes would improve the use of existing infrastructure through demand-management behaviors like carpooling, but implementations have often been characterized by unpredicted phenomena that are sometimes detrimental to system performance. The development of traffic models that can capture these sorts of behaviors is a key step for helping managed lanes deliver on their promised gains. Towards this goal, this paper presents an approach for solving for driver behavior of entering and exiting managed lanes at the macroscopic (i.e., fluid approximation of traffic) scale. Our method is inspired by recent work in extending a dynamic-system-based modeling framework from traffic behaviors on individual roads, to models at junctions, and can be considered a further extension of this dynamic-system paradigm to the route/lane choice problem. Unlike traditional route choice models that are often based on discrete-choice methods and often rely on computing and comparing drivers' estimated travel times from taking different routes, our method is agnostic to the particular choice of physical traffic model and is suited specifically towards making decisions at these interfaces using only local information. These features make it a natural drop-in component to extend existing dynamic traffic modeling methods.

Matthew A. Wright, Roberto Horowitz, Alex A. Kurzhanskiy

To help mitigate road congestion caused by the unrelenting growth of traffic demand, many transit authorities have implemented managed lane policies. Managed lanes typically run parallel to a freeway's standard, general-purpose (GP) lanes, but are restricted to certain types of vehicles. It was originally thought that managed lanes would improve the use of existing infrastructure through incentivization of demand-management behaviors like carpooling, but implementations have often been characterized by unpredicted phenomena that is often to detrimental system performance. This paper presents several macroscopic traffic modeling tools we have used for study of freeways equipped with managed lanes, or "managed lane-freeway networks." The proposed framework is based on the widely-used first-order kinematic wave theory. In this model, the GP and the managed lanes are modeled as parallel links connected by nodes, where certain type of traffic may switch between GP and managed lane links. Two types of managed lane topologies are considered: full-access, where vehicles can switch between the GP and the managed lanes anywhere; and separated, where such switching is allowed only at certain locations called gates. We also describe methods to incorporate in three phenomena into our model that are particular to managed lane-freeway networks. The inertia effect reflects drivers' inclination to stay in their lane as long as possible and switch only if this would obviously improve their travel condition. The friction effect reflects the empirically-observed driver fear of moving fast in a managed lane while traffic in the adjacent GP lanes moves slowly due to congestion. The smoothing effect describes how managed lanes can increase throughput at bottlenecks by reducing lane changes. We present simple models for each of these phenomena that fit within the general macroscopic theory.

Matthew A. Wright, Gabriel Gomes, Roberto Horowitz et al.

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.

Matthew A. Wright, Roberto Horowitz, Alex A. Kurzhanskiy

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further nonlinearities in the network dynamics. This paper considers the node model problem, which refers to methods for solving for cross-flows when roads meet at a junction. We present a simple hybrid dynamic system that, given a macroscopic snapshot of the roads entering and exiting a node, intuitively models the node's throughflows over time. This dynamic system produces solutions to the node model problem that are equal to those produced by many popular node models without intuitive physical meanings. We also show how the earlier node models can be rederived as executions of our dynamic system. The intuitive physical description supplied by our system provides a base for control of the road junction system dynamics, as well as the emergent network dynamics.

Matthew Wright, Gabriel Gomes, Roberto Horowitz et al.

We propose a macroscopic modeling framework for a network of roads and multi-commodity traffic. The proposed framework is based on the Lighthill-Whitham-Richards kinematic wave theory; more precisely, on its discretization, the Cell Transmission Model (CTM), adapted for networks and multi-commodity traffic. The resulting model is called the Link-Node CTM (LNCTM). In the LNCTM, we use the fundamental diagram of an "inverse lambda" shape that allows modeling of the capacity drop and the hysteresis behavior of the traffic state in a link that goes from free flow to congestion and back. A model of the node with multiple input and multiple output links accepting multi-commodity traffic is a cornerstone of the LNCTM. We present the multi-input-multi-output (MIMO) node model for multi-commodity traffic that supersedes previously developed node models. The analysis and comparison with previous node models are provided. Sometimes, certain traffic commodities may choose between multiple output links in a node based on the current traffic state of the node's input and output links. For such situations, we propose a local traffic assignment algorithm that computes how incoming traffic of a certain commodity should be distributed between output links, if this information is not known a priori.

Elena G. Dorogush, Alex A. Kurzhanskiy

In this paper we address the problem of dynamic pricing for toll lanes on freeways. The proposed toll mechanism is broken up into two parts: (1) the supply side feedback control that computes the desired split ratios for the incoming traffic flows between the general purpose and the toll lanes; and (2) the demand side price setting algorithm that aims to enforce the computed split ratios. The split ratio controller is designed and tested in the context of the link-node Cell Transmission Model with the modified node model of in/out flow distribution. The equilibrium structure of this traffic model is presented; and the case, in which the existence of a toll lane is meaningful, is discussed. For the price setting, two alternative approaches are presented. The first one is commonly used, and it relies on the known Value of Time (VoT) distribution. Its shortcoming, however, is in the difficulty of the VoT distribution estimation. The second approach employs the auction mechanism, where travelers make bids on places in the toll lane. The advantage of this approach is that it enables direct control over how many vehicles will be allowed into the toll lane.