1,408 research outputs found
A diffusion-based analysis of a multi-class road traffic network
This paper studies a stochastic model that describes the evolution of vehicle
densities in a road network. It is consistent with the class of (deterministic)
kinematic wave models, which describe traffic flows on the basis of
conservation laws that incorporate the macroscopic fundamental diagram (a
functional relationship between vehicle density and flow). Our setup is capable
of handling multiple types of vehicle densities, with general macroscopic
fundamental diagrams, on a network with arbitrary topology.
Interpreting our system as a spatial population process, we derive, under a
natural scaling, fluid and diffusion limits. More specifically, the vehicle
density process can be approximated with a suitable Gaussian process, which
yield accurate normal approximations to the joint (in the spatial and temporal
sense) vehicle density process. The corresponding means and variances can be
computed efficiently. Along the same lines, we develop an approximation to the
vehicles' travel-time distribution between any given origin and destination
pair. Finally, we present a series of numerical experiments that demonstrate
the accuracy of the approximations and illustrate the usefulness of the
results
Cellular Automata Models of Road Traffic
In this paper, we give an elaborate and understandable review of traffic
cellular automata (TCA) models, which are a class of computationally efficient
microscopic traffic flow models. TCA models arise from the physics discipline
of statistical mechanics, having the goal of reproducing the correct
macroscopic behaviour based on a minimal description of microscopic
interactions. After giving an overview of cellular automata (CA) models, their
background and physical setup, we introduce the mathematical notations, show
how to perform measurements on a TCA model's lattice of cells, as well as how
to convert these quantities into real-world units and vice versa. The majority
of this paper then relays an extensive account of the behavioural aspects of
several TCA models encountered in literature. Already, several reviews of TCA
models exist, but none of them consider all the models exclusively from the
behavioural point of view. In this respect, our overview fills this void, as it
focusses on the behaviour of the TCA models, by means of time-space and
phase-space diagrams, and histograms showing the distributions of vehicles'
speeds, space, and time gaps. In the report, we subsequently give a concise
overview of TCA models that are employed in a multi-lane setting, and some of
the TCA models used to describe city traffic as a two-dimensional grid of
cells, or as a road network with explicitly modelled intersections. The final
part of the paper illustrates some of the more common analytical approximations
to single-cell TCA models.Comment: Accepted for publication in "Physics Reports". A version of this
paper with high-quality images can be found at: http://phdsven.dyns.cx (go to
"Papers written"
Dynamic network loading: a stochastic differentiable model that derives link state distributions
We present a dynamic network loading model that yields queue length distributions, accounts for spillbacks, and maintains a differentiable mapping from the dynamic demand on the dynamic queue lengths. The model also captures the spatial correlation of all queues adjacent to a node, and derives their joint distribution. The approach builds upon an existing stationary queueing network model that is based on finite capacity queueing theory. The original model is specified in terms of a set of differentiable equations, which in the new model are carried over to a set of equally smooth difference equations. The physical correctness of the new model is experimentally confirmed in several congestion regimes. A comparison with results predicted by the kinematic wave model (KWM) shows that the new model correctly represents the dynamic build-up, spillback, and dissipation of queues. It goes beyond the KWM in that it captures queue lengths and spillbacks probabilistically, which allows for a richer analysis than the deterministic predictions of the KWM. The new model also generates a plausible fundamental diagram, which demonstrates that it captures well the stationary flow/density relationships in both congested and uncongested conditions
A kinematic wave theory of capacity drop
Capacity drop at active bottlenecks is one of the most puzzling traffic
phenomena, but a thorough understanding is practically important for designing
variable speed limit and ramp metering strategies. In this study, we attempt to
develop a simple model of capacity drop within the framework of kinematic wave
theory based on the observation that capacity drop occurs when an upstream
queue forms at an active bottleneck. In addition, we assume that the
fundamental diagrams are continuous in steady states. This assumption is
consistent with observations and can avoid unrealistic infinite characteristic
wave speeds in discontinuous fundamental diagrams. A core component of the new
model is an entropy condition defined by a discontinuous boundary flux
function. For a lane-drop area, we demonstrate that the model is well-defined,
and its Riemann problem can be uniquely solved. We theoretically discuss
traffic stability with this model subject to perturbations in density, upstream
demand, and downstream supply. We clarify that discontinuous flow-density
relations, or so-called "discontinuous" fundamental diagrams, are caused by
incomplete observations of traffic states. Theoretical results are consistent
with observations in the literature and are verified by numerical simulations
and empirical observations. We finally discuss potential applications and
future studies.Comment: 29 pages, 10 figure
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Modeling and optimizing network infrastructure for autonomous vehicles
Autonomous vehicle (AV) technology has matured sufficiently to be in testing on public roads. However, traffic models of AVs are still in development. Most previous work has studied AV technologies in micro-simulation. The purpose of this dissertation is to model and optimize AV technologies for large city networks to predict how AVs might affect city traffic patterns and travel behaviors. To accomplish these goals, we construct a dynamic network loading model for AVs, consisting of link and node models of AV technologies, which is used to calculate time-dependent travel times in dynamic traffic assignment. We then study several applications of the dynamic network loading to predict how AVs might affect travel demand and traffic congestion. AVs admit reduced perception-reaction times through technologies such as (cooperative) adaptive cruise control, which can reduce following headways and increase capacity. Previous work has studied these in micro-simulation, but we construct a mesoscopic simulation model for analyses on large networks. To study scenarios with both autonomous and conventional vehicles, we modify the kinematic wave theory to include multiple classes of flow. The flow-density relationship also changes in space and time with the class proportions. We present multiclass cell transmission model and prove that it is a Godunov approximation to the multiclass kinematic wave theory. We also develop a car-following model to predict the fundamental diagram at arbitrary proportions of AVs. Complete market penetration scenarios admit dynamic lane reversal -- changing lane direction at high frequencies to more optimally allocate road capacity. We develop a kinematic wave theory in which the number of lanes changes in space and time, and approximately solve it with a cell transmission model. We study two methods of determining lane direction. First, we present a mixed integer linear program for system optimal dynamic traffic assignment. Since this program is computationally difficult to solve, we also study dynamic lane reversal on a single link with deterministic and stochastic demands. The resulting policy is shown to significantly reduce travel times on a city network. AVs also admit reservation-based intersection control, which can make greater use of intersection capacity than traffic signals. AVs communicate with the intersection manager to reserve space-time paths through the intersection. We create a mesoscopic node model by starting with the conflict point variant of reservations and aggregating conflict points into capacity-constrained conflict regions. This model yields an integer program that can be adapted to arbitrary objective functions. To motivate optimization, we present several examples on theoretical and realistic networks demonstrating that naïve reservation policies can perform worse than traffic signals. These occur due to asymmetric intersections affecting optimal capacity allocation and/or user equilibrium route choice behavior. To improve reservations, we adapt the decentralized backpressure wireless packet routing and P0 traffic signal policies for reservations. Results show significant reductions in travel times on a city network. Having developed link and node models, we explore how AVs might affect travel demand and congestion. First, we study how capacity increases and reservations might affect freeway, arterial, and city networks. Capacity increases consistently reduced congestion on all networks, but reservations were not always beneficial. Then, we use dynamic traffic assignment within a four-step planning model, adding the mode choice of empty repositioning trips to avoid parking costs. Results show that allowing empty repositioning to encourage adoption of AVs could reduce congestion. Also, once all vehicles are AVs, congestion will still be significantly reduced. Finally, we present a framework to use the dynamic network loading model to study shared AVs. Results show that shared AVs could reduce congestion if used in certain ways, such as with dynamic ride-sharing. However, shared AVs also cause significant congestion. To summarize, this dissertation presents a complete mesoscopic simulation model of AVs that could be used for a variety of studies of AVs by planners and practitioners. This mesoscopic model includes new node and link technologies that significantly improve travel times over existing infrastructure. In addition, we motivate and present more optimal policies for these AV technologies. Finally, we study several travel behavior scenarios to provide insights about how AV technologies might affect future traffic congestion. The models in this dissertation will provide a basis for future network analyses of AV technologies.Civil, Architectural, and Environmental Engineerin
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