Research

19 pages, 2774 KiB

Open AccessArticle

Cooperative Control for Signalized Intersections in Intelligent Connected Vehicle Environments

by Anton Agafonov, Alexander Yumaganov and Vladislav Myasnikov

Mathematics 2023, 11(6), 1540; https://doi.org/10.3390/math11061540 - 22 Mar 2023

Cited by 2 | Viewed by 1537

Cooperative control of vehicle trajectories and traffic signal phases is a promising approach to improving the efficiency and safety of transportation systems. This type of traffic flow control refers to the coordination and optimization of vehicle trajectories and traffic signal phases to reduce [...] Read more.

Cooperative control of vehicle trajectories and traffic signal phases is a promising approach to improving the efficiency and safety of transportation systems. This type of traffic flow control refers to the coordination and optimization of vehicle trajectories and traffic signal phases to reduce congestion, travel time, and fuel consumption. In this paper, we propose a cooperative control method that combines a model predictive control algorithm for adaptive traffic signal control and a trajectory construction algorithm. For traffic signal phase selection, the proposed modification of the adaptive traffic signal control algorithm combines the travel time obtained using either the vehicle trajectory or a deep neural network model and stop delays. The vehicle trajectory construction algorithm takes into account the predicted traffic signal phase to achieve cooperative control. To evaluate the method performance, numerical experiments have been conducted for three real-world scenarios in the SUMO simulation package. The experimental results show that the proposed cooperative control method can reduce the average fuel consumption by 1% to 4.2%, the average travel time by 1% to 5.3%, and the average stop delays to 27% for different simulation scenarios compared to the baseline methods. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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8 pages, 433 KiB

Open AccessArticle

An Evolutionary View on Equilibrium Models of Transport Flows

by Evgenia Gasnikova, Alexander Gasnikov, Yaroslav Kholodov and Anastasiya Zukhba

Mathematics 2023, 11(4), 858; https://doi.org/10.3390/math11040858 - 08 Feb 2023

Cited by 4 | Viewed by 902

Abstract

In this short paper, we describe natural logit population games dynamics that explain equilibrium models of origin-destination matrix estimation and (stochastic) traffic assignment models (Beckmann, Nesterov–de Palma). Composition of the proposed dynamics allows to explain two-stages traffic assignment models. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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20 pages, 25439 KiB

Open AccessArticle

Identification of Location and Camera Parameters for Public Live Streaming Web Cameras

by Aleksander Zatserkovnyy and Evgeni Nurminski

Mathematics 2022, 10(19), 3601; https://doi.org/10.3390/math10193601 - 01 Oct 2022

Cited by 1 | Viewed by 1321

Abstract

Public live streaming web cameras are quite common now and widely used by drivers for qualitative analysis of traffic conditions. At the same time, they can be a valuable source of quantitative information on transport flows and speed for the development of urban [...] Read more.

Public live streaming web cameras are quite common now and widely used by drivers for qualitative analysis of traffic conditions. At the same time, they can be a valuable source of quantitative information on transport flows and speed for the development of urban traffic models. However, to obtain reliable data from raw video streams, it is necessary to preprocess them, considering the camera location and parameters without direct access to the camera. Here we suggest a procedure for estimating camera parameters, which allows us to determine pixel coordinates for a point cloud in the camera’s view field and transform them into metric data. They are used with advanced moving object detection and tracking for measurements. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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Graphical abstract

18 pages, 559 KiB

Open AccessArticle

Elementary Cellular Automata as Invariant under Conjugation Transformation or Combination of Conjugation and Reflection Transformations, and Applications to Traffic Modeling

by Valery Kozlov, Alexander Tatashev and Marina Yashina

Mathematics 2022, 10(19), 3541; https://doi.org/10.3390/math10193541 - 28 Sep 2022

Cited by 1 | Viewed by 1108

Abstract

This paper develops the analysis of properties of the cellular automata class introduced by the authors. It is assumed that the set of automaton cells is finite and forms a closed lattice, and there are two states for each automaton cell. We consider [...] Read more.

This paper develops the analysis of properties of the cellular automata class introduced by the authors. It is assumed that the set of automaton cells is finite and forms a closed lattice, and there are two states for each automaton cell. We consider a new concept. This concept is the average velocity of a cellular automaton, which characterizes the average intensity of changes in the states of the automaton’s cells for a given initial state. The automaton velocity is equal to 1 if the state of any cell changes at each step. The spectrum of average velocities of a cellular automaton is the set of average velocities for different initial states. Since the state space is finite, the automaton, starting from a certain moment of time, is in periodically repeating states of a cycle, and thus, the research of the velocity spectrum is related to the problem of studying the set of the automaton cycles. For elementary cellular automata, the introduced class consists of a subclass of automata such that the conjugation trasformation of an automaton is the automaton itself (Subclass A) or the reflection of the automaton (Subclass B). For this class, it is proved that the spectrum of the automaton contains the value

v_{0}

if and only if the spectrum of the complementary automaton contains the value

1 - v_{0}

(the sum of the index of elementary cellular automaton and the complementary automaton is 255). For automata of Subclasses A and B, the set of cycles and the velocity spectrum are studied. For Subclass A, a theorem has been proved such that in accordance with this theorem, if two automata complementary to each other start evolving in the same initial state, then the sum of their average velocities is equal to 1. This theorem for Subclass A is generalized to cellular automata, invariant under the conjugation transformation, of more general type than elementary automata. Generalizations of the theorem have been given for the class of one-dimensional cellular automata with a neighborhood containing

2 r + 1

cells (the next state of the cell depends on the present states of this cell, r cells on the left and r cells on the right) and for some traditionally considered classes of two-dimensional automata. Some elementary cellular automata belonging to the class considered in the paper can be interpreted as transport models. The properties of the spectra for these automata are studied and compared with the properties of elementary cellular automata not invariant under the considered transformations and can also be interpreted as transport models. The analytical results obtained for these simple models can be used to study the qualitative properties and limiting behavior of more complex transport models. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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18 pages, 2902 KiB

Open AccessArticle

Development of Parallel Algorithms for Intelligent Transportation Systems

by Boris Chetverushkin, Antonina Chechina, Natalia Churbanova and Marina Trapeznikova

Mathematics 2022, 10(4), 643; https://doi.org/10.3390/math10040643 - 19 Feb 2022

Cited by 3 | Viewed by 1626

Abstract

This paper deals with the creation of parallel algorithms implementing macro-and microscopic traffic flow models on modern supercomputers. High-performance computing contributes to the development of intelligent transportation systems based on information technologies and aimed at the effective regulation of traffic in large cities. [...] Read more.

This paper deals with the creation of parallel algorithms implementing macro-and microscopic traffic flow models on modern supercomputers. High-performance computing contributes to the development of intelligent transportation systems based on information technologies and aimed at the effective regulation of traffic in large cities. As a macroscopic approach, the quasi-gas-dynamic traffic model approximated by explicit finite-difference schemes is proposed. One- and two-dimensional variants of the system are considered, and the concept of lateral velocity and different equations for obtaining it are discussed. The microscopic approach is represented by the multilane cellular automata model. The previously developed model is extended to reproduce synchronized flow in accordance with Kerner’s three-phase theory. The new version starts from the Kerner–Klenov–Schreckenberg–Wolf model and operates with the concept of the synchronization gap. Macroscopic models are relevant for determining the common characteristics of road traffic, while microscopic models are useful for a detailed description of cars’ movement. Both approaches possess inner parallelism. The parallel algorithms are based on the geometrical parallelism principle with different boundary conditions at interfaces of the subdomains. Sufficiently high speedups were reached when up to 100 processors were involved in calculations. The proposed algorithms can serve as the core of ITS. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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11 pages, 675 KiB

Open AccessArticle

A Methodology for Estimating Vehicle Route Choice from Sparse Flow Measurements in a Traffic Network

by Alex A. Kurzhanskiy

Mathematics 2022, 10(3), 527; https://doi.org/10.3390/math10030527 - 08 Feb 2022

Viewed by 1162

Abstract

While traffic speed data and travel time estimates are increasingly more available from commercial vendors, they are not sufficient for proper management and performance evaluation of transportation networks. Effective traffic control and demand management requires information about volumes, which is provided by fixed [...] Read more.

While traffic speed data and travel time estimates are increasingly more available from commercial vendors, they are not sufficient for proper management and performance evaluation of transportation networks. Effective traffic control and demand management requires information about volumes, which is provided by fixed location sensors, such as loop detectors or cameras, and those are sparse. This paper proposes a method for estimating route choice using sparse flow measurements and estimated speed on the road network based on compressed sensing technology widely used in image processing, where from a handful of scattered pixels, a full image is recovered. What is known includes flows at origins and at selected links of the road network, where the detection is present; speed estimates are available for all network links. We find coefficients that split origin flows among routes starting at those origins. The advantage of the proposed methodology is that it does not rely on simulation that is prone to calibration errors but only on measured data. We also show how vehicle flows can be estimated at links with no detection, which enables computing performance measures for road networks lacking complete sensor coverage. Finally, we propose a method for selecting plausible routes between origins and destinations. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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20 pages, 5741 KiB

Open AccessArticle

Evaluation of the Approach for the Identification of Trajectory Anomalies on CCTV Video from Road Intersections

by Rifkat Minnikhanov, Igor Anikin, Aigul Mardanova, Maria Dagaeva, Alisa Makhmutova and Azat Kadyrov

Mathematics 2022, 10(3), 388; https://doi.org/10.3390/math10030388 - 27 Jan 2022

Cited by 5 | Viewed by 1811

Abstract

The approach for the detection of vehicle trajectory abnormalities on CCTV video from road intersections was proposed and evaluated. We mainly focused on the trajectory analysis method rather than objects detection and tracking. Two basic challenges have been overcome in the suggested approach—spatial [...] Read more.

The approach for the detection of vehicle trajectory abnormalities on CCTV video from road intersections was proposed and evaluated. We mainly focused on the trajectory analysis method rather than objects detection and tracking. Two basic challenges have been overcome in the suggested approach—spatial perspective on the image and performance. We used trajectory approximation by polynomials as well as the Ramer-Douglas-Peucker N thinning technique to increase the performance of the trajectory comparison method. Special modification of trajectory similarity metric LCSS was suggested to consider the spatial perspective. We used clustering to discover two types of classes—with normal and abnormal trajectories. The framework, which implements the suggested approach, was developed. A series of experiments were carried out for testing the approach and defining recommendations for using different techniques in the scope of it. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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10 pages, 903 KiB

Open AccessArticle

Computing a Group of Polynomials over a Galois Field in FPGA Architecture

by Sergei V. Shalagin

Mathematics 2021, 9(24), 3251; https://doi.org/10.3390/math9243251 - 15 Dec 2021

Cited by 1 | Viewed by 1869

Abstract

For the most extensive range of tasks, such as real-time data processing in intelligent transport systems, etc., advanced computer-based techniques are required. They include field-programmable gate arrays (FPGAs). This paper proposes a method of pre-calculating the hardware complexity of computing a group of [...] Read more.

For the most extensive range of tasks, such as real-time data processing in intelligent transport systems, etc., advanced computer-based techniques are required. They include field-programmable gate arrays (FPGAs). This paper proposes a method of pre-calculating the hardware complexity of computing a group of polynomial functions depending on the number of input variables of the said functions, based on the microchips of FPGAs. These assessments are reduced for a group of polynomial functions due to computing the common values of elementary polynomials. Implementation is performed using similar software IP-cores adapted to the architecture of user-programmable logic arrays. The architecture of FPGAs includes lookup tables and D flip-flops. This circumstance ensures that the pipelined data processing provides the highest operating speed of a device, which implements the group of polynomial functions defined over a Galois field, independently of the number of variables of the said functions. A group of polynomial functions is computed based on common variables. Therefore, the input/output blocks of FPGAs are not a significant limiting factor for the hardware complexity estimates. Estimates obtained in using the method proposed allow evaluating the amount of the reconfigurable resources of FPGAs, required for implementing a group of polynomial functions defined over a Galois field. This refers to both the existing FPGAs and promising ones that have not yet been implemented. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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14 pages, 1575 KiB

Open AccessArticle

Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation

by Yaroslav Kholodov, Andrey Alekseenko, Viktor Kazorin and Alexander Kurzhanskiy

Mathematics 2021, 9(16), 2001; https://doi.org/10.3390/math9162001 - 21 Aug 2021

Cited by 4 | Viewed by 1618

Abstract

This paper presents a generalized second-order hydrodynamic traffic model. Its central piece is the expression for the relative velocity of the congestion (compression wave) propagation. We show that the well-known second-order models of Payne–Whitham, Aw–Rascal and Zhang are all special cases of the [...] Read more.

This paper presents a generalized second-order hydrodynamic traffic model. Its central piece is the expression for the relative velocity of the congestion (compression wave) propagation. We show that the well-known second-order models of Payne–Whitham, Aw–Rascal and Zhang are all special cases of the featured generalized model, and their properties are fully defined by how the relative velocity of the congestion is expressed. The proposed model is verified with traffic data from a segment of the Interstate 580 freeway in California, USA, collected by the California DOT’s Performance Measurement System (PeMS). Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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17 pages, 500 KiB

Open AccessFeature PaperArticle

Finding Equilibria in the Traffic Assignment Problem with Primal-Dual Gradient Methods for Stable Dynamics Model and Beckmann Model

by Meruza Kubentayeva and Alexander Gasnikov

Mathematics 2021, 9(11), 1217; https://doi.org/10.3390/math9111217 - 27 May 2021

Cited by 4 | Viewed by 2157

Abstract

In this paper, we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated Frank–Wolfe algorithm widely used for the Beckmann [...] Read more.

In this paper, we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated Frank–Wolfe algorithm widely used for the Beckmann model, these gradients methods solve the dual problem and then reconstruct a solution to the primal one. We deal with the universal gradient method, the universal method of similar triangles, and the method of weighted dual averages and estimate their complexity for the problem. Due to the primal-dual nature of these methods, we use a duality gap in a stopping criterion. In particular, we present a novel way to reconstruct admissible flows in the stable dynamics model, which provides us with a computable duality gap. Full article

(This article belongs to the Special Issue Numerical Methods and Algorithms Applied in Intelligent Transportation Systems)

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