Special Issue "Numerical Methods and Algorithms Applied in Intelligent Transportation System"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 July 2022.

Special Issue Editor

Prof. Dr. Yaroslav Kholodov
E-Mail Website
Guest Editor
Insitute of Data Science and Artificial intelligence Head, Laboratory of Data Analysis and Bioinformatics, Innopolis University, 420500 Innopolis, Russia
Interests: data analysis; intelligent transportation systems; numerical methods; computer simulations; applied mathematics

Special Issue Information

Dear Colleagues,

Transport problems of modern metropolises are well known and particularly important. Emerging road traffic tasks require complex solutions and application of various classes of mathematical models due to the wide variety of timescales associated with the processes in the urban transportation system.

The describing of such models and algorithms is the main goal of this issue. The issue will focus on the numerical algorithms of transport modeling which can be explored theoretically or be developed for practical applications.

Prof. Dr. Yaroslav Kholodov
Guest Editor

Manuscript Submission Information

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Keywords

  • Intelligent transportation systems
  • Numerical methods
  • Algorithms
  • Transport modeling

Published Papers (4 papers)

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Research

Article
Evaluation of the Approach for the Identification of Trajectory Anomalies on CCTV Video from Road Intersections
Mathematics 2022, 10(3), 388; https://doi.org/10.3390/math10030388 - 27 Jan 2022
Viewed by 108
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
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Article
Computing a Group of Polynomials over a Galois Field in FPGA Architecture
Mathematics 2021, 9(24), 3251; https://doi.org/10.3390/math9243251 - 15 Dec 2021
Viewed by 375
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
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Article
Generalization Second Order Macroscopic Traffic Models via Relative Velocity of the Congestion Propagation
Mathematics 2021, 9(16), 2001; https://doi.org/10.3390/math9162001 - 21 Aug 2021
Viewed by 487
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
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Article
Finding Equilibria in the Traffic Assignment Problem with Primal-Dual Gradient Methods for Stable Dynamics Model and Beckmann Model
Mathematics 2021, 9(11), 1217; https://doi.org/10.3390/math9111217 - 27 May 2021
Viewed by 677
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
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