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Mathematics
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Application of Mathematical Methods to Transportation: Modeling and Analysis
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Application of Mathematical Methods to Transportation: Modeling and Analysis

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 2413

Special Issue Editors

Prof. Dr. Gang Ren

E-Mail Website
Guest Editor
School of Transportation, Southeast University, 2 Sipailou, Nanjing 210096, China
Interests: multimodal transportation system simulation; traffic behavior and safety analysis; emergency traffic management; active transport optimization; transportation resilience
Special Issues, Collections and Topics in MDPI journals
Dr. Qi Cao

E-Mail Website
Guest Editor
School of Transportation, Southeast University, 2 Sipailou, Nanjing 210096, China
Interests: traffic behavior and safety analysis; data mining and analyses; traffic congestion tracking; trajectory processing; active transport optimization; transportation resilience

Special Issue Information

Dear Colleagues,

During the last decade, there has been a remarkable surge in the utilization of mathematical methods to tackle multifaceted issues in transportation systems, ranging from traffic congestion to efficient resource allocation. At present, with the advent of big data, smart cities, and an increased focus on sustainability, the need for advanced mathematical models and rigorous analytical techniques in this domain is more pressing than ever.

This Special Issue aims to consolidate and showcase the latest advancements and innovative applications of mathematical methods in transportation modeling and analysis. It seeks to provide a comprehensive view of how these methods are revolutionizing our understanding and management of modern transportation systems.

The topics of interest for publication include, but are not limited to:

  1. Development and application of novel mathematical models for traffic flow prediction and control, including those employing machine learning algorithms.
  2. Use of optimization techniques for solving complex problems such as vehicle routing, public transportation scheduling, and multimodal transportation system simulation.
  3. Stochastic modeling for analyzing uncertainty and risk in transportation systems, including passenger demand fluctuations, travel time variability, and network resilience.
  4. Game theoretical frameworks for studying strategic interactions among stakeholders in transportation markets and networks.
  5. Network analysis and graph theory applications for understanding and optimizing the structure and dynamics of transportation networks.
  6. Data-driven modeling and statistical analyses for extracting valuable insights from large-scale transportation datasets, including traffic flow patterns, user behavior, and environmental impacts.
  7. Simulation-based approaches to assess and compare alternative transportation policies, scenarios, or technologies.
  8. Integration of mathematical models with decision support systems to enhance transportation planning and policy formulation at local, regional, and national levels.

Prof. Dr. Gang Ren
Dr. Qi Cao
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • transportation modeling and analysis
  • traffic flow prediction and control
  • vehicle routing
  • public transportation scheduling
  • multimodal transportation system simulation
  • passenger demand fluctuations
  • travel time variability
  • network resilience

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Published Papers (3 papers)

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Research

22 pages, 6893 KiB  
Article
Resilience Measurement of Bus–Subway Network Based on Generalized Cost
by Yulong Pei, Fei Xie, Ziqi Wang and Chuntong Dong
Mathematics 2024, 12(14), 2191; https://doi.org/10.3390/math12142191 - 12 Jul 2024
Viewed by 499
Abstract
Buses and subways are crucial modes of transportation for residents, yet frequent disturbances pose serious challenges to their daily commutes. To tackle these disruptions and boost the stability of the transportation network, it is vital to accurately measure the resilience of a bus–subway [...] Read more.
Buses and subways are crucial modes of transportation for residents, yet frequent disturbances pose serious challenges to their daily commutes. To tackle these disruptions and boost the stability of the transportation network, it is vital to accurately measure the resilience of a bus–subway composite network under such events. Therefore, this study utilizes the generalized cost between stations as weights with which to construct a bus–subway weighted composite network. Subsequently, three indicators, namely reachability, path importance, and weighted coreness, are proposed to evaluate the significance of the nodes, thereby combining the improved CRITIC-TOPSIS method to identify the critical nodes. Then, deliberate attacks and preferential restorations are conducted on the nodes, considering their importance and the critical nodes sequences, respectively. Finally, network resilience changes are characterized by the network connectivity coefficient and global accessibility, and the network resilience is compared under different attack and recovery strategies. The research results indicate that resilience is lowest when using reachability sequences to attack and recover the network. The network’s recovery is most significant when using the critical nodes sequences. When 70% of the nodes are restored, the network’s performance is essentially fully recovered. Additionally, the resilience of a bus–subway network is higher than that of a single bus network. This study applies the generalized cost to weight the transportation network, and considers the impact of multiple factors on the ease of connectivity between the nodes, which facilitates the accurate measurement of the resilience of a bus–subway network and enhances the ability to cope with disruptions. Full article
(This article belongs to the Special Issue Application of Mathematical Methods to Transportation: Modeling and Analysis)
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24 pages, 6068 KiB  
Article
Integrated Optimization of Production Scheduling and Haulage Route Planning in Open-Pit Mines
by Changyou Xu, Gang Chen, Huabo Lu, Qiuxia Zhang, Zhengke Liu and Jing Bian
Mathematics 2024, 12(13), 2070; https://doi.org/10.3390/math12132070 - 2 Jul 2024
Viewed by 571
Abstract
In mining, deposits are divided into blocks, forming the basis for open-pit mine planning, covering production and haulage route planning. Current studies often stage optimization and lack the consideration of road capacity, leading to suboptimal solutions. A novel approach integrates production scheduling and [...] Read more.
In mining, deposits are divided into blocks, forming the basis for open-pit mine planning, covering production and haulage route planning. Current studies often stage optimization and lack the consideration of road capacity, leading to suboptimal solutions. A novel approach integrates production scheduling and haulage route planning through a bilevel optimization model. The upper-level model integrates ore mining constraints to establish a mixed-integer production scheduling model, minimizing haulage costs. Spatiotemporal correlation constraints for block mining are determined using a two-stage algorithm. The lower-level model incorporates road capacity, forming a haulage route optimization model based on multicommodity network flow. A solution algorithm with a distance penalty strategy facilitates feedback between the upper and lower levels, achieving optimal solutions. Tested on a real open-pit coal mine with over 5 million blocks, this approach reduces haulage costs by 10.06% compared to stage optimization. Additionally, this approach allows for adjusting haulage demand in both temporal and spatial dimensions, effectively preventing road congestion. This study advances rational mining processes and enhances the efficiency of open-pit mining haulage systems. Full article
(This article belongs to the Special Issue Application of Mathematical Methods to Transportation: Modeling and Analysis)
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17 pages, 2519 KiB  
Article
Cooperative Vehicle Infrastructure System or Autonomous Driving System? From the Perspective of Evolutionary Game Theory
by Wei Bai, Xuguang Wen, Jiayan Zhang and Linheng Li
Mathematics 2024, 12(9), 1404; https://doi.org/10.3390/math12091404 - 3 May 2024
Viewed by 784
Abstract
In this paper, we explore the trade-offs between public and private investment in autonomous driving technologies. Utilizing an evolutionary game model, we delve into the complex interaction mechanisms between governments and auto manufacturers, focusing on how strategic decisions impact overall outcomes. Specifically, we [...] Read more.
In this paper, we explore the trade-offs between public and private investment in autonomous driving technologies. Utilizing an evolutionary game model, we delve into the complex interaction mechanisms between governments and auto manufacturers, focusing on how strategic decisions impact overall outcomes. Specifically, we predict that governments may opt for strategies such as constructing and maintaining infrastructure for Roadside Infrastructure-based Vehicles (RIVs) or subsidizing high-level Autonomous Driving Vehicles (ADVs) without additional road infrastructure. Manufacturers’ choices involve deciding whether to invest in RIVs or ADVs, depending on governmental policies and market conditions. Our simulation results, based on scenarios derived from existing economic data and forecasts on technology development costs, suggest that government subsidy policies need to dynamically adjust in response to manufacturers’ shifting strategies and market behavior. This dynamic adjustment is crucial as it addresses the evolving economic environment and technological advancements, ensuring that subsidies effectively incentivize the desired outcomes in autonomous vehicle development. The findings of this paper could serve as valuable decision-making tools for governments and auto manufacturers, guiding investment strategies that align with the dynamic landscape of autonomous driving technology. Full article
(This article belongs to the Special Issue Application of Mathematical Methods to Transportation: Modeling and Analysis)
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