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Mathematics
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Application of Mathematical Modeling and Simulation to Transportation
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Application of Mathematical Modeling and Simulation to Transportation

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 3437

Special Issue Editor

Dr. Noureddine Lakouari

E-Mail Website
Guest Editor
Computer Science Department, National Institute of Astrophysics, Optics and Electronics, Luis Enrique Erro # 1, Tonantzintla, Puebla 72840, Mexico
Interests: intelligent transportation systems (ITS); mathematical modeling; optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Transportation is a crucial sector that significantly boosts countries’ development. This Special Issue aims to explore innovative applications of mathematical modeling and simulation in transportation. Its focus will be on the latest research, methodologies, and practical implementations that use mathematical tools to address the complex challenges facing the transportation sector.

We invite original research articles, reviews, and case studies that cover a wide range of topics, including, but not limited to, the following:

  • Environmental impact assessments of transportation systems;
  • Freight and logistics modeling;
  • Intelligent transportation systems (ITSs);
  • The modeling of traffic behavior and patterns;
  • The optimization of transportation networks;
  • Policy modeling and evaluation in transportation;
  • Public transportation planning and management;
  • Traffic flow theory and its applications;
  • The simulation of transportation systems and infrastructures.

Dr. Noureddine Lakouari
Guest Editor

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

  • intelligent transportation systems (ITSs)
  • mathematical modeling
  • optimization
  • sustainable transportation
  • traffic flow theory
  • transportation challenges
  • transportation infrastructure
  • transportation networks

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

18 pages, 600 KiB  
Article
A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph
by Bo Xu, Xiaodong Ji and Zhengrong Cheng
Mathematics 2025, 13(1), 134; https://doi.org/10.3390/math13010134 - 1 Jan 2025
Cited by 2 | Viewed by 959
Abstract
The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP [...] Read more.
The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is defined in mathematical equations. Second, three models for RTSP are proposed, which are the Dynamic Robust Shortest Path (DRSP) model, the Dynamic Greedy Robust Shortest Path (DGRSP) model and the Dynamic Mean Shortest Path (DMSP) model. Then, three solution methods are designed. Finally, a numerical study is conducted to compare the efficiency of the models and corresponding solution methods. It shows that the DGRSP model and DMSP model generally present better results than the others. In the real road network test, they have the minimum average-regret-ratio of DGSP 7.8% and DMSP 7.1%; while in the generated network test, they both have a minimum average-regret-ratio of 0.5%. Full article
(This article belongs to the Special Issue Application of Mathematical Modeling and Simulation to Transportation)
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24 pages, 1434 KiB  
Article
Optimizing Traveler Behavior Between MADINA and JEDDA Using UPPAAL Stratego: A Stochastic Priced Timed Games Approach
by Moez Krichen and Ahmed Harbaoui
Mathematics 2024, 12(21), 3421; https://doi.org/10.3390/math12213421 - 31 Oct 2024
Viewed by 876
Abstract
This study looks at how travelers move between MADINA and JEDDA, using the UPPAAL Stratego tool to tackle the complexities of urban mobility. As cities grow, effective transportation planning becomes more challenging. Travelers have three options: car, bus, and train. The choices for [...] Read more.
This study looks at how travelers move between MADINA and JEDDA, using the UPPAAL Stratego tool to tackle the complexities of urban mobility. As cities grow, effective transportation planning becomes more challenging. Travelers have three options: car, bus, and train. The choices for car and bus travel are impacted by traffic conditions, which can vary between heavy and light, affecting both travel time and cost. We propose a detailed mathematical model that captures all possible scenarios related to these travel options, incorporating the uncertainties of real life. This allows us to simulate different traffic situations. By using UPPAAL Stratego, we evaluate three strategies: the Safe Strategy, which minimizes risk; the Fast Strategy, which aims to reduce travel time; and the Fast and Safe Strategy, which seeks a balance between speed and safety. This paper starts with an introduction to the Stochastic Priced Timed Games approach, highlighting its relevance in modeling dynamic travel environments. We then provide an overview of UPPAAL Stratego, showcasing its abilities in generating, optimizing, and comparing strategies. Next, we outline our mathematical model, explaining the assumptions, parameters, and data sources we used. Our simulation results illustrate how each strategy performs under different conditions, shedding light on traveler preferences and behaviors. The findings underscore the significance of accounting for traffic variability in travel planning and offer important insights for urban transportation policies aimed at improving the traveler experience and optimizing resource use. Additionally, we emphasize the theoretical contributions of our model by demonstrating its applicability to real-world scenarios and its potential to inform future research in urban mobility optimization. Ultimately, this research adds to the growing knowledge of smart transportation systems, demonstrating how formal mathematical modeling can address complex real-world challenges and inform future urban mobility strategies. Full article
(This article belongs to the Special Issue Application of Mathematical Modeling and Simulation to Transportation)
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14 pages, 3707 KiB  
Article
Supply–Demand Matching of Engineering Construction Materials in Complex Mountainous Areas Based on Complex Environment Two-Stage Stochastic Programing
by Liu Bao, Peigen Zhang, Ze Guo, Wanqi Wang, Qing Zhu and Yulin Ding
Mathematics 2024, 12(17), 2683; https://doi.org/10.3390/math12172683 - 29 Aug 2024
Viewed by 866
Abstract
Effective supply and demand matching for construction materials is a crucial challenge in large-scale railway projects, particularly in complex and hazardous environments. We propose a two-stage stochastic programing model that incorporates environmental uncertainties, such as natural disasters, into the supply chain optimization process. [...] Read more.
Effective supply and demand matching for construction materials is a crucial challenge in large-scale railway projects, particularly in complex and hazardous environments. We propose a two-stage stochastic programing model that incorporates environmental uncertainties, such as natural disasters, into the supply chain optimization process. The first stage determines optimal locations and capacities for material supply points, while the second stage addresses material distribution under uncertain demand. We further enhance the model’s efficiency with Benders decomposition algorithm. The performance of our model is rigorously compared with existing optimization approaches, demonstrating its superior capability in handling environmental uncertainties and complex logistical scenarios. This study provides a novel framework for optimizing supply chains in challenging environments, offering significant improvements over traditional models in both adaptability and robustness. Full article
(This article belongs to the Special Issue Application of Mathematical Modeling and Simulation to Transportation)
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