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Mathematics
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Mathematical Methods in System Engineering Modeling and Simulation
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Mathematical Methods in System Engineering Modeling and Simulation

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

Deadline for manuscript submissions: 30 September 2026 | Viewed by 717

Special Issue Editors

Prof. Dr. Dahai Liu

E-Mail Website
Guest Editor
School of Graduate Studies in College of Aviation, Embry-Riddle Aeronautical University, Daytona Beach Campus, Daytona Beach, FL 32114, USA
Interests: systems engineering; operations research; modeling and simulation; machine learning; human factors engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Yongxin Liu

E-Mail Website
Guest Editor
Department of Mathematics in College of Arts and Sciences, Embry-Riddle Aeronautical University, Daytona Beach Campus, Daytona Beach, FL 32114, USA
Interests: artificial intelligence; cyber-physical systems
Special Issues, Collections and Topics in MDPI journals
Dr. Hongyun Chen

E-Mail Website
Guest Editor
Department of Civil Engineering in College of Engineering, Embry-Riddle Aeronautical University, Daytona Beach Campus, Daytona Beach, FL 32114, USA
Interests: traffic safety; operation; vulnerable roadway users; traffic signal control; statistical analysis in traffic engineering; ITS; transportation cybersecurity
Dr. Lu Gao

E-Mail Website
Guest Editor
Department of Civil and Environmental Engineering, University of Houston, Houston, TX 77004, USA
Interests: big data in construction industry and asset management; artificial intelligence; machine learning; data science; natural language processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical models form the foundation of systems engineering modeling and simulation, providing rigorous tools for representing, analyzing, and optimizing complex system infrastructures. In complex systems engineering such as transportation systems, these methods enable the modeling of dynamic interactions among system components and infrastructure. Mathematical formulations support the simulation of systems operations under diverse conditions and constraints.

Optimization techniques complement these simulations by improving design, scheduling, routing, and control strategies. Applications include system optimization, flow management, demand-responsive services, and network configuration. Combining modeling, simulation, and optimization allows researchers and engineers to test “what-if” scenarios, assess resilience, and enhance performance, safety, and sustainability.

Recent advances integrate machine learning, agent-based simulation with Operations Research to handle uncertainty and multi-objective decision problems in various connected systems, e.g., transportation networks, logistic planning, operational optimization cyber-defense, etc. Such approaches improve safety, security, and efficiency, and support data-driven policy design.

This Special Issue welcomes contributions advancing mathematical methods in systems engineering modeling and simulation, particularly those addressing transportation systems. Research that unites theoretical rigor, computational innovation, and real-world applicability will strengthen the capability of engineers to design and manage intelligent, adaptive, and sustainable transportation infrastructures.

Prof. Dr. Dahai Liu
Dr. Yongxin Liu
Dr. Hongyun Chen
Dr. Lu Gao
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 250 words) can be sent to the Editorial Office for assessment.

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

  • optimization
  • simulation
  • operations research
  • decision-making
  • stochastic modeling
  • transportation systems

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

Published Papers (2 papers)

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Research

29 pages, 3476 KB  
Article
Nonhomogeneous Poisson Process Software Reliability Growth Model with Dependent Failures and an Exponentially Decaying Fault Detection Rate
by Kwang Yoon Song, Onon-Ujin Otgonbayar and In Hong Chang
Mathematics 2026, 14(12), 2126; https://doi.org/10.3390/math14122126 (registering DOI) - 14 Jun 2026
Abstract
Effectively modeling software failure behavior is crucial for reliability assessment and planning of releases. However, many current software reliability growth models assume that failures are independent and fault detection mechanisms are simplified. However, these assumptions may not accurately represent real-world testing environments. This [...] Read more.
Effectively modeling software failure behavior is crucial for reliability assessment and planning of releases. However, many current software reliability growth models assume that failures are independent and fault detection mechanisms are simplified. However, these assumptions may not accurately represent real-world testing environments. This study introduces a novel Nonhomogeneous Poisson Process (NHPP)-based Software Reliability Growth Model (SRGM) that includes dependent failure behavior and exponentially decaying fault detection rates to better reflect the software debugging process. The proposed model was validated using real failure datasets and compared with 17 existing models. The performance of the model was assessed using various goodness-of-fit criteria, such as errors, prediction accuracy, and metrics based on information theory. To provide a more thorough evaluation, a multi-criteria decision-making approach was used to rank the competing models based on their overall performance. Furthermore, a one-at-a-time sensitivity analysis was conducted to examine how the initial values of the parameters affected the model’s behavior. These findings indicate that the sensitivity of the model to this parameter varies depending on the dataset used. The results indicate that the proposed model achieved superior performance across multiple evaluation criteria and consistently obtained the best overall ranking under the integrated multi-criteria framework. In Dataset 1, the proposed model achieved the best performance in most goodness-of-fit criteria, whereas in Dataset 2 it produced the best results across all twelve evaluation criteria. The results show that the proposed model offers improved or competitive performance compared to existing models and provides greater flexibility in capturing complex failure processes within software systems. Full article
(This article belongs to the Special Issue Mathematical Methods in System Engineering Modeling and Simulation)
25 pages, 1297 KB  
Article
LLM-Guided Hybrid Simulation for Airport Cyber-Resilience Assessment
by Tejaswini Sanjay Katale, Lu Gao, Yongxin Liu, Dahai Liu and Hongyun Chen
Mathematics 2026, 14(11), 1923; https://doi.org/10.3390/math14111923 - 1 Jun 2026
Viewed by 306
Abstract
Airport systems rely on tightly connected digital and physical components, so cyber disruptions can affect both service performance and passenger movement. Existing airport simulation studies often focus on either queue-based passenger processing or pedestrian movement but rarely combine both in a framework suited [...] Read more.
Airport systems rely on tightly connected digital and physical components, so cyber disruptions can affect both service performance and passenger movement. Existing airport simulation studies often focus on either queue-based passenger processing or pedestrian movement but rarely combine both in a framework suited for cyber-resilience analysis. This paper presents a hybrid simulation framework that integrates discrete-event simulation (DES), JuPedSim-based microscopic pedestrian modeling, and structured large language model (LLM) decision support to examine how cyber disruptions propagate through passenger-facing airport operations. The DES layer models service processes such as check-in, information desks, and security screening, while the pedestrian layer models movement, congestion, route choice, and spatial occupancy. Under degraded display or guidance conditions, the LLM generates structured passenger-level post-security decisions, such as going directly to the gate, checking a display, asking staff, waiting, visiting optional activity areas, or first moving to a wrong intermediate area. The framework is evaluated through a 500-passenger terminal case study with one baseline case and four disruption cases. Results show that check-in and security degradation produce the largest throughput loss, queue growth, and completion-time increase, while guidance degradation mainly affects post-security behavior. Spatial heatmaps further show where bottlenecks emerge and how congestion shifts across the terminal. Additional Rotterdam checkpoint validation, Palma benchmark analysis, and LLM ablation results support the framework’s ability to reproduce plausible queue, timing, throughput, and behavior-sensitive disruption patterns. The study provides a practical methodology for exploratory airport cyber-resilience assessment under coupled service, movement, and degraded-guidance conditions. Full article
(This article belongs to the Special Issue Mathematical Methods in System Engineering Modeling and Simulation)
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