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Stream/Area:
-
Subject:
-
Paper ID:
IJSREM67582
Volume:
10 |
9 |
Sep 2026
Pages:
1-6
Publication Frequency:
Monthly (12 issues per year)
License:International Journal of Scientific Research in Engineering and Management follows the Creative Commons Attribution 4.0 (CC BY 4.0) License, allowing free use and distribution with proper attribution.
Department of Mathe
Sourashtra College
Department of Mathe
Sourashtra College
Transportation networks are dynamic systems in which travel time, traffic demand, congestion, road capacity, operating conditions, and incident effects vary over time. A route that is attractive under free-flow conditions may therefore become inefficient when demand increases or an incident reduces capacity. This paper develops an expanded mathematical framework for representing and optimizing such networks using time-dependent weighted directed graphs. Each transportation link is associated with a time-dependent traversal function and capacity, while route selection is formulated as a multi-objective optimization problem involving travel time, operating cost, and congestion exposure. Flow conservation, capacity, temporal propagation, and FIFO-compatible conditions are incorporated to maintain feasible route evaluation. A structured architecture is proposed in which network data, demand information, temporal conditions, a travel-time estimation layer, a route-generation engine, and a multi-objective decision layer operate as an integrated pipeline. A corresponding data-flow model describes the movement of static network data and dynamic observations through the system. A synthetic example illustrates how departure time changes can modify route evaluation. The numerical values are illustrative and are not presented as empirical transportation observations. The expanded framework provides a foundation for theoretical analysis, real-world validation, uncertainty modelling, resilience analysis, real-time re-optimization, and large-scale computational experimentation.
KEYWORDS
This paper developed an expanded mathematical and architectural framework for modelling and optimizing dynamic transportation networks using time-dependent graphs. By allowing edge traversal time to vary with entry time and congestion, the framework captures a central characteristic of transportation systems that static network models may overlook. The multi-objective formulation provides a structured mechanism for considering travel time, operating cost, and congestion exposure simultaneously. The proposed architecture and data-flow representation clarify how network data, dynamic observations, travel-time estimation, route generation, optimization, and monitoring can be connected in an integrated system. The synthetic example demonstrates the basic temporal effect on route evaluation without making empirical claims. Future research should focus on validated real-world datasets, uncertainty modelling, resilience, real-time data integration, scalable computation, and rigorous comparative evaluation
[1] Gendreau, M., Ghiani, G., & Guerriero, E. (2015). Time-dependent routing problems: A review. Computers & Operations Research, 64, 189–197. https://doi.org/10.1016/j.cor.2015.06.001 [2] Adamo, T., Gendreau, M., Ghiani, G., & Guerriero, E. (2024). A review of recent advances in time-dependent vehicle routing. European Journal of Operational Research, 319(1), 1–15. https://doi.org/10.1016/j.ejor.2024.06.016 [3] Wu, H., Cheng, J., Huang, S., Ke, Y., Lu, Y., & Xu, J. (2019). Time-dependent graphs: Definitions, applications, and algorithms. Data Science and Engineering. [4] Bookbinder, J. H. (1980). The dynamic transportation problem: A survey. Naval Research Logistics Quarterly, 27(1), 65–87. https://doi.org/10.1002/nav.3800270107 [5] Rakhmangulov, A., Osintsev, N., & Mishkurov, P. (2025). Spatio-temporal graphs in transportation: Challenges, optimization, and prospects. Systems, 13(4), 263.
Publication Date
9/30/2026
Peer Review Type
Double-Blind Peer Review
Review Rounds: 2
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Conflict of Interest
The authors declare no conflict of interest related to this research work.
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