Authors :
Jeetendra Jangid
Volume/Issue :
Volume 11 - 2026, Issue 10 - October
DOI :
https://doi.org/10.38124/ijisrt/26Oct791
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Abstract :
Urban traffic congestion is a dynamic systems problem involving interacting traffic streams, signal phases, queues, road capacity and changing demand. This paper develops a mathematically explicit Group-Theoretic framework in which traffic states are acted upon by a set of admissible traffic-control transformations. The key object is therefore not the set of raw traffic states itself, but a transformation group (or, where physical constraints prevent closure or invertibility, an admissible transformation structure) acting on the traffic-state space. Closure, associativity, identity and inverse are interpreted through composition, sequencing, no-change operation and restoration of compatible trafficcontrol transformations. A four-arm intersection model is formulated using queue-length vectors and signal-control transformations. A performance functional based on queue, delay and stopping cost is then coupled with the group action so that the mathematical structure organizes candidate control operations while an optimization rule selects an operationally feasible action. The framework is compatible with established group-based signal timing, adaptive signal control, queueing and optimization literature. The paper also identifies an important limitation: not every real-world traffic-control operation has an inverse, and therefore a strict group should only be defined over transformations satisfying the required algebraic properties. The proposed framework is intended as a foundation for simulation and field validation rather than as an experimentally proven traffic-improvement method.
Keywords :
Group Theory; Group Action; Intelligent Transportation Systems; Traffic Signal Control; Urban Infrastructure; Adaptive Signal Control; Queue Length; Mathematical Modelling; Traffic Optimization.
References :
- Wong, S. C. (1996). Group-based optimisation of signal timings using the TRANSYT traffic model. Transportation Research Part B: Methodological, 30(3), 217–244. https://doi.org/10.1016/0191-2615(95)00028-3
- Wong, S. C. (2002). Group-based optimization of a time-dependent TRANSYT traffic model for area traffic control. Transportation Research Part B: Methodological, 36(4), 291–312. https://doi.org/10.1016/S0191-2615(01)00004-2
- Lee, J., Wong, S. C., et al. (2017). Group-based hierarchical adaptive traffic-signal control Part I: Formulation. Transportation Research Part B: Methodological, 105, 1–18. https://doi.org/10.1016/j.trb.2017.08.008
- Lee, J., Wong, S. C., et al. (2017). Group-based hierarchical adaptive traffic-signal control Part II: Implementation. Transportation Research Part B: Methodological, 104, 376–397. https://doi.org/10.1016/j.trb.2017.08.009
- Wong, S. C. (1997). Group-based optimisation of signal timings using parallel computing. Transportation Research Part C: Emerging Technologies, 5(2), 123–139. https://doi.org/10.1016/S0968-090X(97)00006-5
Urban traffic congestion is a dynamic systems problem involving interacting traffic streams, signal phases, queues, road capacity and changing demand. This paper develops a mathematically explicit Group-Theoretic framework in which traffic states are acted upon by a set of admissible traffic-control transformations. The key object is therefore not the set of raw traffic states itself, but a transformation group (or, where physical constraints prevent closure or invertibility, an admissible transformation structure) acting on the traffic-state space. Closure, associativity, identity and inverse are interpreted through composition, sequencing, no-change operation and restoration of compatible trafficcontrol transformations. A four-arm intersection model is formulated using queue-length vectors and signal-control transformations. A performance functional based on queue, delay and stopping cost is then coupled with the group action so that the mathematical structure organizes candidate control operations while an optimization rule selects an operationally feasible action. The framework is compatible with established group-based signal timing, adaptive signal control, queueing and optimization literature. The paper also identifies an important limitation: not every real-world traffic-control operation has an inverse, and therefore a strict group should only be defined over transformations satisfying the required algebraic properties. The proposed framework is intended as a foundation for simulation and field validation rather than as an experimentally proven traffic-improvement method.
Keywords :
Group Theory; Group Action; Intelligent Transportation Systems; Traffic Signal Control; Urban Infrastructure; Adaptive Signal Control; Queue Length; Mathematical Modelling; Traffic Optimization.
