Graph theoretic simulation based approach for urban traffic optimization using Hamiltonian inspired routing and sector based time staggering in Vellore

Urban traffic congestion, particularly in medium-sized cities, remains a significant problem in rapidly expanding cities. By using a graph-theoretic modeling approach based on Hamiltonian-inspired sector routing and sector-specific time schedules, this study aims to improve traffic flow in Vellore, Tamil Nadu, India. In a graph, the city’s road system is represented by roadways as linking edges and intersections as nodes. Depending on their operational schedules, key urban sectors such as public administration, retail, healthcare, and education are allocated specific time slots. The sector-level routing layer produces a circulation sequence based on the Hamiltonian cycle over the modeled sectors and assigns feasible shortest-path routes over the physical road network to individual commuters. Shortest-path techniques are used to examine two scenarios: (i) conventional operating hours and (ii) modified sector timings in conjunction with Hamiltonian Circuit optimization. Simulation outcomes indicate that the integrated temporal-spatial optimization framework reduces end-to-end delays and agent queue lengths while enhancing overall routing efficiency. Simulation results show that Scenario B reduces End-to-End Delay (ETE) by 43.8–48.7% and Agent Queue Count (AQC) by 45.2–60.1% compared to Scenario A across different active agent ratios. These findings demonstrate the promise of combining sector-based timing and Hamiltonian routing as a workable, scalable, and affordable way to reduce traffic and promote environmentally friendly urban transportation in Indian cities. Combining sector-based time variables with Hamiltonian circuit modeling to optimize urban traffic. Vellore’s road network is represented graph-theoretically as nodes (intersections) and edges (road segments). Two scenarios are compared: staggered operational hours with Hamiltonian Circuit optimization and traditional operating hours with shortest path routing. End-to-end delay (ETE) and agent queue count (AQC) are used to evaluate performance. The findings indicate that in Indian cities, integrating sector-based time variables with Hamiltonian circuits increases route efficiency, lowers congestion, and promotes sustainable traffic management.