Optimizing Traffic Light Timing Using Graph Theory: A Case Study at Urban Intersections
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Summary
This study addresses the problem of traffic congestion and suboptimal signal timing at the Usman Salengke-Poros Malino-K.H. Wahid Hasyim intersection in Gowa Regency, Indonesia. Motivated by the high cost and technical complexity of adaptive traffic systems, the research aims to develop a cost-effective, scalable solution using graph theory and Webster’s method. The authors seek to reduce vehicle delays and improve throughput by modeling compatible traffic flows—movements that can occur simultaneously without conflict—to determine optimal signal durations. The methodology involved manual field observations conducted between August and October 2024. Researchers collected primary data on road geometry and traffic volumes during peak hours (morning, midday, and afternoon) across three days. Traffic counts for light vehicles, heavy vehicles, and motorcycles were converted into passenger car units (PCU). The study employed compatibility graph theory to model the intersection, where nodes represented traffic flows and edges indicated compatible pairs. This graph was transformed into a weighted directed dual graph based on road width and vehicle volume. Using Webster’s formula, the authors calculated the optimal cycle length, lost time, and green/red signal durations for each phase. MATLAB software was utilized for simulation and analysis. The results identified a peak traffic volume of 1,383 PCU/hour on the Usman Salengke North approach. The analysis determined an optimal traffic light cycle duration of 95 seconds, a significant reduction from the original 128-second cycle. The optimized timing allocated 39 seconds of green light for the North and South phases (Usman Salengke), 28 seconds for the East phase (Poros Malino), and 17 seconds for the West phase (K.H. Wahid Hasyim). These adjustments resulted in a 33.3% decrease in total average vehicle waiting time and a 20% improvement in traffic throughput. The study successfully simplified the intersection analysis by identifying three distinct signal phases based on flow compatibility and weight calculations. The significance of this research lies in its demonstration that graph theory provides a practical, low-cost alternative to expensive adaptive traffic systems. By relying on manual data collection and mathematical modeling, the approach offers a systematic and scalable method for optimizing urban intersections, particularly in regions with limited technological infrastructure. The findings suggest that optimizing signal timing through compatibility modeling can effectively mitigate congestion and enhance traffic efficiency without requiring real-time sensor integration.
Provenance
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | OpenAlex-citations | — | — | 1 | 2026-06-20 |
| archive | success | unpaywall | — | — | 2 | 2026-06-26 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-20 |
| chunk | success | chunk | — | — | 1 | 2026-06-20 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-20 |
| promote | success | — | — | — | 1 | 2026-06-20 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-20 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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