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Fig 1.

Vehicle collision distance-time-velocity diagram.

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Fig 2.

Methodology framework.

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Fig 3.

API module application flowchart.

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Fig 4.

SDK module application flowchart.

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Fig 5.

Descriptions of distance-time-velocity relationship in the four situations in the rear-end collision model.

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Table 1.

Result matrix—vehicle rear-end collision probability on a certain segment in a certain simulation cycle.

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Fig 6.

Aimsun interface of the simulated section.

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Table 2.

Example of data for determining risk thresholds.

Risk data from moderate traffic condition (Volume: 1500 veh/h).

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Table 3.

Largest cluster center with different cluster number.

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Fig 7.

Largest cluster center value (VC) with different cluster number for different volume conditions.

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Table 4.

Results of cluster centers.

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Table 5.

The number of high-risk status before and after adding vehicle violations for different traffic conditions.

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Fig 8.

Comparisons of different types of violation.

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Fig 9.

Influence of violation under different traffic volume.

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Fig 10.

Space-time diagram under different traffic condition with no violations.

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Fig 11.

Space-time diagram of traffic flow risk for different violation types.

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