<p>Accurate capacity estimation at unsignalized intersections depends mainly on two parameters: (1) the critical gap (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({t}_{c}\)</EquationSource> </InlineEquation>) and (2) the follow-up time (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({t}_{f}\)</EquationSource> </InlineEquation>). Usually gap estimation methods are assessed by how close they produce <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({t}_{c}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({t}_{f}\)</EquationSource> </InlineEquation>, not by how well they predict capacity. In addition, capacity estimation methods treat <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({t}_{f}\)</EquationSource> </InlineEquation> as fixed, even though field measurements show it varies with queue position and with traffic conditions. This study offers a framework based on simulation that shifts the evaluation from parameter matching to capacity prediction. With the SUMO microscopic simulation model, we produced more than 20,000 gap acceptance events under 21 major-street flows that ranged from 10 to 2,000 veh/hr. We applied nine critical gap estimation methods and compared the capacity that each method predicted with the simulated capacity. We also studied follow-up in detail and found a 42–43% difference between the cautious first-follower value and the saturated platoon value across three minimum-gap (minGap) scenarios. The main result is a new hybrid rule that depends on the conflicting major-street flow. For the default minGap = 2.50 m scenario, our method uses the saturated value (2.41&#xa0;s) when flow is ≤ 812 veh/hr (low-to-moderate) and switches to the first-follower value (3.44&#xa0;s) at higher flows. This single change reduced the root-mean-square error (RMSE) to 54.7 veh/hr, representing a 20.6% improvement over the best fixed-parameter model (Wu’s method, RMSE = 68.9 veh/hr). Sensitivity analysis across three minGap values (0.50, 1.50, 2.50 m) confirms the robustness of this approach, with RMSE reductions of 14.8–21.8% compared to the best fixed-parameter method for each scenario.</p>

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A hybrid flow-dependent model for gap-acceptance capacity estimation

  • Usama Elrawy Shahdah,
  • Sania Reyad Elagamy,
  • Marwa Elharoun,
  • Eman K. Ali

摘要

Accurate capacity estimation at unsignalized intersections depends mainly on two parameters: (1) the critical gap ( \({t}_{c}\) ) and (2) the follow-up time ( \({t}_{f}\) ). Usually gap estimation methods are assessed by how close they produce \({t}_{c}\) and \({t}_{f}\) , not by how well they predict capacity. In addition, capacity estimation methods treat \({t}_{f}\) as fixed, even though field measurements show it varies with queue position and with traffic conditions. This study offers a framework based on simulation that shifts the evaluation from parameter matching to capacity prediction. With the SUMO microscopic simulation model, we produced more than 20,000 gap acceptance events under 21 major-street flows that ranged from 10 to 2,000 veh/hr. We applied nine critical gap estimation methods and compared the capacity that each method predicted with the simulated capacity. We also studied follow-up in detail and found a 42–43% difference between the cautious first-follower value and the saturated platoon value across three minimum-gap (minGap) scenarios. The main result is a new hybrid rule that depends on the conflicting major-street flow. For the default minGap = 2.50 m scenario, our method uses the saturated value (2.41 s) when flow is ≤ 812 veh/hr (low-to-moderate) and switches to the first-follower value (3.44 s) at higher flows. This single change reduced the root-mean-square error (RMSE) to 54.7 veh/hr, representing a 20.6% improvement over the best fixed-parameter model (Wu’s method, RMSE = 68.9 veh/hr). Sensitivity analysis across three minGap values (0.50, 1.50, 2.50 m) confirms the robustness of this approach, with RMSE reductions of 14.8–21.8% compared to the best fixed-parameter method for each scenario.