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Multilane Roundabout Capacity: Methodology Formation and Model Formulation

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Abstract

Roundabouts are widely spreading around the globe because of their safety advantages over other crossroads. In the absence of actual roundabout flow theories, entry capacities are empirically formulated here versus geometric and traffic predictors collected from 13 saturated roundabouts on major roads in Bahrain. The formulation methodology covered five stages to be compatible with as many international models as possible. These included simple modelling techniques, multivariate analysis considering extensive single and joint predictors, and complex formulation employing collinearity diagnoses. A quadratic model fitted best the entry capacity versus circulating flow for dual-entry lanes and exponential for triple-lanes. The model underestimated the entry capacities compared with UK, SIDRA, and French models except at high circulating flows. The standard capacity model showed significant positive associations with entry lanes, entry width square, circulating width, splitter island width, circulating flow square, and exiting flow; and negative with circulating lanes, entry width, radius of central island, width of circulating lanes square, circulating flow, and exiting flow square. The dominant predictors for the model treated for collinearity included circulating flow, exiting flow, number of entry lanes, number of circulating lanes, inscribed diameter, entry width, flare length, and width of circulating lanes. The UK, the French and SIDRA capacity models showed substantial differences with the developed model and between them. The 3-way relationship between maximum entry, exiting, and circulating flows showed a uniform diagonal relationship across the resultant 3-dimensional box when the circulating flow axis is inverted. Though limited spatial related parameters influence roundabout maximum entry flow, yet other insignificant parameters should not be ignored since they are necessary for constructional and operational purposes.

Highlights

•Entry Capacities for roundabouts with dual and triple-entry lanes are modelled using extensive geometric predictors along with circulating and exiting flows.

• The methods include simple modelling procedures, to match several international models, and comprehensive multivariate analysis with collinearity treatments using variance inflation factor.

• A logarithmic form best relates maximum entry flow to circulating flow for dual-entry lanes and an exponential for triple-lanes.

• The significant predictors for treated model are circulating flow, exiting flow, and several spatial related predictors as number of entry lanes, number of circulating lanes, inscribed diameter, entry width, flare length, and width of circulating lanes.

• The UK, the French and SIDRA capacity models showed substantial differences with the model and between them. The reasons behind such great differences require careful investigation.

• The 3-way relationship between the capacity, exiting, and circulating flows showed a uniform diagonal relationship across the resultant 3-dimensional box when the circulating flow axis is inverted.

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Acknowledgements

The author wishes to thank Bahrain Road Directorate; Ministry of Public Work and many other engineers for their assistance in gathering the data for the study.

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  1. Civil Engineering Department, University of Bahrain, Manama, Kingdom of Bahrain

    Hashim M.N. Al-Madani

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Appendix

Appendix

Maximum entry flow model (ve, max) for multi-lane roundabouts after treating collinearity effect between the variables.

$$\begin{array}{lllllll}{v}_{e,\mathit{\max}}=&-1511.64+387.4\mathrm{X}{n}_e-298.9\mathrm{X}{n}_c \\& +48.3\mathrm{X}w-0.00028079\mathrm{X}{v}_c^2+\left(2.241240082243\mathrm{X}10^{\wedge}{\mkern6mu} -11\right){v}_c^4 \\& -\left(5.43817189\mathrm{X}10^{\wedge}{\mkern6mu} -19\right){v}_c^6-0.004644774{\left({l}^{\prime}\mathrm{X}{v}_{ex}\right)}^{1.001016} \\& +0.056283216{\left({n}_c\mathrm{X}{v}_{ex}\right)}^{1.1068}+409.6829079\log \left({D\mathrm{X}v}_c\right) \\& -8.30523530\mathrm{X}10^{\wedge}{\mkern6mu} -16\left(e{\mathrm{X}v}_{ex}^2\right)+8.2858654060\mathrm{X}10^{\wedge}{\mkern6mu} \\& -19{\left(e{\mathrm{X}v}_{ex}^2\right)}^2-2.797576600\mathrm{X}10\hat{\mkern6mu} -22{\left(e{\mathrm{X}v}_{ex}^2\right)}^3 \\& +0.0000592103\left({e\mathrm{X}v}_{ex}\right)-0.0000000452273{\left(e{\mathrm{X}v}_{ex}\right)}^2 \\& +1.3856\mathrm{X}10\hat{\mkern6mu} -11{\left(e{\mathrm{X}v}_{ex}\right)}^3\end{array}$$

subject to: ne =2 or 3, nc =2 or 3, 10 m<l’<96 m, 6 m<e<16 m, 60 m<D< 200 m, & 8 m<w<20 m.

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Al-Madani, H.M. Multilane Roundabout Capacity: Methodology Formation and Model Formulation. Int. J. ITS Res. 20, 223–237 (2022). https://doi.org/10.1007/s13177-021-00286-x

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