Entry Capacity Modelling of Roundabouts under Heterogeneous Traffic Flow Conditions

Abstract

The objectives of this study is to develop entry capacity models for both un-signalized and signalized roundabouts under heterogeneous traffic flow conditions. Required data have been collected from 27 un-signalized and 15 signalized roundabouts spanning across 11 states of India. To develop the entry capacity model for un-signalized roundabouts, initially two types of models are developed namely, empirical models and gap acceptance based models. Empirical models are based upon statistical approach whereas gap acceptance models rely on the driver’s behaviour and vehicle-to-vehicle interactions. An empirical model is developed by taking geometric variables and circulating flow as explanatory variables, while the gap acceptance based model is developed by employing critical gap, follow up time and circulating flow as explanatory variables. To reflect the driver behavioral habits and site conditions in a single model, semi-analytical model is developed in this study. In order to reflect the actual driver behavioral habits under local conditions,critical gap and follow up time are estimated by using proposed Influence area for gap acceptance (INAGA) method in this study. The critical gap values found to be varying from 0.54 s to 2.87 s, which are nearly half the values (4 s to 4.6 s) of developed nations like USA and European countries. To ascertain the applicability of proposed INAGA method, the said method is compared with traditionally followed raff and equilibrium of probabilities method. It is observed that the critical gap values estimated by equilibrium of probabilities method differs from corresponding values estimated by INAGA method by 2.10 to 27.03 %. While the values obtained by raff method are quite similar and differ by 0.41 to 3.27 % only. Models based on Artificial intelligence techniques such as Artificial Neural Network (ANN), Generic Programming (GP), Adaptive Neuro Fuzzy Inference Systems (ANFIS) are also developed for un-signalized roundabouts. A comparative study on all developed models is carried out. Also signalized roundabout entry capacity model is developed by using the concept of signalized analogy in which geometric variables and signalization variables are taken as explanatory variables. It has been observed from the collected data set that the Composition of traffic varies as (0.14 to 55.07)%, (10.52 to 78.9)%, (6.84 to 77.9)%, (0.06 to 36.51)%,(0.04 to 7.49)% for heavy vehicles (HV), light motor vehicles (LMV), Motorcycles (MC)/scooters, Bicycles (BC) and Animal drawn vehicles (ADV)/Human drawn vehicles (HDV) respectively at selected un-signalized roundabouts. Similarly, the Composition of traffic varies as(18.92-77.18)%, (2.92- 33.28)%, (11.84-57.58)%, (1.71-11.63)%,(0.41-13.48)%, (0.14-0.78)% and (2.27-26.54)% for two wheelers (2W), Three wheelers (3W), Cars, Light commercial vehicles (LCV), Bus, Truck and Cycle at selected signalized roundabouts respectively. The co-efficient of determination (R2) value of empirical based model and gap acceptance based model are found to be 0.93 and 0.78 respectively. And the p-value in the test of Analysis of variance (ANOVA) is found to be 0.00 (p-value<0.05) for both empirical and gap acceptance based model, which signifies that the models are statistically fit at 95% confidence level. By developing the semi-analytical model, the R2 and p-value in the test of ANOVA are found to be 0.92 and 0.00 respectively. And from the significance test, the value of Nash-Sutcliffe co-efficient (E), mean (μ) and standard deviation (σ) are found to be (0.91, 0.99, 0.13) and (0.87, 0.93, 0.11) respectively which signifies that the proposed semi-analytical model is statistically significant at 95% confidence level. It is observed that Bayesian regularization back propagation training function (TrainBR), in combination with hyperbolic tangent sigmoid transfer function (Tansig) based ANN model has highest R2 value of 0.97 and lowest root mean square error (RMSE) value of 167.89 among all ten models developed. Therefore, this model is chosen for the capacity prediction in this study. Among three developed models such as Genetic Programming (GP), Age layered population structure Genetic Programming (ALPS GP) and Grammatical Evolution Genetic Programming (GEGP); GEGP model is found to be best fit by employing modified rank index (MRI) among these GP based models. By applying multiple non-linear regression analysis (MNLR), the proposed signalized roundabout capacity model is found to be best fit at 95 % confidence level in which the R2 is measured to be 0.95. Sensitivity analysis reported that weaving section variables such as weaving length (Wl), weaving width (WW) and signal phase variable such as green time (G) are major variables for the determination of signalized roundabout entry capacity. Among the proposed un-signalized roundabout entry capacity models such as semi-analytical model, ANN model, GEGP model and ANFIS model; ANFIS model placed in 1st rank, whereas both ANN and GEGP model are placed in 2nd rank and Semi-analytical model is placed in 3rd rank respectively. It is ascertained from statistical test that ANFIS model holds good for roundabout capacity estimation. But from practical application point of view, this model seems to be poor as expression of the equation could not be built up. Whereas, in comparison to ANFIS model, Semi-analytical model can be widely acceptable for its simplicity and manageability. Hence Semi-analytical model is recommended for the estimation of roundabout entry capacity under heterogeneous traffic flow conditions. Regression based models are simple from application point of view but these models have shown higher prediction error in comparison to Artificial intelligence based models. Sensitivity analysis reports that critical gap is the prime variable and sharing 18.43 % in the semi-analytical based roundabout entry capacity model. As compared to Girabase formula (France), Brilon wu formula (Germany) and HCM 2010 models, the proposed semi-analytical model is quite reliable under low to medium range of traffic volumes. The proposed model is suggested for application in the field by practitioners because the model provides unique equation for prediction. The priority of explanatory variables can be easily examined in the proposed model. The model can be easily modified by inclusion or exclusion of geometric variables. The model can be widely acceptable for its simplicity and manageability. Sensitivity analysis is quite useful for planning and design prospective because of major contributing variables are easily identified in the proposed model. The common PCU factors are determined to convert the heterogeneous traffic into homogeneous one, thus it give a reliable estimation of roundabout entry capacity. These findings will be helpful for the researchers, planners and designers for making key decision.