Article citation information:Munshi, A.K., Patnaik, A.K. Modelling roundabout entry capacity for mixed traffic flow using ANN: a case study in India. Scientific Journal of Silesian University of Technology. Series Transport. 2024, 123, 209-226. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2024.123.10.Aarohi Kumar MUNSHI, Ashish Kumar PATNAIKMODELLING ROUNDABOUT ENTRY CAPACITY FOR MIXED TRAFFIC FLOW USING ANN: A CASE STUDY IN INDIASummary. Roundabouts, as an unsignalized intersection, have an effective preventative measure designed to control straight-line crashes. Efficient traffic flow in cities depends upon appropriate capacity estimation of roundabouts. This study attempts to develop models for roundabout entry capacity by applying Artificial Neural Network (ANN) analysis for mixed traffic flow conditions. Data was gathered from 27 roundabouts spread across India. The influence area for gap acceptance (INAGA) concept was used as a graphical method to identify critical gap (Tc) of entry flow at roundabouts. This study indicated that the Bayesian Regularisation Neural Network (BRNN) based model has the best R2 and RMSE of 0.97 and 167.8. The connection weight approach and Garson algorithm evaluate the significance of each explanatory variable and identify follow-up time (Tf) as a critical parameter with values of 11.10 and 21.15%, respectively.Keywords: INAGA, ANN entry capacity, Garson algorithm1. INTRODUCTIONRoundabout is an efficient traffic control measure in the form of safety and operational aspects. Circular intersections substantially mitigate head-on collisions, notably right-angle accidents, as well as facilitate the easy movement of more traffic with reduced queuing time. In comparison to signalized junctions, it has fewer conflict points. At signalized intersections, 32 potential sources of conflict are identified, but at roundabouts, the number falls to 8. As a result, roundabouts are regarded to be vital infrastructure in any country's urban traffic system. The roundabout capacity is a key statistic for evaluating operational performance, delay, and queue length.The upholding of driver conduct, specifically lane discipline, is inadequately managed in conditions of heterogeneous traffic. In addition, the dimensions, transmission capacities of vehicles, and geometrical features of intersections in developing countries are very different from those of vehicles in affluent nations. Drivers get aggressive while attempting to manoeuvre around one another in congested areas. In such conditions, vehicle speeds vary as a result of the inherent differences between vehicles. At roundabouts, significant contributing vehicles, such as small-sized cars (SC) and two-wheelers (2W), consistently seek to merge into the mainstream flow of traffic. This results in an extremely chaotic traffic situation due to the inconsistent spacing between vehicles. HCM (2010) presents a comprehensive methodology for estimating the entrance capacity of roundabouts, however, it fails to account for people's driving behaviour under local conditions. Hence, emphasis has been given to develop the capacity models for roundabouts under constrained conditions. Essential methodologies, such as empirical models, gap acceptance models, and microscopic simulation modelling, serve as a basis for existing roundabout capacity models. Empirical models are often solved by applying regression analysis, with capacity serving as the dependent variable and other factors, such as prevailing flow and site geometry, contributing as explanatory variables [1]. It has been identified that the entry capacity varies negatively exponentially about the opposing flow and that as the opposing flow increases, the entry capacity decreases and vice versa [2], [3]. The capacity model on the concept of gap acceptance theory reflects the decision of drivers on variables like critical gap and follow-up time. For drivers in the minor stream, the minimum acceptable duration before merging into the major stream is termed as the ‘critical gap’ while the ‘follow-up time’ refers to the time difference between vehicles in a queue during congested traffic conditions [4]. In contrast, microscopic simulation models are influenced by the interactions and motions of vehicles within a simulated network. Three primary terms can be used to describe the actions of vehicles on the route: car-following, lane-changing, and the gap acceptance concept, which includes critical gap and follow-up time. Various microscopic simulation models have been developed for parametric findings, with the flows and turns being controlled [5], [6]. Artificial neural networks (ANNs) are frequently used by professionals in academia, as they can model complicated and nonlinear data sets accurately and with the least amount of error [7]. The capacity prediction of roundabouts through ANN outperforms the gap acceptance and empirical models, further it encourages employing machine learning techniques for a proactive operational plan for roundabouts [8], [9]. Accordingly, an ANN-based entrance capacity model for Indian urban cities has been developed.Data was obtained from 27 roundabouts in India during peak traffic hours. The graphical method of influence area, INAGA, is used to predict driver response factors such as critical gap ( Tc) and follow-up time ( Tf) in order to provide capacity models for roundabouts. The effectiveness of the ANN models was evaluated using the connection weight method and Garson's approach.The paper is structured into four sections, with section 1 providing an overview of the context of the study and a review of the relevant literature. The subsequent section discusses study sites and data-collecting procedures. The methodology and analysis of the ANN capacity models are comprehensively described in Section 3. The final section of the paper provides the conclusion of this study. It also addresses the limitations of the study and suggests avenues for future research. 2. SELECTION OF STUDY SITES AND DATA COLLECTION PROCEDURE A total of 27 roundabouts were selected for data collection to develop capacity models. The twelve cities depicted in Fig. 1 in the four corners of India all consist of roundabouts. The roundabouts were selected following the specified criteria. Roundabouts, which have 4 approach legs, tend to be placed in commercial, industrial, and residential areas. The roundabouts tend to be at grade intersections and are unsignalized. Further, the influence of cyclists and pedestrians is modest at these roundabouts. The measured geometric specifications of roundabouts are presented in Appendix 1.Fig. 1. Location of Cities on India MapThe collection of traffic flow data is from high-rise buildings in close proximity to the roundabouts. This approach was taken to ensure the acquisition of comprehensive and relevant data sets. The videography method utilized in this study is straightforward and economical. It is also convenient to use a post-processing method for data extraction. Videos capturing the morning and evening traffic flow peaks under clear weather conditions were utilized to account for the significant contribution of both the critical gap ( Tc) and follow-up time ( Tf) to the gap acceptance capacity model. Moreover, half an hour of queuing time on the approach legs was seen over the course of the two hours of observation. The gap variables were then extracted from the recorded videos. The variables that contributed to the capacity model for roundabouts, including flow, geometrics, and gap variables, were utilized in regression analysis and ANN modelling, as detailed in Tab. 1. During low-traffic volume times, a measuring tape was used to take measurements of geometric variables. The ‘weaving width’ refers to the road width that runs around the central island and is utilized by vehicles to navigate in a clockwise direction. Both single and multi-lane variants of the road are possible. The total distance of a segment of a rotary through which weaving takes place is referred to as the ‘weaving length’. Google Earth software measurements were employed to validate the field-measured inventory data for streets. The methodologies and analysis approach are detailed in the following section.Tab. 1Analysis of contributing variables for this studyVariablesUnitsMinimumMaximumMeanStandard deviationObserved entry capacity ( Qe) PCU/h25133461712.5772.75Circulating flow ( qc) PCU/h22037781051.28711.42Weaving length ( Wl) m29.7659.5243.396.09Weaving width ( Ww) m9.119.0416.805.34Entry width ( Ew) m621.2214.173.87Diameter of central island ()m12.6662.3242.6211.77Critical gap ( Tc) seconds0.682.661.730.58Follow-up time ( Tf) seconds0.882.341.780.523. METHODS AND ANALYSISThis section discusses extensively the Gap acceptance variable and the existing models' viability. Furthermore, the ANN model is being developed for the prediction of roundabout entry capacity. Additionally, the entry capacity model's suitability and the relative significance of the input variables are specified.3.1. Gap Acceptance VariablesFor capacity models of roundabouts, significant factors that are considered to describe driver conduct under real-world traffic conditions include critical gap and follow-up time. An inadequate approach for obtaining critical gap and follow-up time values results in partial capacity estimation of a roundabout. In order to determine the critical gap, both the newly accepted equilibrium probability method and the widely utilized Raff method considered homogeneous traffic flow and consistent driving conduct. Nevertheless, with a zero rejection of gap data, these approaches fail to produce reliable results. Therefore, it is presumed that this is a significant issue in mixed traffic conditions. In mixed traffic situations, zero gaps are typically rejected for congested and normal traffic flow. Subsequently, to surmount these shortcomings and variations, the INAGA method, which was recently devised, is implemented to produce dependable outcomes [10]. The INAGA technique can calculate the critical gap without having a specific distribution function as an assumption. As a result, the INAGA method is a graphical method of assumption; upon observing the mainstream where the merging of entry and circulating flows is most, a trapezoidal-shaped influencing area may be meticulously assumed.3.2. Existing Model EvaluationThe Girabase formula (France), Brilon-Wu formula (Germany), and HCM 2010 (USA) models are used for a new set of roundabouts to evaluate their ability to anticipate traffic flow. In a study, the feasibility of using explanatory variables to establish a relationship between capacity, other geometric functions, and gap acceptance has been analysed [11]. As illustrated in Fig. 2, the aforementioned techniques generate a relation between the data obtained from field observations and the predicted capacity. (b) (c) Fig. 2. Prediction of capacity by using international capacity modelsFigures 2(b) and (c) show that, in comparison to capacities observed under field conditions, the predicted entry capacities of the Brilon-Wu formula (Germany) and the HCM 2010 approaches are, respectively, higher, and lower. This shift in capacity estimates can be attributed to a couple of factors. The first cause is the fact that metropolitan Indian streets see a wide range of vehicle types. The second issue is likely the vastly different driving conduct of Indian drivers compared to those of drivers in Western countries. In mixed traffic flow, vehicles with varied manoeuvrability coexist. The prevalence of two-wheelers over cars of all kinds predominates in Indian traffic. A breach of the principle of priority happens whenever two-wheelers (2W) in the approaching stream emphatically establish a gap in the route of the primary traffic flow. Homogeneous traffic, on the other hand, involves vehicles moving in a streamlined pattern whilst consistently maintaining some distance. When applied to data sets containing mixed traffic flows, models that were fitted under homogeneous traffic conditions overestimate entry capacity under high circulating flows, resulting in inaccurate model fitting. Measurements of driver behaviour metrics, such as critical gap and follow-up time, under actual conditions, might help reduce discrepancies in capacity projections. Furthermore, the significance of geometric variables in capacity prediction analysis is acknowledged. By integrating geometric and gap acceptance variables as explanatory variables in the context of mixed traffic flow conditions, gap acceptance capacity models are subsequently devised. However, the capacity values of the proposed Bayesian Regularisation Neural Network (BRNN) model and the Girabase formula in Fig. 2(a) are comparable.3.3. Artificial Neural Network (ANN) ModellingModern data analysis techniques, such as ANN modelling, offer an alternative to the traditional statistical regression method. A linear model aims to establish a linear relationship between independent and dependent variables. However, in ANN modelling, the coefficient, and intercept variables are associated with neural network weights and biases. The hidden layers in the neural network are accomplished to evaluate the critical relationships, such as the nonlinear relationship between dependent and independent variables. For estimating roundabout capacity, the authors discovered that ANN modelling outperformed regression models [1]. In regression models, there is a probability of the occurrence of constraints between explanatory variables and capacity. However, ANN modelling can establish an appropriate relationship between explanatory variables and capacity even if there is a constraint relationship between explanatory variables and capacity.The current study employs two distinct training algorithms, namely the Bayesian Regularisation Neural Network (BRNN) and Levenberg-Marquardt Neural Network (LMNN) to develop the ANN models. As illustrated in Fig. 3, feed-forward perceptron with back propagation training algorithm (FFBP) type of ANN with hyperbolic tangent activation functions is developed using explanatory variables like weaving length (Wl), critical gap ( Tc), weaving width ( Ww), entry width( Ew), circulating flow ( qc), follow up gap ( Tf), and central island diameter (D) and dependent variables like entry capacity ( Qe). Nodes of feed-forward type ANN are organised in layers, with information flowing forward from input layers to output layers through hidden layers. The backpropagation algorithm is employed to train the hidden units to produce the intended output in situations where the output is unknown. In this technique, the error observed in the output layer is back propagated to the hidden layers according to the connecting weights. The weights are adjusted by the delta rule. The same approach is repeated for each training data sample. One complete cycle through the training data set is termed an epoch. The number of times that the set of training data will be entered into the network is termed as the number of epochs.Fig. 3. Neural network diagram with 7 explanatory variablesA total of 110 data points were used to forecast the ANN capacity models. The entire dataset was split in half, with 70% being used for the training phase and 30% for the testing phase. Several iterations are performed to determine the best ANN capacity model, as detailed in Tab. 2. the best ten ANN models are selected through root-mean-square error (RMSE) and overall R2 values. Finally, the most suitable ANN model is selected from ten ANN models. In this study, three Levenberg-Marquardt Neural Network (LMNN) and seven Bayesian Regularisation Neural Network (BRNN) based capacity models are developed. The transfer function introduces non-linearity to the neural network. It transforms the weighted sum of inputs and biases into the output of a neuron. In the present model, the hyperbolic tangent sigmoid transfer function (Tansig) squashes input values to a range between -1 and 1. It is a smooth, differentiable function, crucial for backpropagation during training. The training function Bayesian regularisation back propagation (Train BR) is responsible for adjusting the weights and biases of the network during the training phase. Its goal is to minimize the difference between the predicted outputs and the observed values. The optimisation algorithms use the gradient of the loss function concerning the parameters to update the weights and biases iteratively. The learning function involves setting hyperparameters, including the learning rate and possibly other parameters that control the training process. The learning rate determines the step size during weight updates and influences the convergence and stability of the training, and hence an adaptive learning function gradient descent with momentum (Learn GDM) is employed for the study. The performance function quantifies the difference between the predicted values and the observed values. Consequently, mean square error with regularisation (MSEREG) is a performance function that combines the Mean Square Error (MSE) with a regularisation term to prevent overfitting and control the complexity of a model during training and predicts the capacity of a developed model by using ANN. In addition to these, the number of iterations (epochs) varied from 500 to 1000 to get the best result. Based on the RMSE results and overall R2, the most suitable model is selected. It is observed from Tab. 2 that BRNN based model having four numbers of hidden neurons is the best fitted as the RMSE and overall R2 values of the model were found to be 167.89 and 0.97 respectively.Tab. 2Network details with several iterations (Trial 1-10)Trial No.12345No. of hidden layer11111No. of hidden neurons34678Transfer functionTansigTansigTansigTansigTansigTraining functionTrain LMTrain BRTrain BRTrain BRTrain BRAdaptive learning functionLearn GDMLearn GDMLearn GDMLearn GDLearn GDMPerformance functionMSEMSEREGMSEREGMSEREGMSEREGNo. of epochs500100010007001000RMSE267.28167.8212.21216.63230.30Overall R20.920.970.960.960.95Trial No.678910No. of hidden layer11111No. of hidden neurons34768Transfer functionLogsigLogsigLogsigLogsigLogsigTraining functionTrain BRTrain BRTrain BRTrain LMTrain LMAdaptive learning functionLearn GDMLearn GDLearn GDMLearn GDMLearn GDPerformance functionMSEREGMSEMSEREGMSEMSENo. of epochs500100010001000700RMSE222.14190.3214.00218.2240.9Overall R20.950.960.960.950.95Note: Tansig: Hyperbolic tangent sigmoid transfer functionLogsig: Log-sigmoid transfer functionTrain LM: Levenberg-Marquardt backpropagation training functionTrain BR: Bayesian regularization backpropagation training functionLearn GD: Gradient descent adaptive learning functionLearn GDM: Gradient descent with momentum MSE: Mean square errorMSEREG: Mean square error with regularizationAn ANN equation was formulated in the present study by utilizing 7 explanatory variables and observing through a trained network. By using the weights and biases observed in this analysis as provided in Tab. 3, the following mathematical expressions were developed for the capacity prediction of roundabouts. For this, the procedure follows three steps. In the first step, A1 to A4 is to be calculated using equation 1(a) to 1(d). The Input (I) and output (O) weights of four hidden neurons are represented in the Tab. 4. The values obtained from A1 to A4 is to be used in the equation 2(a) to 2(d) to get the desired values of B1 to B4 . The third step belongs to C1 which will give the final expression as per equation (3). Hence the normalized capacity equation (Qen) will be written as in equation (4).Tab. 3Connecting weights and biases with normalized entry capacity prediction modelNo. of hidden neuronsWeightsBiasesI1 (Wl)I2 ( Tc)I3 (Ww)I4 (Ew)I5 (qc)I6 (Tf)I7 (D)O (Qe) IO1-0.068-0.5390.2980.261-0.563-0.537-0.3481.0400.1420.38920.221-0.3290.0030.545-0.5600.528-0.3430.697-0.602-30.3880.2820.029-0.262-0.309-0.6500.2500.873-1.450-4-0.061-1.1840.047-0.285-0.752-0.497-0.913-0.772-0.021-A1=0.1424-0.0682 Wl-0.5399 Tc+0.2984 Ww-0.2619 Ew-0.5635 qc - 0.5374 Tf-0.3486 D 1(a)A2=- 0.6025+0.2217 Wl-0.329 Tc+0.0031 Ww+0.5453 Ew-0.5607 qc + 0.5281 Tf-0.3439 D 1(b)A3=- 1.4505+0.3888 Wl+0.2827 Tc+0.0295 Ww-0.2624 Ew-0.3095 qc - 0.6504 Tf-0.2506 D 1(c)A4=- 0.0210-0.0611 Wl-1.184 Tc+0.0474 Ww-0.2852 Ew-0.7529 qc - 0.4978 Tf-0.9136 D 1(d)Tab. 4Connecting weights of four hidden neuronsNo. of hidden neuronsWeightsI1 (Wl)I2 ( Tc)I3 (Ww)I4 (Ew)I5 (qc)I6 (Tf)I7 (D)O (Qe)1-0.0682-0.53990.29840.2619-0.5635-0.5374-0.34861.040220.2217-0.3290.00310.5453-0.56070.5281-0.34390.697430.38880.28270.0295-0.2624-0.3095-0.65040.25060.87364-0.0611-1.1840.0474-0.2852-0.7529-0.4978-0.9136-0.7726The expression for evaluating B term is written as follows:B1= 1.0402 eA1 - e-A1eA1 + e-A1 2(a) B2= 0.6974 eA2 - e-A2eA2 + e-A2 2(b)B3= 0.8736 eA3 - e-A3eA3 + e-A3 2(c) B4= -0.7726 eA4 - e-A4eA4 + e-A4 2(d)Then the final term C will be evaluated asC1=0.3898+B1+B2+B3+B4 (3) Qen= eC1 - e-C1eC1 + e-C1 (4)The aforementioned equation (4) yields a capacity value between -1 and 1, which will be denormalized according to equation (5). Qe=0.5 Qen+1Qemax- Qemin+ Qemin (5)Where, Qemax is the maximum and Qemin is the minimum values of roundabouts entry capacity (Qe) under the provided data set accordingly. 3.4. Suitability of entry capacity modelTo ensure the development of a suitable entry capacity model, a number of statistical tests are performed to evaluate the reliability of the ANN model as detailed in Tab. 5. The statistical tests include best-fit calculations, error-calculating variables, mathematical calculations, cumulative probability values, and predictions with an accuracy level of less than 20%. The coefficient of determination (R2), which executes from 0 to 1, represents the degree of goodness of fit, and higher values indicate a better fit. Nash-sutcliffe model efficiency coefficient (E) is generally used to assess the prediction ability of the developed model. The value of ‘E’ can range from -∞ to 1. If the value of ‘E’ is close to 1, then it is known to be more accurate in the developed model. The absolute value is measured by the modulus value of the difference between observed and predicted values. The average absolute error (AAE) is measured as the average of the absolute difference between observed and predicted values, whereas the maximum of the measured absolute errors is known as maximum absolute error (MAE). The Root Mean Square Error (RMSE) is intended to indicate a model's accuracy, and a smaller value is preferable. The ranges of AAE and RMSE are in between 0 to ∞. The detailed formula for evaluating the R2, E, AAE, MAE and RMSE are given as equations 6(a) to 6(e). The Oi and Pi are the observed and predicted values of entry capacity at roundabouts, while Omean, Pmean represents the mean values of the observed and predicted data sets, whereas ‘i’ and ‘n’ are the variable sequence and total number of data respectively. Further, the ratio of predicted capacity to observed capacity is denoted as CP/CO, and ‘μ’ and ‘σ’ are the mean and standard deviation of natural logarithmic values of CP/CO. Values for ‘μ’ and ‘σ’ are close to 1 and 0 in the present study, respectively, indicating that the proposed models can make reliable predictions. The cumulative probability density function has, ‘P50 values’ considered to be the most probable value with a probability of exceedance of about more than 50% while ‘P90 values’ are the conservative estimate having a 90% probability of exceedance. Values (P50 and P90) are observed to be near to 1, suggesting greater effectiveness for the provided data set. The log-normal distribution function is employed, and further log-normal and histogram graphs are plotted to evaluate the accuracy percentage of a model.R2= i=1n Oi-Omean Pi-Pmean2i=1nOi-Omean2 i=1nPi-Pmean2 6(a)E=1- i=1n(Oi-Pi)2i=1n(Oi-Omean)2 6(b)AAE=1ninOi-Pi 6(c)MAE= maximum( Oi-Pi) 6(d)RMSE=1n i=1nOi-Pi2 6(e)Tab. 5Statistical test of developed modelModelDataSplittingCo-relation AnalysisError CalculationsMathematical Calculations of CP/COCumulative Probability of CP/CO± 20% Prediction Accuracy (%)R2EAAEMAERMSEµσRatio* atLog- normalHistogramP50P90BRNN ModelTraining0.930.93149.2455.1184.81.000.110.991.1392.32%100%Testing0.950.94167.9418.7197.91.050.220.951.2291.01%94%Note: R2 = Coefficient of determination, E = Nash-Sutcliffe coefficient, AAE = Average Absolute Error, MAE = Maximum Absolute Error, RMSE = Root Mean Square Error, CP = Predicted Capacity, CO = Observed Capacity3.5. Relative Importance of Input VariablesTo assess the relative importance of input variables in ANN modelling, two methods such as Connection weight approach and Garson’s algorithm are applied in this study. In connection weight approach, the product of each input and output weights (Aij) are calculated in the Tab. 6. Then for each hidden neuron Aij is divided by sum of all input variables to obtain Bij in details given in the Tab. 7. Then for each hidden neuron, the sum of the product Sj is calculated. For example,S1= B11+B21+B31+B41+B51+B61+B71 7(a)Tab. 6Products of each input and output weights (Aij)No. of hidden neuronsI1 (Wl)I2 ( Tc)I3 (Ww)I4 (Ew)I5 (qc)I6 (Tf)I7 (D)1-0.0709-0.56160.31030.2724-0.5861-0.559-0.362620.1546-0.22940.00210.3802-0.3910.3682-0.239830.33960.24690.0257-0.2292-0.2703-0.56810.218940.04720.9147-0.03660.22030.58160.38460.7058Tab. 7Ratio of (Aij) with sum of all input variables (Bij) and sum of product (Sj)No. of hidden neuronsI1 (Wl)I2( Tc)I3(Ww)I4(Ew)I5(qc)I6(Tf)I7(D)10.04550.3605-0.1992-0.17490.37630.35890.232823.4432-5.10910.04678.4677-8.70828.2004-5.34073-1.4359-1.0439-0.10860.96911.14292.4021-0.925540.01670.3246-0.01290.07810.20640.13640.2504SumS1= 2.069S2= -5.4678S3= -0.2741S4= 9.3401S5= -6.9825S6= 1.0979S7= -5.783The analysis suggests that the BRNN model is best for the present study. Additionally, this study applied the Connection weight technique and Garson's algorithm for assessing the relevance of explanatory variables in ANN modelling [12]. The input variables' contributions are detailed in Tab. 8. The Connected Weights technique, as given in equation 7(a), allows greater influence on input variables with larger absolute weights on the output calculation of the hidden layer and the overall performance of the network. Garson's algorithm employs the same procedure to assess the contribution of input variables, and the ranking of each input variable is determined by equation 7(b).Relative Importance= S1S1+S2+S3+S4+S5+S6+S7 7(b)Where S1, S2, ……S7 is the sum of product in each hidden neuron. Tab. 8 presents the ranking of input variables based on the absolute value of Connection weight. Follow-up time (Tf), entry width (Ew) and circulating flow (qc), with absolute values of 11.10, 9.34, and 6.98, are specified in first, second, and third order. Tab. 5 even indicates that follow-up time (Tf), critical gap ( Tc) and circulating flow (qc) contribute around 21.15%, 19.56%, and 19.50% to model fitting, respectively. Approximately 60% of capacity modelling comes from these three variables (Tf, Tc and qc) which characterise traffic behaviour under mixed traffic situations. The remaining contributing variables (Ww, Ww, Ew and D) that pertain to the geometric state of the roundabout collectively account for around 40% of the capacity prediction that has been formulated in the present investigation. The use of Connection weight approach and Garson algorithm revealed that weaving width (Ww) has a modest influence on the development of the model.Tab. 8Contribution of input variables in BRNN modelInput variablesConnection weight approachGarson algorithmSum(Absolute Value)RankRelative importance (%)RankI1 (Wl)2.0767.726I2 ( Tc)5.47519.562I3 (Ww)0.2773.537I4 (Ew)9.34212.805I5 (qc)6.98319.503I6 (Tf)11.10121.151I7 (D)5.78415.7144. CONCLUSIONSANN-based model has been receiving wide appreciation over regression-based models as it is capable of establishing nonlinear relationship between dependent and independent variables. In this study, ten ANN-based models were developed for roundabout entry capacity prediction purpose. It was observed that the BRNN based model has the highest R2 value of 0.97 and lowest RMSE value of 167.89 among all ten models. Therefore, this model was selected for the capacity prediction in this study. The comparison of various existing capacity models with the ANN model is depicted in Fig. 4.Moreover, to appraise the BRNN model, several statistical tests were performed under a given data set. Sensitivity analysis is carried out using Connection weight approach and Garson algorithm to observe the influence of input variables in the proposed BRNN model according to Garson algorithm, gap acceptance variables including follow-up time (Tf), critical gap ( Tc), and circulating flow (qc) all played significant roles in the model fitting, with corresponding contributions of 21.15, 19.56, and 19.50 percent. Based on the findings of the Connection Weight approach, the following parameters are prioritised in the model development process: follow-up time (Tf), entry width (Ew), and circulating flow (qc). These parameters have respective absolute values of 11.10, 9.34, and 6.98 for the connection weight approach. It was also found that weaving width (Ww) has contributed just 3.53% to the overall model and that the absolute value of the connection weight was only 0.27. Planners and designers now have a practical tool in the form of the proposed models (ANN) for predicting capacity under traffic situations analogous to those in other developing countries; however, further research is needed to determine the effect of pedestrian crossings on this estimation.Fig. 4. Comparison of various capacity models References ADDIN ZOTERO_BIBL {"uncited":[],"omitted":[],"custom":[]} CSL_BIBLIOGRAPHY Yap Yok Hoe, Helen M Gibson, Ben J Waterson. 2013. “An International Review of Roundabout Capacity Modelling”. Transport Reviews 33(5): 593-616. DOI: https://doi.org/10.1080/01441647.2013.830160. ADDIN ZOTERO_ITEM CSL_CITATION {"citationID":"If452bQT","properties":{"formattedCitation":"Hamim, Hossain, and Hadiuzzaman, \\uc0\\u8220{}Developing Empirical Model with Graphical Tool to Estimate and Predict Capacity of Rural Highway Roundabouts.\\uc0\\u8221{}","plainCitation":"Hamim, Hossain, and Hadiuzzaman, “Developing Empirical Model with Graphical Tool to Estimate and Predict Capacity of Rural Highway Roundabouts.”","noteIndex":1},"citationItems":[{"id":444,"uris":["http://zotero.org/users/11075084/items/HHYH85WL"],"itemData":{"id":444,"type":"article-journal","abstract":"Transportation infrastructure plays a significant role in the economic growth of developing countries where heavy vehicles act as the backbone in transporting goods and people via highways. However, presence of heavy vehicles in traffic stream lowers the overall operating speed and flow in rural highways especially at the vicinity of intersections. This research aims at developing an empirical model for estimating and predicting capacity of highway roundabouts considering both geometric and traffic parameters. Based on data collected from six roundabouts along the national highways in Bangladesh, multivariate regression method has been used to develop an empirical model as a function of entry width, rotary lane width, distance between entry and nearest exit, central island diameter, and circulating traffic flow to estimate and predict the capacity of rural highway roundabouts. For incorporating the presence of heavy vehicles in the model, all vehicle types are converted to passenger car equivalent units. A comparative study with established methods (i.e., HCM 2016, TRRL, IRC and German method) proves the superiority of the developed model in terms of predictive capacity. Furthermore, a Python based program called PyNomo, has been executed with the help of several add-on packages (e.g., numpy, scipy, pyx) to generate a compound parallel scale nomograph consisting of multiple variables using the developed empirical model. Considering the impact of heavy vehicles in the socio-economic development of a country, the nomograph will aid the practitioners and engineers as a quick and easily interpretable graphical tool for planning and designing roundabouts in rural highways.","container-title":"International Journal of Transportation Science and Technology","DOI":"10.1016/j.ijtst.2021.10.002","ISSN":"2046-0430","issue":"4","journalAbbreviation":"International Journal of Transportation Science and Technology","page":"726-737","source":"ScienceDirect","title":"Developing empirical model with graphical tool to estimate and predict capacity of rural highway roundabouts","volume":"11","author":[{"family":"Hamim","given":"Omar Faruqe"},{"family":"Hossain","given":"Md. Saddam"},{"family":"Hadiuzzaman","given":"Md."}],"issued":{"date-parts":[["2022",12,1]]}}}],"schema":"https://github.com/citation-style-language/schema/raw/master/csl-citation.json"} Hamim Omar Faruqe, Md. Saddam Hossain, Md. Hadiuzzaman. 2022. “Developing Empirical Model with Graphical Tool to Estimate and Predict Capacity of Rural Highway Roundabouts”. International Journal of Transportation Science and Technology 11(4): 726-737. DOI: https://doi.org/10.1016/j.ijtst.2021.10.002.Ahmad Abdullah, Rajat Rastogi. 2016. “Regression model for entry capacity of a roundabout under mixed traffic condition – an Indian case study”. Transportation Letters 9(5): 243-257. DOI: https://doi.org/10.1080/19427867.2016.1203603.Qu Xiaobo, Jin Zhang, Shuaian Wang, Zhiyuan Liu. 2014. “Modelling follow up time at a single-lane roundabout”. Journal of Traffic and Transportation Engineering 1(2): 97-102. DOI: https://doi.org/10.1016/S2095-7564(15)30093-3.Fortuijn Lambertus G.H. 2009. “Turbo Roundabouts: Estimation of Capacity”. Transportation Research Record 2130(1): 83-92. DOI: https://doi.org/10.3141/2130-11.Valdez Marilyn, Ruey Long Cheu, Carlos Duran. 2011 “Operations of Modern Roundabout with Unbalanced Approach Volumes”. Transportation Research Record 2265(1): 234-243. DOI: https://doi.org/10.3141/2265-26.Karlaftis M.G., E.I. Vlahogianni. 2011. “Statistical methods versus neural networks in transportation research: Differences, similarities and some insights”. Transportation Research Part C: Emerging Technologies 19(3): 387-399. DOI: https://doi.org/10.1016/j.trc.2010.10.004.Özuysal M., S.P. Çalışkanelli, S. Tanyel, T. Baran. 2004. “Capacity prediction for traffic circles: applicability of ANN”. Proceedings of the Institution of Civil Engineers – Transport 162(4): 195-206. ISSN: 0965-092X. E-ISSN: 1751-7710. DOI: https://doi.org/10.1680/tran.2009.162.4.195.Anagnostopoulos Apostolos, Fotini Kehagia, Georgios Aretoulis. 2022. “Application of Artificial Neural Network for Modelling and Predicting Roundabout Capacity”. In: Road Safety & Simulation International Conference. National Technical University of Athens Road Safety Observatory, Hellenic Institute of Transportation Engineers. 08-10 June 2022. Athens, Greece.Patnaik Ashish Kumar, Yadu Krishna, Shweta Rao, Prashant Kumar Bhuyan. 2017. “Development of Roundabout Entry Capacity Model Using INAGA Method for Heterogeneous Traffic Flow Conditions”. Arab J Sci Eng 42(9): 4181-4199. DOI: https://doi.org/10.1007/s13369-017-2677-x.Mauro Raffaele. 2010. Calculation of Roundabouts: Capacity, Waiting Phenomena and Reliability. Berlin, Heidelberg: Springer Berlin. ISBN 978-3-642-04550-9.Ghanizadeh Ali Reza, Nasrin Heidarabadizadeh, Farhang Jalali. 2020. “Artificial neural network back-calculation of flexible pavements with sensitivity analysis using Garson’s and connection weights algorithms”. Innov. Infrastruct. Solut. 5(2): 63. DOI: https://doi.org/10.1007/s41062-020-00312-z.Appendix 1Geometric specifications of selected unsignalized roundaboutsSl. No.Site CityLegAtApproach width ( Aw) Entry width (Ew) Weaving width ( Ww) Weaving length ( Wl) Diameter of central island (D)1Sector-2 SquareRourkela, OdishaE9.581112.534.0223.83W18.7313.4428.543.82N22.781221.0936.74S18.415.7529.5640.912SAIL SquareRourkela, OdishaE6.5319.363249.3150W17.5114.1720.9843.84N2219.7432.4548.54S19.9218.3626.0544.273Ambagan SquareRourkela, OdishaE11.2415.127.1943.9938W15.1419.8135.0150.22N23.411.5923.4341.59S18.9118.2333.7253.774Plant Side SquareRourkela, OdishaE6.215.4331.1243.3148.87W8.113.6824.2541N18.0119.1730.9645S19.216.1229.5845.075Traffic Gate SquareRourkela, OdishaE12.6715.5223.3143.7943.55W8.635.4119.6339.87N21.2715.7432.2551.7S20.138.521.5837.926Birsa SquareRourkela, OdishaN10.5817.5533.250.9560.12N-E9.6316.6132.7252.33E12.0618.933.9158.72W12.7717.222847.677Panposh SquareRourkela, OdishaE16.0714.327.948.2130.28S16.9513.7623.7542.87W14.0215.0829.5641.868Ainthapalli SquareSambalpur, OdishaN-E8.0112.9327.5735.5647.88N-W14.1813.219.5743.18S-E13.1218.9730.9546.97S-W11.6613.3324.8537.959Master Canteen SquareBhubaneswar, OdishaN25.9917.7226.7848.6545.91S25.5614.5528.9953.44E16.8514.832.2649.71W12.816.7927.644.2310Gopabandhu SquareBhubaneswar, OdishaN10.118.3332.5649.8351.62E10.8417.6829.0747.35W10.0117.8223.9946.5811Jobra SquareCuttack, OdishaN10.219.6831.2548.7137.21S8.216.52746.71N-E10.7315.422041.9W15.7715.0429.8746.5712Palbani SquareBaripada, OdishaE9.4718.9830.5747.87W9.417.9631.3552.358.88N9.5316.4727.9450.15S10.4512.4121.4440.8613Dargadhi SquareBaripada, OdishaE10.4214.9823.645W11.8618.9731.3352.7639.38N10.8918.1232.753.28S12.3119.0233.4550.6414Salt-lake SquareKolkata, West BengalNE8.8515.8530.146.08NW8.8511.5221.9642.0833.55SE8.8513.572235.09SW8.8511.8528.3236.0815Albert Ekka SquareRanchi, JharkhandN-E15.454.729.4832.08S19.585.28.229.4210.76N-W13.386.3115.3931.5716Old Bus Stand SquareBilaspur, ChhattisgarhE718.1934.8651.25W7.218.2527.3548.7N9.464.4315.2130.1555S9.8116.930.1556.217Ramnagar SquareNagpur, MaharashtraNE13.931123.8540.31NW11.5213.9423.5736.66W11.2611.3125.4737.83SW13.2911.2223.9436.436.54E6.9313.0422.3338.12SE15.335.914.831.2S11.455.1211.0228.9618Medical SquareNagpur, MaharashtraN6.746.1413.3938.96NE7.329.517.4538.52SE6.3818.3627.0143.8S10.9716.7130.0247.6351.22SW9.6216.7728.4749.22NW6.7113.9733.0241.1519Chacka JunctionThiruvananthapuram, KeralaNE7.6416.3432.0144.32NW6.2114.7126.02545.3446.8SE8.4316.9426.9839.8SW6.9815.9430.0144.2420Womens College, VazhuthakaduThiruvananthapuram,KeralaN18.3919.132.6746.85S17.5916.5920.540.4234.28E6.7713.8528.843.45W13.8816.4725.2640.8921MVP Colony SquareVisakhapatnam, Andhra PradeshE8.1217.328.947.98W8.1918.7929.9850.0545.47N8.0914.6527.5943.1S7.9820.1229.652.322Diamond Park JunctionVisakhapatnam, Andhra PradeshE14.5119.82853.29W14.0115.8131.6547.1354.8N18.1918.525.1447.79S15.5216.8822.513823BR Ambedkar SquareVisakhapatnam, Andhra PradeshE11.218.9330.0245.69W11.7115.322.9138.3140.1N10.0419.0729.9541.22S11.0514.7924.941.0224Dornama Raju SquareVisakhapatnam, Andhra PradeshN14.2912.1531.8441.59S20.851429.8441.2240.65E15.8614.5822.940.26W20.4710.1222.8647.8625Sector 43-44 JunctionChandigarhNE13.9716.8933.1744.72NW13.7519.4633.2545.88SE11.6818.4830.0450.8950SW11.3816.8830.5841.8126Sector 42 JunctionChandigarhNE8.2819.7929.5551.59NW9.3919.1429.7245.1449SE8.1419.8729.5646.13SW8.3814.9827.948.6227Sector 49 JunctionChandigarhN10.416.93456S1016.430.548.357E10.619.33151.6W1116.232.852.5Note: N = North, S = South, E = East, W = West, NE = North-East, NW = North-West, SE = South-East, SW = South- WestReceived 06.12.2023; accepted in revised form 29.03.2024Scientific Journal of Silesian University of Technology. Series Transport is licensed under a Creative Commons Attribution 4.0 International License PAGE 226A.K. Munshi, A.K. Patnaik Department of Civil and Environmental Engineering, Research Scholar, Birla Institute of Technology Mesra, Ranchi 835215, Jharkhand, India. Email: phdcee10051.20@bitmesra.ac.in. ORCID: https://orcid.org/0009-0003-5808-82872 Department of Civil and Environmental Engineering, Assistant Professor, Birla Institute of Technology Mesra, Ranchi 835215, Jharkhand, India. Email: ashishpatnaik@bitmesra.ac.in. ORCID: https://orcid.org/0000-0002-8674-9148 Modelling roundabout entry capacity for mixed traffic flow using ANN… PAGE 225.Scientific Journal of Silesian University of Technology. Series TransportZeszyty Naukowe Politechniki Śląskiej. Seria TransportVolume 1232024p-ISSN: 0209-3324e-ISSN: 2450-1549DOI: https://doi.org/10.20858/sjsutst.2024.123.10Journal homepage: http://sjsutst.polsl.pl/9j/4AAQSkZJRgABAQEA3ADcAAD/2wBDAAIBAQEBAQIBAQECAgICAgQDAgICAgUEBAMEBgUGBgYF
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