Roundabout entry capacity models: genetic programming approach & 1 Ashish Kumar Patnaik MTech PhD student, Transportation Division, Department of Civil Engineering, NIT Rourkela, Rourkela, India (Orcid:0000-0002-8674-9148) & 2 Saswat Chaulia MTech Former MTech student, Transportation Division, Department of Civil Engineering, NIT Rourkela, Rourkela, India (Orcid:0000-0002-4564-1229) & 3 Prasanta Kumar Bhuyan PhD Assistant Professor, Transportation Division, Department of Civil Engineering, NIT Rourkela, Rourkela, India (corresponding author: pkbtrans@gmail.com) (Orcid:0000-0003-0268-4154) 1 2 3 The aim of this study was to develop three roundabout entry capacity models (RECMs) by employing evolutionary-based regression techniques such as genetic programming (GP), age-layered population structure genetic programming (ALPSGP) and grammatical evolution genetic programming (GEGP) in mixed traffic conditions. Necessary data were collected from 27 roundabouts located in eight states in India. The influence area for gap acceptance method was used to determine the critical gap. To assess the significance of the models and select the best, the modified rank index was applied. The results showed that the GEGP model performed better than the GP and ALPSGP models. The GEGP model is also applicable in practice because of its simplicity. Sensitivity analysis revealed that the critical gap is the prime variable in the development of RECMs. The findings of this study should be useful for traffic planners and designers in the capacity estimation of roundabouts in mixed traffic conditions in developing countries with traffic characteristics similar to those in India. Notation A w approach width C O observed entry capacity C P predicted entry capacity D diameter of central island E Nash–Sutcliffe model efficiency coefficient E w entry width P 50 50% cumulative probability P 90 90% cumulative probability Q e observed entry capacity q c circulating flow R 1 ranking of model based on best-fit calculations R 2 ranking of model based on error variables R 3 ranking of model based on arithmetic calculations (ratio of predicted and observed entry capacities) R 4 ranking of model based on 50% and 90% cumulative probabilities R 5 ranking of model based on prediction of entry capacity within ±20% accuracy T c critical gap T f follow-up time W l weaving length W nw width of non-weaving section W w weaving width μ mean σ standard deviation 1. Introduction and background A roundabout is a typical type of un-signalised intersection where the minor stream of traffic flow merges with the major stream of traffic flow around a central island, providing vehicular traffic movement in the clockwise or anti-clockwise direction depending on the left-hand or right-hand driving rule of the country. Roundabouts have many advantages overother signalised intersections in terms of safety and operational effi- ciency. For example, a signalised intersection has 32 conflict points whereas a roundabout with one circulating lane and one entry lane and a roundabout with two circulating lanes and two entry lanes have 8 and 16 conflict points, respectively. In comparison with signalised intersections, the other advantages of roundabouts as an alternative include traffic calming at the intersection without the use of signals, lower overall delay, pedestrian safety and less maintenance costs. The roundabout capacity is the major influencing variable and is employed in operational performance to describe the present traffic condition. According to the Transportation Research Board’ s Highway Capacity Manual (HCM) (TRB, 2010), capacity is the maximum entry flow that can be accommodated in the 1 Cite this article Patnaik AK, Chaulia S and Bhuyan PK Roundabout entry capacity models: genetic programming approach. Proceedings of the Institution of Civil Engineers – Transport, https://doi.org/10.1680/jtran.17.00089 Transport Research Article Paper 1700089 Received 08/07/2017; Accepted 25/05/2018 ICE Publishing: All rights reserved Keywords: roads & highways/traffic engineering/transport management