Browsing by Author "Vikram, Durgesh"

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Conventional Optimization Technique Based Methodology to Estimate Gap Acceptance Functions
(Springer, 2020-07) Vikram, Durgesh
The definition of a critical gap in literature supports that it not only varies from driver to driver but also for (over) rejected gaps by a driver. In this light, multinomial probit (MNP) models were proposed in the past as gap acceptance functions. There are few methodologies available in the literature to estimate these functions. These methodologies are either computationally expensive or involve sophisticated mathematics. This is possibly one of the reasons due to which MNP models are not explored extensively as a tool to model critical gaps. Further, estimation of such gap acceptance functions always leads to maximization of likelihood functions. This paper proposes a methodology based on a conventional optimization technique for the first time to estimate the parameters of a class of gap acceptance functions. It is also shown that the estimation results match with those from another method, namely CHOMP. The proposed method turns out to be a simple yet effective one.
Effect of Side Friction Parameter on Urban Road Traffic: Under Mixed Traffic Scenario
(J-Stage, 2019) Vikram, Durgesh
USHighway Capacity Manual and Indian Highway Capacity Manualdefine road capacity as the maximum sustainable flow rate at which vehicles or persons can reasonably be expected to traverse a point under the given roadway, geometric, traffic, environmental, and control conditions. The capacity of the roadway system often gets reduced by the roadside activities called side friction. In India, side friction prevails predominantly in urban areas due to a significant rise in population and economic activities. These activities restrain the urban road system to serve at full operating capacity. In this study, the impact of a side friction parameter (on-street parking, and non-motorized vehicles) on the performance of an urban road has been measured. Secondarily, the product limit method of capacity estimation has been implemented to overcome the randomness observed in capacity value. A microsimulation model is developed to validate the results.
Effective Technique to Estimate Cross Model Parameters
(ASCE, 2017-11) Vikram, Durgesh
The Cross model has been successfully used for modeling the shear thinning behavior of asphalt binders. Usually minimization ofleast squares/absolute error is used for obtaining model parameters. The curve fitted using these techniques shows more deviation at thoseparts of the domain where there are fewer observations. To improve the curve fit and eliminate this bias, an area minimization technique isproposed in this study. To the best of the authors’knowledge, this technique is proposed for the first time in model parameter estimation. Thispaper discusses and compares least-squares and area minimization for fitting the complex viscosity master curves of four different asphaltbinders at six different reference temperatures. The results clearly demonstrate that area minimization offers a solution that has less deviationthroughout the domain of the observed data when compared with least-squares error.
Impact of vehicular traffic stream on pedestrian crossing behavior at an uncontrolled mid-block section
(Elsevier, 2021-03) Vikram, Durgesh
A term Total Crossing Time (TCT) is coined in this study. TCT of a pedestrian includes the time spent by the pedestrian in waiting and his/her crossing of a road. This paper argues that considering a distribution of TCT is required for analysis instead of analyzing a crisp value of TCT of pedestrians. This study quantifies, perhaps for the first time, that by what extent vehicular traffic streams affect TCT distribution of pedestrians crossing an uncontrolled mid-block section of an urban road. For this, a suitable parameter of traffic stream that influences TCT distribution is identified. The suitable parameter of traffic is found to be the traffic density. Further, it is hypothesized that pedestrians can only perceive a range of traffic density and not discrete values of density. In order to incorporate this, traffic density observed on the road is categorized into nine groups; and, for each group of densities corresponding TCT distribution is computed. Curve fitting, using two kinds of density functions, for each of the nine TCT distributions is performed and Pearson Type-III density function is found to be a more appropriate distribution. Additionally, the parameters of the fitted Pearson Type-III distribution are found to be dependent on the corresponding mean of the traffic density group. Hence, a simple regression model is also suggested using which one can predict TCT distribution if traffic density of the stream is known. The findings of this study is going to be useful for researchers/practitioner those who are interested in simulating pedestrians, crossing an uncontrolled mid-block section of a road.
Optimum assignment of trains to platforms under partial schedule compliance
(Elsevier, 2008) Vikram, Durgesh
The paper develops a linear mixed integer programming formulation for allocating platforms optimally to trains arriving at a busy multi-platform station. The formulation does not assume that all trains arrive as per schedule, in fact it assumes that the exact arrival times of trains are known shortly (an hour or so) before the actual arrivals of the trains. Such variation in arrival times often necessitates delaying of trains (on the entry tracks) due to non-availability of platforms; these delays may also cause queuing up of trains on the tracks. While determining the optimum allocation the formulation takes into account the inconvenience caused due to (i) delay, (ii) allocation of non-preferred platforms (some platforms may be preferred for some trains – as is the case in India), and (iii) last minute reassignment of platforms. The constraints ensure that all physical and safety related restrictions are satisfied. Various problems developed from the schedule of arrivals at a busy station in India are also solved and the results analyzed.
Stabilized finite element computations with a two-dimensional continuum model for disorderly traffic flow
(Elsevier, 2022-01) Vikram, Durgesh
A two-dimensional continuum model of traffic flow is proposed. The model incorporates disorderly traffic, lane indiscipline, streamwise variation of the width of the road, as well as the impact of edges of the road, on the traffic. A stabilized finite element formulation is employed to solve the governing equations. The performance of the model is demonstrated using numerical experiments. Several features that are commonly observed in high speed flow of fluids, such as oblique shocks, normal shocks, slip lines, and expansion fans, are observed in the traffic flow simulated via the proposed model. The model is utilized to predict the traffic capacity of a road with varying road width. It is found that the narrow section behaves as a throat in a converging diverging nozzle in high speed fluid flow. The proposed model explains several phenomena observed in real traffic streams.
A Stabilized Finite Element Formulation for Continuum Models of Traffic Flow
(Tech Science Press, 2011) Vikram, Durgesh
A stabilized finite element formulation is presented to solve the governing equations for traffic flow. The flow is assumed to be one-dimensional. Both, PW-type (Payne-Whitham) 2-equation models and the LWR-type (Lighthill-Whitham-Richards) 1-equation models are considered. The SUPG (Streamline-Upwind/Petrov-Galerkin) and shock capturing stabilizations are utilized. These stabilizations are sufficient for the 1-equation models. However, an additional stabilization is necessary for the 2-equation models. For the first time, such a stabilization is proposed. It arises from the coupling between the two equations and is termed as IEPG (Inter-Equation/Petrov-Galerkin) stabilization. Two behavioral models are studied: Greenshields' (GS) and Greenberg's (GB) models. Numerical tests are carried out for cases involving traffic expansion as well as shock. Excellent agreement with the exact solution is observed. The need of the IEPG stabilization for the 2-equation traffic models is demonstrated. An interesting observation is made for the first time regarding the Greenberg's (GB) model in the presence of a shock. The model is found to be inconsistent in the sense that it leads to different shock speed from the continuity and behavior equations. As a result, the 2-equation model leads to secondary waves in the presence of shocks
Study on viscosity of conventional and polymer modified asphalt binders in steady and dynamic shear domain
(Springer, 2018-02) Vikram, Durgesh
This study focuses on evaluating the flow behavior of conventional and polymer modified asphalt binders in steady- and dynamic-shear domain, for a temperature range of 20–70 °C, using a Dynamic Shear Rheometer (DSR). Steady-shear viscosity and frequency sweep tests were carried out on two conventional (VG 10 and VG 30) and two polymer (SBS and EVA) modified asphalt binders. Applicability of the Cox–Merz principle was evaluated and complex viscosity master curves were analyzed at five different reference temperatures. Cross model was used to simulate the complex viscosity master curves at different temperatures.
Understanding and modelling disorderly traffic streams
(Springer, 2019) Vikram, Durgesh
Disorderly traffic streams are those that, simply stated, do not have parallel lines (or lanes) of vehicles but have vehicles distributed more haphazardly in the road space. Vehicles in such streams, while moving longitudinally, change their lateral positions frequently. Their trajectories have a more pronounced wander along the width or the lateral dimension as opposed to those vehicles that primarily move in lanes. This property of disorderly streams dictates that its mathematical models must admit two spatial dimensions (the longitudinal and the lateral). Further, the observed impact of road geometry features like width, curvature, etc., on stream behavior, irrespective of whether the stream is disorderly, also suggests that realistic models of traffic streams must describe the streams using two spatial dimensions. Unfortunately, most of the theories of traffic dynamics are one-dimensional—they only consider the longitudinal dimension. This paper, while describing many of the existing approaches to modelling vehicular traffic behavior builds a case for strengthening two-dimensional modelling approaches that are all, still in their infancy. Given the (1) large increase in computation and data handling capabilities over the last decade and (2) significant strides made in developing tools for observing traffic dynamics at scales and accuracy levels that were previously unimaginable, the authors believe the time has come to develop, calibrate and validate reasonable twodimensional models of traffic dynamics.