NUMERICAL SIMULATION OF TRAFFIC FLOW PROBLEMS

Abstract

Traffic congestion remains a major societal and economical problem across the world, with no visible sign of substantial reduction in future. Traffic control systems are based on the concept of avoiding traffic instabilities and of homogenizing the traffic flow in such a way that the risk of accidents is minimized and mean velocity or the traffic flow is maximized. Computer simulation is a powerful tool for traffic operation analysis, for example, for the design and control of transportation systems. The objective of transportation research consists of deriving suitable models to describe the flow conditions on highways or on urban street and predicting the effect of traffic control and its operational performance through computer simulation. The applicability of traffic simulation models lies in their capability to replicate how congestions, an undesirable phenomena observed in real traffic, occur when disturbances are present in transportation systems. Traffic flow models have been developed over nearly seven decades of research and application. These models can be broadly categorized into microscopic and macroscopic, in terms of level of detail and process representation. Microscopic models describe traffic behavior as emerging from discrete entities interacting with each other. They range from simple analytical models, like car following models, to detailed simulation models, like the FRESIM and NETSIM simulation software. Macroscopic models like LWR model and higher order continuum models describe the aggregate behavior of traffic by characterizing the fundamental relationships between vehicle speed, flow and density. Traffic simulation modeling has developed either microscopically or macroscopically in conventional simulation packages like CORSIM, a microscopic simulation model and FREFLO, a macroscopic simulation model. A key limitation of these existing simulation models is their incapability of capturing the inherent stochasticity in vehicle behaviour in real traffic that arises from the interaction of individual vehicles. Thus, usefulness of most of the conventional simulation models is limited to characterizing the long run behaviour of traffic flow and cannot be used for real time traffic analysis and control. To overcome the limitations associated with the iii conventional simulation techniques a new paradigm is required. The study of cellular automata (CA) is done for that purpose. Cellular automata are mathematical idealizations of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values. A cellular automaton consists of a regular uniform lattice, usually finite in extent, with discrete variables occupying various sites. The state of a cellular automaton is completely specified by values of variables at each site. Variables at each site are updated simultaneously, based on values of variables in their neighbourhood at the preceding time step, and according to a definite set of "local rules." Performance matrices are obtained through computer simulation of evolution of cellular automaton over time. Traffic cellular automata (TCA) models are capable of explicitly representing individual vehicle interactions and relating these interactions to macroscopic traffic flow parameters, such as throughput, travel time, and vehicle speed. TCA models can more adequately capture the complexity of real traffic by allowing different vehicles to possess different driving behaviours like acceleration/deceleration, lane change rules, reaction times etc. In a rapidly urbanizing country transportation sector is growing swiftly. This has led to overcrowded roads and pollution. Vehicular emissions of dust particles, smog and noise have reached or even exceeded levels of those from industrial production or private households, and are harmful to the environment and human health. The recognition of traffic noise as one of the main sources of environmental pollution has led to the development of models that enable the prediction of traffic noise level from fundamental variables like density, flow and speed of vehicles, distance from roads and condition of roads. Road traffic noise prediction models can be developed by using traffic cellular automata simulation models. Thus predicting traffic noise is a possible application of TCA models in the frame work of acoustic noise control. TCA models usually have only a few parameters, which often mean easy calibration. Vehicle dynamics may be governed by one or two parameters for acceleration/deceleration. TCA models, by being either deterministic or stochastic, can be more effective in accounting for inherent variability of most real traffic. In turn, this allows us to characterize not only average values of flow rate but also their higher moments. With the help of TCA models, microscopic and macroscopic traffic flow iv parameters and their interactions can be studied; driver behavior can be incorporated properly through probability. The computational efficiency and comparatively low computational cost of TCA models made it possible to conduct large-scale real time simulations of urban traffic. Thus present thesis entitled Numerical simulation of traffic flow problems deals with development of a modified traffic cellular automata model for homogeneous and mixed type traffic. The objective of this thesis is to study the applicability of one type of microscopic simulation model, cellular automata in identifying the prevailing traffic situations in road networks and reproducing the measured macroscopic behaviour of traffic flow. Research work is organized in to seven chapters. First chapter is introductory in nature and gives a brief account of general theory of traffic flow and noise emission due to road traffic. The developments of traffic cellular automata models from origin to recent findings are also presented. At the end of the chapter, summary of the whole work--is embodied. In second chapter, a velocity dependent acceleration rate (VDAR) TCA model based upon Nagel-Schrekenberg (NaSch) model is presented by reducing cell size and considering variable acceleration rate depending upon speed of each individual vehicle, to simulate homogeneous and mixed type traffic. Effect of slow-to-start behaviour among vehicles given in Lagrange model of traffic flow is discussed on a single-lane road. Comparisons are made between VDAR model and NaSch model. It is observed in fundamental diagram that, transition line from free-flow to congested-flow is curved for VDAR model due to velocity dependent acceleration rate. In third chapter, VDAR TCA model presented in second chapter is extended to two-lane model. Slow-to-start rule given in BJH model, which describes the behaviour of jammed vehicle, is implemented in the modified two-lane model and effect of variability in traffic flow over lane changing behaviour among vehicles is studied. Using results of numerical simulations, fundamental diagrams of traffic flow are analyzed and it is observed that s-t-s probability has more effect than braking probability over lane changing manoeuvre. In fourth chapter, the problem of optimization and control of homogeneous and mixed- type traffic along a highway under the influence of traffic light is analyzed. Two traffic light strategies i.e. synchronized and green-wave are compared. It is observed that for densities lower than critical density, saturated current does not depend upon cycle time but upon strategy and green-wave switching strategy is found to be better traffic light strategy for VDAR TCA model. In fifth chapter, phase transition on a highway for homogeneous traffic in VDAR TCA model with an off-ramp is studied. Numerical simulations with open boundary conditions are carried out. Comparisons are made between NaSch model and VDAR TCA model. It is observed that transition from free-flow to congested-flow and from free-flow to saturated-flow is affected because of dissimilar acceleration capabilities. In chapter sixth, the influence of stochastic nature of traffic flow over traffic noise emission is studied using VDAR TCA model. A series of measurements have been carried out on NH-58 and B & K 2260 noise analyzer is used to measure the noise level. Influence of speed fluctuations, arising due to bad condition of road, vehicle, weather, etc. over noise emission level of different type of vehicles is studied in Indian conditions. A value of braking parameter p, which represents stochastic nature of traffic flow, is estimated for Indian road condition which is found suitable when compared with real observed data. In seventh chapter, concluding observations with a significant analysis of the work presented in earlier chapters of this study is carried out. In addition, a brief discussion on the scope for future work is presented.