MATHEMATICAL MODELING OF TRAFFIC FLOW AND NOISE EMISSION

Abstract

Nowadays, traffic flow and congestion is one of the main societal and economical problems related to transportation in industrialized countries. To control and influence traffic flows on highways detector equipments and variable message sign systems have been installed in the recent years. Traffic control systems are based on the idea to avoid traffic instabilities and to homogenize the traffic flow in such a way that the risk of accidents is minimized and the mean velocity or the traffic flow is maximized. Modeling of traffic flow has been a key tool to predict the behavior of transportation system. The objective of mathematical research consists in deriving suitable models to describe the flow conditions on highways or urban streets. The applicability of these models lies in their capability to replicate how congestions, an undesirable phenomenon that is observed in real traffic, occur when disturbances are present in transportation systems. Traditionally, there are two approaches (Microscopic & Macroscopic) dominated over traffic flow modeling throughout the past five decades. Due to analogy to fluid dynamics, macroscopic modeling approach is found most suitable for real—time simulations, short term traffic predictions, developing and controlling online speed control systems etc. Macroscopic traffic modeling is based on the assumption that a traffic stream on a single lane can be considered as continuum of moving particles i.e. in the macroscopic traffic flow models the traffic on a highway is idealized to a homogeneous fluid and vehicles are represented by identical fluid particles in a tube. Due to the complexity of controlling heterogeneous traffic flow operations, caused by among others the interaction between user-class and interplay between the available traffic, a model based approach is needed. Relatively less attention has been given to the study of higher order multi-class models. Recently, besides the well known free flow and traffic jams, a new phase is identified and named synchronized flow. It is observed nearly all occasions, localized near ramps and it is thus believed that ramps are important for the stability of the synchronized traffic flow. Being an essential element for managing transportation network, traffic signal plays an important role in controlling traffic flow in urban traffic. Very little effort is made to optimize traffic flow through traffic light control strategies. In rapidly urbanishing country, the transportation sector is going rapidly. This has led to overcrowded roads and pollution. Vehicle emissions of dust particles, smog, and noise have reached or even exceeded levels comparable to 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 such as the flow and velocity of vehicles, the distance from the road to the observer, etc. Thus the present thesis entitled Mathematical modeling of traffic flow and noise emission deals with the development of a new higher order anisotropic continuum model for traffic flow. The model comprises a system of two partial differential equations. Some qualitative properties together with linear stability analysis have been studied. The model has been extended to multi-class traffic flow with heterogeneous drivers. Phase transition between free flow to traffic jam states has also been investigated by modifying the model for an on-ramp situation. Effect of traffic lights on the traffic flow has been examined. A ii mathematical model for predicting traffic noise is developed and examined on Indian conditions. The work has been compiled in form of seven chapters containing the following matter: Chapter 1 is introductory in nature and gives a brief account of the general theory of traffic flow and noise emission due to road traffic. The developments of the continuum traffic flow theory from origin to recent findings are also presented. At the end of the chapter, summary of the whole work embodied in the thesis. In the chapter 2, a new continuum model based upon an improved car-following model is developed by using a series expansion of the headway in terms of the density. The new model contains an additional speed gradient term (Anisotropic term) in comparison to the Berg's model [Berg et al., 2000]. This anisotropic term guarantees the property that the characteristic speeds are always less than or equal to the macroscopic flow speed. The stability of traffic flow is analyzed and found out that this new continuum model obeys the same stability criterion as Berg's model for zero anisotropic parameter. Chapter 3 is devoted to the qualitative properties of the same traffic flow model developed in the second chapter. The traveling wave solution is discussed and find out the condition for the shock wave. The nonlinear theory of the cluster effect in a traffic flow i.e., the effect of appearance of a region of high density and low average velocity of vehicle in an initially homogeneous flow is also discussed. In chapter 4, phase transition on a highway in a modified anisotropic continuum model with an on-ramp is studied. The phase diagram for three representative values of the upstream boundary flux and for the whole range of the on-ramp flux is presented. Several states like pinned localized cluster (PLC), triggered stop-and-go (TSG), recurring hump lll state (RH), the oscillatory congested traffic (OCT) and the homogeneous congested traffic (HCT) are observed in phase transition from free flow to traffic jam state. Chapter 5 contains the problem of optimizing and control of traffic flow along a highway by traffic lights. The single light situation and the synchronized light strategy are investigated. The effect of traffic lights in an initially homogeneous flow is discussed. It is found that the plot of flow against density depends on cycle time and the distance between the lights. It is concluded that the road capacity can be optimized by adjusting the cycle time of traffic lights on a highway. Chapter 6 is devoted to study the extended anisotropic model for multi-class traffic flow with heterogeneous drivers. Each user class is characterized by their choice of speeds in a traffic stream. Numerical simulations show that the model is able to explain some of the observed traffic phenomena such as platoon dispersion that challenge old homogeneous models presented in the literature [Hoogendoom and Bovy, 1996, 2000; Wong and Wong 2002]. The study of traffic flow parameters and its subsequent effect in terms of the noise impact have been studied and validated with the theoretical model. Chapter 7 deals with a mathematical model for A-weighted equivalent level. It is derived by applying the inverse square law of sound pressure incorporating with modified theories of traffic noise model according to the effective ground effect along the propagation path. A series of measurement have been carried out on NH-58 and B & K 2260 noise analyzer is used to measure the noise level. The noise level predicted from the developed model is compared with the measured one.