Nonlinear kinetic theory of vehicular traffic

We prove the existence and uniqueness of a continuous solution F = φ + w of the initial-value problem for vehicular traffic according to the nonlinear Prigogine-Herman model, where φ is a suitable t- and x-independent car distribution.We then show that the perturbation w is strongly continuous and strongly differentiable any number of times with respect to the probability of not passing q. Moreover, the derivatives $\text{?}{}^{\mathrm{m}}\text{w}\text{?q}{}^{\mathrm{m}}$ (in the strong sense) satisfy linear systems.We finally investigate the behavior of w(t) as t → + ∞ and, under the assumption that the probability of not passing remains unchanged after the instant t = 0, we prove that lim ∥w(t)∥ = 0 as t → + ∞.     

Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems

This paper deals with nonlinear hydrodynamic modelling of traffic flow on roads and with the solution of related nonlinear initial and boundary value problems. The paper is in two parts. The first one provides the general framework of hydrodynamic modelling of traffic flow. Some new models are proposed and related to the ones which are known in the literature. The second one is on mathematical methods related to the solution of initial-boundary value problems. A critical analysis and an overview on research perspectives conclude the paper.     

Nonlinear hydrodynamic models of traffic flow in the presence of tollgates

A nonlinear hydrodynamic model of traffic flow is here proposed in order to refine the modeling of driver's behaviour. This model is able to describe the car density and flow evolution in the presence of tollgates too. In any case, the associate evolution problem is a classical Dirichlet problem related to the flow measurement. Numerical simulations related to the solution of initial-boundary value problems are obtained by employing a scientific program written by the software Mathematica.     

Improving throughput in a wireless LAN with application to the Canadian army's situational awareness system

This paper employs optimization to improve the performance of the system the Canadian Army uses to give a Commander a picture of where his forces are. This system uses the Army's wireless battlefield communication network to send vehicle positions as data messages. The difficulty is that, when vehicles compete to send these reports, the messages sometimes collide and this wastes valuable network capacity. At the heart of the problem is the channel access control mechanism. We show how a simple change to this mechanism can improve the system's performance significantly.     

Performance analysis of AAL multiplexer with CBR traffic and bursty traffic

This paper models and evaluates the AAL multiplexer to analyze AAL protocol in ATM networks. We consider an AAL multiplexer in which a single periodically deterministic CBR traffic stream and several variable size bursty background traffic streams are multiplexed and one ATM cell stream goes out. We model the AAL multiplexer as aB ^X +D/D/1/K queue and analyze this queueing system. We represent various performance measures such as loss probability and waiting time in the basis of cell and packet.     

Non-linear analysis of a traffic flow

A nonlinear mathematical model, which takes into account the dissipative mechanism, is used to describe the signal transmission in a traffic flow. It is shown that dissipative mechanisms, under certain conditions, may produce attenuation effects against the typical nonlinear steepening of waves. An asymptotic analysis is carried out to discuss wave features when the governing hyperbolic system of equations is objective to different kinds of approximations.     

Heavy traffic analysis of controlled multiplexing systems

The paper develops the mathematics of the heavy traffic approach to the control and optimal control problem for multiplexing systems, where there are many mutually independent sources which feed into a single channel via a multiplexer (or of networks composed of such subsystems). Due to the widely varying bit rates over all sources, control over admission, bandwidth, etc., is needed to assure good performance. Optimal control and heavy traffic analysis has been shown to yield systems with greatly improved performance. Indeed, the heavy traffic approach covers many cases of great current interest, and provides a useful and practical approach to problems of analysis and control arising in modern high speed telecommunications. Past works on the heavy traffic approach to the multiplexing problem concentrated on the uncontrolled system or on the use of the heavy traffic limit control problem for applications, and did not provide details of the proofs. This is done in the current paper. The basic control problem for the physical system is hard, and the heavy traffic approach provides much simplification. Owing to the presence of the control, as well as to the fact that the cost function of main interest is “ergodic”, the problem cannot be fully treated with “classical” methods of heavy traffic analysis for queueing networks. A basic result is that the optimal average costs per unit time for the physical problem converge to the optimal cost per unit time for the limit stationary process as the number of sources and the time interval goes to infinity. This convergence is both in the mean and pathwise senses. Furthermore, a “nice” nearly optimal control for the limit system provides nearly optimal values for the physical system, under heavy traffic, in both a mean and pathwise sense. This revised version was published online in June 2006 with corrections to the Cover Date.     

Time-series analysis of traffic updates in loss systems

The paper deals with time-series analysis of one-line traffic measurements in loss systems. Discrete-time stochastic models are derived for finite-capacity trunk groups with non-exponential distributions of interarrival and service times. The modelling accuracy is characterized by a prediction error. Simulation results are used to assert situations when the application of the proposed modelling technique is practical. Finally the adaptive Kalman filter is used to deal with cases when the statistics of observed processes are not known a priori.     

The cost-benefit analysis of traffic safety measures based on behavior analysis

The purpose of cost-benefit analysis is to provide information for better decision-making for the future which is full of uncertainty. The results of cost-benefit analysis are not based on empirical evidence but on prediction with a theoretical basis. This paper shows what kind of traffic safety measure is most effective for the prevention of traffic accidents on the basis of behavior analysis.The role played by the human being is significant in driving. In this study, the behavioral units of driving are stipulated from the viewpoint that the driver's behavior is materialized at a point where human, vehicle and environmental factors are concerned. According to the psychological idea that behavior shifts with the shifts of environment, the shifts of driver's behavior by the establishment of traffic safety measures will be discussed. On the other hand, the correspondence between accident examples and behavioral units will be discussed by accident analysis, and in conclusion the decrease in accidents will be predicted by the shifts of behavior due to traffic safety measures. The method for deciding the priority order of establishing traffic safety measures will be explained considering the expenses for taking these measures.     

Nonlinear analysis and complementarity theory

We present in this paper a short survey of some recent interactions between Nonlinear Analysis and Nonlinear Complementarity. Considering the new relations between Nonlinear Analysis and Complementarity Theory, put in evidence in this paper, we define several open research subjects profitable to both domains.     

Nonlinear thermoelastic analysis of layered structures

The nonlinear thermoelastic behavior of orthotropic layered slabs and cylinders including radiation boundaries, temperature-dependent material properties, and stress-dependent layer interface conditions is investigated. A one-dimensional finite element formulation employing quadratic layer and linear interface elements is used to perform the analyses. The transient heat conduction portion of the program is temporally discretized via an implicit linear time interpolation algorithm which includes Crank-Nicolson, Galerkin, and Euler backward differencing. The nonlinear heat conduction equations are iteratively evaluated using a modified Newton-Raphson scheme. Direct iteration between heat conduction and stress analysis is employed when stress-dependent interface thermal resistance coefficients are utilized. Verification problems are presented to demonstrate the accuracy of the finite element code.     

An analysis of Gipps's car-following model of highway traffic

A mathematical analysis of Gipps's (1981) car-following modelis performed. This model is of practical importance as it powersthe UK Transport Research Laboratory highway simulation packageSISTM. Uniform flow solutions and a speed–headway functionare derived under simplifying conditions. A linear stabilityanalysis of uniform flow is then performed, and stable and unstableregimes are identified. Finally, some numerical simulationsfor a variety of parameter regimes are presented.     

Nonlinear finite element analysis of concrete structures

This paper deals with three-dimensional nonlinear finite element analysis of concrete structures. A new three-parameter failure criterion, formulated in terms of three stress invariants, is suggested for plain concrete. The criterion can accurately describe available experimental data throughout the stress range from tensile stresses to high compressive stresses. The constitutive matrix of a cracked concrete element is deduced by coupling the normal and tangential effects of crack bands. The modeling of reinforcement and its interaction with concrete are also discussed. Numerical examples of plain and reinforced concrete are presented. The computational results compare satisfactorily with experimental data.This research is supported by the Chinese National Committee of Science and Technology and the Chinese National Bureau of Nuclear Safety.     

Nonlinear analysis in a Lorenz-like system

In this paper we study the nonlinear dynamics of a Lorenz-like system. More precisely, we study the stability and bifurcations which occur in a new three parameter quadratic chaotic system. We also study the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters. As a consequence we show the existence of chaotic attractors when these cycles disappear.     

Nonlinear vibration analysis of tapered Timoshenko beams

The nonlinear flexural vibration analysis of tapered Timoshenko beams is conducted. The equations of motion for tapered Timoshenko beams are established in which the effects of nonlinear transverse deformation, nonlinear curvature as well as nonlinear axial deformation are taken into account. The nonlinear fundamental frequencies of tapered Timoshenko beams with two simply supported or clamped ends are presented.     

城市公共交通拥堵的经济分析与计量

基于公共品视角,分析城市交通产品供求特性以及造成拥堵的成因,构建了三部门动态一般均衡模型,分析交通产品供求稳态与冲击对拥堵的影响和动态调控机制,并从产业供求角度提出治理意见.根据动态均衡条件,并以上海城市交通样本构建动态联立方程,进行了实证检验.     

Nonlinear analysis of a novel three-scroll chaotic system

This paper reports the nonlinear dynamics of a novel three-scroll chaotic system. The local stability of hyperbolic equilibrium and non-hyperbolic equilibrium are investigated by using center manifold theorem. Pitchfork bifurcation, degenerate pitchfork bifurcation and Hopf bifurcation are analyzed when the parameters are varied in the space of parameter. For a suitable choice of the parameters, the existence of singularly degenerate heteroclinic cycles and Hopf bifurcation without parameters are also investigated. Some numerical simulations are given to support the analytic results.     

Nonlinear functional analysis and optimal economic growth

A problem of existence and characterization of solutions of optimal growth models in many sector economies is studied. The social utility to be optimized is a generalized form of a preference depending additively on consumption at the different dates of the planning period. The optimization is restricted to a set of admissible growth paths defined by production-investment-consumption relations described by a system of differential equations. Sufficient conditions are given for existence of a solution in a Hilbert space of paths, without convexity assumptions on either the utilities or the technology, using techniques of nonlinear functional analysis. A characterization is given of the utilities which are continuous with respect to the Hilbert space norm. Under convexity assumptions a characterization is also given of optimal and efficient solutions by competitive prices.     

Nonlinear similarity analysis for epileptic seizures prediction

The prediction of epileptic seizures can promise a new diagnostic application and a novel approach for seizure control. This paper proposes an improved dynamical similarity measure to predict epileptic seizures in electroencephalographic (EEG). First, mutual information and Cao's method are employed to reconstruct a phase space of preprocessed EEG recordings by using the positive zero crossing method. Second, a Gaussian function replaces the Heavyside function within correlation integral at calculating a similarity index. The crisp boundary of the Heavyside function is eliminated because of the Gaussian function's smooth boundary. Third, an adaptive detection method based on the similarity index is proposed to predict the epileptic seizures. In light of test results of EEG recordings of rats, it is found that the new dynamical similarity index is insensitive to the selection of the radius value of Gaussian function and the size of segmented EEG recordings. Comparing with the dynamical similarity index proposed by Le Van Quyen et al. [Anticipating epileptic seizures in real time by a non-linear analysis of similarity between EEG recordings, NeuroReport 10 (1999) 2149–2155], the tests of twelve rats show the new dynamical similarity index is better to predict the epileptic seizures.