THE HOMEOMORPHIC PROPERTY OF THE STOCHASTIC FLOW GENERATED BYTHE ONE-DEFAULT MODEL IN ONE DIMENSIONAL CASE

In this paper, we will try to study the same result proved in \cite{10}. So, on the same model and with some assumptions, we will study the property of homeomorphism of the stochastic flow generated by the natural model in a one-dimensional case and with some modifications, based on an important theory of Hiroshi Kunita. This is the main motivation of our research.

System Reliability Optimization of Multi-Source Multi-Sink Stochastic Flow Networks With Budget Constraint

In this paper, we investigate system reliability optimization of multi-source multi-sink flow networks subject to transmission budget constraints. More specifically, we present a mathematical model of the optimization problem and a genetic algorithm (GA) to solve it. The GA is based on determining the optimal set of lower boundary points that maximize system reliability such that transmission cost does not exceed a specified upper bound. Finally, to ensure the efficiency of our approach, we apply our proposed algorithm to various network examples.

Statistical Characteristics of Optical Signals and Images in Machine Vision Systems

The chapter is devoted to the creation of a comprehensive approach to the physical and mathematical description of signals in optoelectronics in machine vision, taking into account the phenomena of interaction of optical radiation with system elements. A new methodology for the study of the statistical properties of input and output signals in optoelectronic systems is proposed, taking into account the availability of grouped statistical properties that do not obey the Poisson statistics. The basis is the joint use of wave and corpuscular description of signals in systems, stochastic flow theories, and elements of statistical detection theory. Information and energetic technology have been developed that integrates the theoretical justification of signal description under various observation conditions and decision-making methods.

Impact of Stochasticity on Traffic Flow Dynamics in Macroscopic Continuum Models

Stochasticity is an indispensable factor for describing real traffic situations. Recent experimental study has shown that a model spanning a two-dimensional speed–spacing (or speed–density) relationship has the potential to reproduce the characteristics of traffic flow in both experiments and empirical observations. This paper studies the impact of stochasticity on traffic flow in macroscopic models utilizing the stochastic flow–density relationship. Numerical analysis is conducted under the periodic boundary to study the impact of stochasticity on stability. Traffic flow upstream of a bottleneck is also investigated to study the impact of stochasticity on the oscillation growth feature. It is shown that there is only a quantitative difference for model stability after introducing stochasticity. In contrast, a qualitative change of the traffic oscillation growth feature can be clearly observed. With the introduction of stochasticity, traffic oscillations begin to grow in a concave way along the road. Sensitivity analysis is also performed. It is found that, under the stochastic flow–density relationship: (i) with the decrease of relaxation time, the second-order model becomes stable; (ii) the smaller the propagation speed of small disturbance, the much stronger the traffic oscillation; (iii) the larger the fluctuation range, the sooner the traffic oscillation fully develops; and (iv) the changing probability has trivial impact on the simulation results. Finally, model calibration and validation are conducted. It is shown that the experimental spatiotemporal patterns can be captured by macroscopic models under the stochastic flow–density relationship, especially the second-order model.