Chaos in a Discrete Dynamic Model of Traffic Flow

2007 ◽  
Author(s):  
Meng Xu ◽  
Ziyou Gao
Keyword(s):  
Traffic Flow ◽  
Dynamic Models ◽  
Chaotic Behavior ◽  
Flow Speed ◽  
Free Flow ◽  
Flow Density ◽  
Fundamental Diagram ◽  
Discrete Dynamic ◽  
Curve Model ◽  
Two Parameters

This paper aims to discuss unstable traffic flow and to identify if chaotic phenomena exist in a traffic flow dynamic system. Two discrete dynamic models are proposed, which are derived from the flow-density-speed fundamental diagram and Del Castillo and Benitez’s exponential curve model and maximum sensitivity curve model. Both the models have two parameters, which are the ratio of free flow and spacing average speed and the ratio of the absolute value of kinematic wave speed at jam density and free flow speed. Chaos is found in the two models when the two values increase separately. The Liapunov exponents were used to examine the characters of the chaotic behavior in the two models. These results are illustrated by numerical examples.

Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Meng Xu ◽  
Ziyou Gao
Keyword(s):  
Wave Speed ◽  
Dynamic Models ◽  
Road Traffic ◽  
Discrete Dynamical System ◽  
Flow Speed ◽  
Free Flow ◽  
Traffic Flows ◽  
Absolute Value ◽  
Curve Model ◽  
Two Parameters

In this paper, we investigate the dynamic behavior of road traffic flows and study if chaotic phenomena exist in a traffic flow dynamic system. Two discrete dynamic models are proposed, which are derived from Del Castillo and Benitez’s exponential curve model and maximum sensitivity curve model. Both models have two parameters, which are the ratio of free flow and spacing average speed and the ratio of the absolute value of kinematic wave speed at jam density and the free flow speed. Chaos is found in the two models when the two values increase separately. The Lyapunov exponents and fractal dimension were used to examine the characters of the chaos in the two models.

Impact of Rainfall Condition on Traffic Flow and Speed: A Case Study in Johor and Terengganu

2014 ◽  
Vol 70 (4) ◽  
Author(s):  
Nordiana Mashros ◽  
Johnnie Ben- Edigbe ◽  
Sitti Asmah Hassan ◽  
Norhidayah Abdul Hassan ◽  
Nor Zurairahetty Mohd Yunus
Keyword(s):  
Traffic Flow ◽  
Monsoon Season ◽  
Flow Speed ◽  
Free Flow ◽  
Road User ◽  
Traffic Data ◽  
Average Volume ◽  
Rainfall Condition ◽  
Free Flow Speed ◽  
The Impact

This paper explores the impact of various rainfall conditions on traffic flow and speed at selected location in Terengganu and Johor using data collected on two-lane highway. The study aims to quantify the effect of rainfall on average volume, capacity, mean speed, free-flow speed and speed at capacity. This study is important to come out with recommendation for managing traffic under rainfall condition. Traffic data were generated using automatic traffic counters for about three months during the monsoon season. Rainfall data were obtained from nearest surface rain gauge station. Detailed vehicular information logged by the counters were retrieved and processed into dry and various rainfall conditions. Only daylight traffic data have been used in this paper. The effect of rain on traffic flow and speed for each condition were then analysed separately and compared. The results indicated that average volumes shows no pronounce effect under rainfall condition compared to those under dry condition. Other parameters, however, show a decrease under rainfall condition. Capacity dropped by 2-32%, mean speed, free-flow speed and speed at capacity reduced by 3-14%, 1-14% and 3-17%, respectively. The paper recommends that findings from the study can be incorporated with variable message sign, local radio and television, and variable speed limit sign which should help traffic management to provide safer and more proactive driving experiences to the road user. The paper concluded that rainfall irrespective of their intensities have impact on traffic flow and speed except average volume.

MODIFIED COMFORTABLE DRIVING MODEL FOR CONGESTED TRAFFIC FLOW

2004 ◽  
Vol 18 (14) ◽  
pp. 1991-2001 ◽  
Author(s):  
RUI JIANG ◽  
QING-SONG WU
Keyword(s):  
Time Series ◽  
Computer Simulation ◽  
Traffic Flow ◽  
Red Light ◽  
Flow Density ◽  
Traffic Patterns ◽  
Fundamental Diagram ◽  
Average Data ◽  
Congested Traffic ◽  
Driving Model

In this paper, the concepts of "jammed status" and "jam headway" [X. B. Li, R. Jiang and Q. S. Wu, Phys. Rev.E68, 016117 (2003)] are introduced into the Modified Comfortable Driving (MCD) model [R. Jiang and Q. S. Wu, J. Phys.A36, 381 (2003)] to simulate the congested traffic flow including synchronized flow and wide moving jams. Using computer simulation, the fundamental diagram, the space–time plots, the time series of the density in the jams, the 1-min average data in the flow-density plane, the traffic patterns induced by red light are investigated. It is shown that the new model can describe both the synchronized flow and the sparse wide jams quite well.

scholarly journals Mixed Vehicular Traffic Flow Model on an Inclined Multilane Road

2020 ◽  
Vol 5 (7) ◽  
pp. 331-342
Author(s):  
Delina Mshai Mwalimo ◽  
Mary Wainaina ◽  
Winnie Kaluki
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Traffic Management ◽  
Flow Model ◽  
Free Flow ◽  
Traffic Density ◽  
Fundamental Diagram ◽  
Traffic Flow Model ◽  
The Road ◽  
Slow Moving

This study outlines the Kerner’s 3 phase traffic flow theory, which states that traffic flow occurs in three phases and these are free flow, synchronized flow and wide moving jam phase. A macroscopic traffic model that is factoring road inclination is developed and its features discussed. By construction of the solution to the Rienmann problem, the model is written in conservative form and solved numerically. Using the Lax-Friedrichs method and going ahead to simulate traffic flow on an inclined multi lane road. The dynamics of traffic flow involving cars(fast moving) and trucks(slow moving) on a multi-lane inclined road is studied. Generally, trucks move slower than cars and their speed is significantly reduced when they are moving uphill on an in- clined road, which leads to emergence of a moving bottleneck. If the inclined road is multi-lane then the cars will tend to change lanes with the aim of overtaking the slow moving bottleneck to achieve free flow. The moving bottleneck and lanechange ma- noeuvres affect the dynamics of flow of traffic on the multi-lane road, leading to traffic phase transitions between free flow (F) and synchronised flow(S). Therefore, in order to adequately describe this kind of traffic flow, a model should incorporate the effect of road inclination. This study proposes to account for the road inclination through the fundamental diagram, which relates traffic flow rate to traffic density and ultimately through the anticipation term in the velocity dynamics equation of macroscopic traffic flow model. The features of this model shows how the moving bottleneck and an incline multilane road affects traffic transistions from Free flow(F) to Synchronised flow(S). For a better traffic management and control, proper understanding of traffic congestion is needed. This will help road designers and traffic engineers to verify whether traffic properties and characteristics such as speed(velocity), density and flow among others determines the effectiveness of traffic flow.

scholarly journals Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Martin Gugat
Keyword(s):  
Traffic Flow ◽  
Control Function ◽  
Piecewise Linear ◽  
Lipschitz Constant ◽  
Initial Density ◽  
Free Flow ◽  
Flow Density ◽  
Initial State ◽  
Lipschitz Continuous ◽  
Continuous State

We consider traffic flow governed by the LWR model. We show that a Lipschitz continuous initial density with free-flow and sufficiently small Lipschitz constant can be controlled exactly to an arbitrary constant free-flow density in finite time by a piecewise linear boundary control function that controls the density at the inflow boundary if the outflow boundary is absorbing. Moreover, this can be done in such a way that the generated state is Lipschitz continuous. Since the target states need not be close to the initial state, our result is a global exact controllability result. The Lipschitz constant of the generated state can be made arbitrarily small if the Lipschitz constant of the initial density is sufficiently small and the control time is sufficiently long. This is motivated by the idea that finite or even small Lipschitz constants are desirable in traffic flow since they might help to decrease the speed variation and lead to safer traffic.

The Waterway Service Level Research of Xijiang Waterway in Zhaoqing Area

2014 ◽  
Vol 505-506 ◽  
pp. 443-448
Author(s):  
Jian Tan ◽  
Wen Lei Cao ◽  
Wei Chun Zhang ◽  
Jia Yi Yang
Keyword(s):  
Traffic Flow ◽  
Load Ratio ◽  
Service Level ◽  
Flow Speed ◽  
Traffic Load ◽  
Flow Density ◽  
The Road ◽  
Comprehensive Service ◽  
Service Quality Evaluation ◽  
Four Levels

The paper introduced the conception of the Waterway Service Level according to the Road Service Level to analyze waterway traffic load conditions.The Waterway Service Leve is a measure of service quality evaluation of comprehensive service and object feeling provided by the waterway subject to a service object and it can be classified into four levels according to vessel traffic flow density,vessel traffic flow speed,a one-way vessel service traffic volume,the traffic load ratio (V/C) and so on.After study,we found it's urgent to improve the waterway capacity and service level of Xijiang Waterway in Zhaoqing area,and the through capacity of the waterway has more room to improve,so we put forward some suggestions for waterway construction and sailing management.

scholarly journals EFFECTS OF ON- AND OFF-RAMPS IN CELLULAR AUTOMATA MODELS FOR TRAFFIC FLOW

2000 ◽  
Vol 11 (02) ◽  
pp. 335-345 ◽  
Author(s):  
G. DIEDRICH ◽  
L. SANTEN ◽  
A. SCHADSCHNEIDER ◽  
J. ZITTARTZ
Keyword(s):  
Phase Separation ◽  
Cellular Automata ◽  
Traffic Flow ◽  
Free Flow ◽  
Local Perturbation ◽  
Traffic Networks ◽  
Input Rate ◽  
Fundamental Diagram ◽  
Different Types ◽  
Density Regime

We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel–Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain density regime ρ low < ρ < ρ high one observes plateau formation in the fundamental diagram. The plateau value depends on the input-rate of cars at the on-ramp. The on-ramp acts as a local perturbation that separates the system into two regimes: A regime of free flow and another one where only jammed states exist. This phase separation is the reason for the plateau formation and implies a behavior analogous to that of stationary defects. This analogy allows to perform very fast simulations of complex traffic networks with a large number of on- and off-ramps because one can parametrise on-ramps in an exceedingly easy way.

Width-Based Cell Transmission Model for Heterogeneous and Undisciplined Traffic Streams

2019 ◽  
Vol 2673 (5) ◽  
pp. 682-692 ◽  
Author(s):  
Afzal Ahmed ◽  
Satish V. Ukkusuri ◽  
Shahrukh Raza Mirza ◽  
Ausaja Hassan
Keyword(s):  
Traffic Flow ◽  
Behavior Modeling ◽  
Flow Diagram ◽  
Transmission Model ◽  
Flow Density ◽  
Cell Transmission Model ◽  
Fundamental Diagram ◽  
Flow Models ◽  
Cell Transmission ◽  
Traffic Flow Models

Traffic streams in many developing countries consist of various modes of transport, with high heterogeneity in driver behavior. Modeling these types of traffic streams, in which traffic rules (speed limit, lane discipline, etc.) are not strictly followed, is a complex task. A review of the existing literature shows that there is a lack of traffic flow models that model the behavior of heterogeneous and undisciplined traffic streams. Like other undisciplined traffic streams, there are no speed limits (hence no speed enforcement) on most of the roads in Karachi, Pakistan. Lane discipline is also not observed by drivers, which results in a varying number of traffic lanes on a road. Therefore, most of the existing traffic flow models/simulation packages developed for disciplined traffic streams cannot appropriately model traffic streams without lane discipline. This research proposes a width-based cell transmission model (WCTM) by developing a fundamental flow-density diagram whose parameters are a function of the road width. Extensive field data have been collected from a selected arterial in Karachi for development of the fundamental traffic flow diagram. The values of the computed parameters are significantly different than the values reported in the literature. The piecewise-linear flow-density relation is developed by optimally estimating the breakpoints. Results show that the quadrilateral and pentagonal-shaped fundamental diagrams fit better with the collected data in comparison with the triangular-shaped fundamental diagram. The proposed WCTM is applied to selected segments of an arterial and results show that the WCTM was able to accurately model different traffic conditions.

OPTIMIZATION OF TRAFFIC LIGHTS AT CROSSROADS

2003 ◽  
Vol 14 (05) ◽  
pp. 539-548 ◽  
Author(s):  
DING-WEI HUANG ◽  
WEI-NENG HUANG
Keyword(s):  
Traffic Flow ◽  
Probabilistic Models ◽  
Urban Traffic ◽  
Speed Limit ◽  
Stochastic Noise ◽  
Traffic Light ◽  
Fundamental Diagram ◽  
Traffic Lights ◽  
Signal Period ◽  
Two Parameters

We study the influence of traffic lights on the traffic flow in cities. The urban traffic is simulated in the cellular automata framework. Both the deterministic and probabilistic models are discussed. The effects of speed limit and stochastic noise are analyzed. The operation of a traffic light is characterized by two parameters: signal period and phase allocation. With two traffic lights on road, one more parameter is prescribed: synchronization shift. The results of tuning these parameters are presented in the fundamental diagram. We examine the traffic flow and discuss the choice of optimized setting in different density regions.

scholarly journals Empirical Approximation for the Stochastic Fundamental Diagram of Traffic Flow on Signalized Intersection

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Nan Zhang ◽  
Xiaoguang Yang ◽  
Wangjing Ma
Keyword(s):  
Traffic Flow ◽  
Bayesian Learning ◽  
Likelihood Estimation ◽  
Signalized Intersection ◽  
Traffic Density ◽  
Flow Density ◽  
Fundamental Diagram ◽  
Flow Process ◽  
Linear Dynamical Systems ◽  
Density Data

The wide scattering nature of the fundamental diagram (FD) with observed flow-density data may be associated with the dynamical traffic flow process, especially on signalized intersection. To describe the uncertainty of FD, in this work we established stochastic fundamental diagram (SFD) which is defined by the distributions of shockwave speed. Our approach is based on a two-level stochastic process of the traffic flow system in terms of the dynamics of traffic density and state mode associated with signal phases which is named switching linear dynamical systems (SLDS). Then, variational Bayesian learning method is adopted to compute the distributions of SFD parameter to approximate the experimental distributions of shockwave calculated by the observed flow-density data. Given traffic flow data from the NGSIM program, the verification result demonstrated that the SFD can be more helpful to capture the main features of the observed widely scattering of the flow-density data compared with FD. With the shockwave speed sampled from the SFD, the SLDS could describe the dynamic characteristics of traffic flow and be applied to the maximum likelihood estimation of traffic density or flow rate. Because it is simple and automatically calculated, the SFD provides an alternative description for fundamental diagram and its uncertainty in the traffic flow.

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