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.

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.

Simple, Generalized Method for Analysis of Traffic Queue Upstream of a Bottleneck

1998 ◽  
Vol 1646 (1) ◽  
pp. 132-140 ◽  
Author(s):  
Alan L. Erera ◽  
Tim W. Lawson ◽  
Carlos F. Daganzo
Keyword(s):  
Traffic Flow ◽  
Piecewise Linear ◽  
Wave Theory ◽  
Flow Density ◽  
Cumulative Number ◽  
Kinematic Wave ◽  
Input Output ◽  
Original Technique ◽  
Time Space ◽  
Bottleneck Capacity

An approach is generalized for enhancing a standard input-output diagram to represent graphically the time and distance that vehicles spend in a queue upstream of a bottleneck. The approach requires the construction of a curve depicting the cumulative number of vehicles to have reached the back of the queue as a function of time. The original technique, described in a previous paper, is reviewed for bottlenecks with constant capacity and for those where capacity changes once. The approach is then generalized to allow multiple changes in bottleneck capacity, and the original assumption of a triangular flow-density ( q-k) relation is relaxed to one that is piecewise-linear concave. Although it is consistent with the kinematic wave theory of traffic flow, the proposed approach is simpler to apply to complex problems because it avoids the laborious construction of a time-space diagram. It allows the estimation of several measures required in the evaluation of the impacts of bottlenecks, including the (accurate) number of vehicles in queue and the physical extents of queues at any time and the total time spent by vehicles in different traffic states.

scholarly journals An Eco-Friendly Multimodal Route Guidance System for Urban Areas Using Multi-Agent Technology

2021 ◽  
Vol 11 (5) ◽  
pp. 2057
Author(s):  
Abdallah Namoun ◽  
Ali Tufail ◽  
Nikolay Mehandjiev ◽  
Ahmed Alrehaili ◽  
Javad Akhlaghinia ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Urban Areas ◽  
Urban Environments ◽  
Ease Of Use ◽  
Transport Infrastructure ◽  
Guidance System ◽  
Planning System ◽  
Flow Density ◽  
Route Guidance ◽  
Agent Based

The use and coordination of multiple modes of travel efficiently, although beneficial, remains an overarching challenge for urban cities. This paper implements a distributed architecture of an eco-friendly transport guidance system by employing the agent-based paradigm. The paradigm uses software agents to model and represent the complex transport infrastructure of urban environments, including roads, buses, trolleybuses, metros, trams, bicycles, and walking. The system exploits live traffic data (e.g., traffic flow, density, and CO2 emissions) collected from multiple data sources (e.g., road sensors and SCOOT) to provide multimodal route recommendations for travelers through a dedicated application. Moreover, the proposed system empowers the transport management authorities to monitor the traffic flow and conditions of a city in real-time through a dedicated web visualization. We exhibit the advantages of using different types of agents to represent the versatile nature of transport networks and realize the concept of smart transportation. Commuters are supplied with multimodal routes that endeavor to reduce travel times and transport carbon footprint. A technical simulation was executed using various parameters to demonstrate the scalability of our multimodal traffic management architecture. Subsequently, two real user trials were carried out in Nottingham (United Kingdom) and Sofia (Bulgaria) to show the practicality and ease of use of our multimodal travel information system in providing eco-friendly route guidance. Our validation results demonstrate the effectiveness of personalized multimodal route guidance in inducing a positive travel behavior change and the ability of the agent-based route planning system to scale to satisfy the requirements of traffic infrastructure in diverse urban environments.

scholarly journals Research on the impact of ship traffic flow on the restricted channel segment of the middle Yangtze River based on traffic wave theory

2021 ◽  
Vol 3 (8) ◽  
Author(s):  
Ting Liu ◽  
Gabriel Lodewijks
Keyword(s):  
Traffic Flow ◽  
Flow Rate ◽  
Flow Simulation ◽  
Wave Theory ◽  
Flow Density ◽  
List Type ◽  
Ship Traffic ◽  
Traffic Wave ◽  
The Impact ◽  
Channel Segment

Abstract Abstract On the basis of the influence of dry season on ship traffic flow, the gathering and dissipating process of ship traffic flow was researched with Greenshields linear flow—density relationship model, the intrinsic relationship between the ship traffic congestion state and traffic wave in the unclosed restricted channel segment was emphatically explored when the ship traffic flow in a tributary channel inflows, and the influence law of multiple traffic waves on the ship traffic flow characteristics in unclosed restricted segment is revealed. On this basis, the expressions of traffic wave speed and direction, dissipation time of queued ships and the number of ships affected were provided, and combined with Monte Carlo method, the ship traffic flow simulation model in the restricted channel segment was built. The simulation results show that in closed restricted channel segment the dissipation time of ships queued is mainly related to the ship traffic flow rate of segments A and C, and the total number of ships affected to the ship traffic flow rate of segment A. And in unclosed restricted channel segment, the dissipation time and the total number of ships affected are also determined by the meeting time of the traffic waves in addition to the ship traffic flow rate of segments. The research results can provide the theoretical support for further studying the ship traffic flow in unclosed restricted channel segment with multiple tributaries Article Highlights The inflow of tributaries' ship traffic flows has an obvious impact on the traffic conditions in the unenclosed restricted channel segment. The interaction and influence between multiple ship traffic waves and the mechanism of generating new traffic waves are explained. The expression of both dissipation time of queued ships and the total number of ships affected in the closed and unclosed restricted channel segment are given.

Evolvement law of a macroscopic traffic model accounting for density-dependent relaxation time

2017 ◽  
Vol 31 (31) ◽  
pp. 1750291 ◽  
Author(s):  
Yu-Qing Wang ◽  
Xing-Jian Chu ◽  
Chao-Fan Zhou ◽  
Bin Jia ◽  
Sen Lin ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Traffic Flow ◽  
Flow Model ◽  
Initial Density ◽  
Traffic Model ◽  
Traffic Flow Model ◽  
Density Dependent ◽  
Macroscopic Traffic Flow ◽  
Boundary Perturbations ◽  
Initial Density Distribution

In this paper, a modified macroscopic traffic flow model is presented. The term of the density-dependent relaxation time is introduced here. The relation between the relaxation time and the density in traffic flow is presented quantitatively. Besides, a factor R depicting varied properties of traffic flow in different traffic states is also introduced in the formulation of the model. Furthermore, the evolvement law of traffic flow with distinctly initial density distribution and boundary perturbations is emphasized.

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.

Macroscopic Simulation of Traffic Flow on Continuum Urban Networks

2014 ◽  
Vol 641-642 ◽  
pp. 887-891 ◽  
Author(s):  
Yan Qun Jiang ◽  
Shu Guang Zhou
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Choice Model ◽  
Macroscopic Model ◽  
Flow Density ◽  
Urban Network ◽  
Urban Networks ◽  
Richards Model ◽  
Macroscopic Simulation ◽  
Dynamical Features

In this paper, a macroscopic model is applied to simulate dynamical features of traffic flow on a continuum urban network. This model is described as the two-dimensional Lighthill-Whitham-Richards model coupled with a reactive dynamic user-optimal route choice model. Numerical results visualize the ability of the model to predict some macroscopic characteristics of traffic flow on networks, i.e. the spatial distribution of flow density and travel cost of users, as well as to capture traffic congestion build-up and dissipation.

scholarly journals Urban Wasteful Transport and Its Estimation Methods

2018 ◽  
Vol 10 (12) ◽  
pp. 4562 ◽  
Author(s):  
Xiangyang Cao ◽  
Bingzhong Zhou ◽  
Qiang Tang ◽  
Jiaqi Li ◽  
Donghui Shi
Keyword(s):  
Traffic Flow ◽  
Traffic Congestion ◽  
Transport Theory ◽  
Road Traffic ◽  
Urban Traffic ◽  
Flow Density ◽  
Urban Road ◽  
Road Capacity ◽  
Density Relationship

The paper studies urban road traffic problems from the perspective of resource science. The resource composition of urban road traffic system is analysed, and the road network is proved as a scarce resource in the system resource combination. According to the role of scarce resources, the decisive role of road capacity in urban traffic is inferred. Then the new academic viewpoint of “wasteful transport” was proposed. Through in-depth research, the paper defines the definition of wasteful transport and expounds its connotation. Through the flow-density relationship analysis of urban road traffic survey data, it is found that there is a clear boundary between normal and wasteful transport in urban traffic flow. On the basis of constructing the flow-density relationship model of road traffic, combined with investigation and analysis, the quantitative estimation method of wasteful transport is established. An empirical study on the traffic conditions of the Guoding section of Shanghai shows that there is wasteful transport and confirms the correctness of the wasteful transport theory and method. The research of urban wasteful transport also reveals that: (1) urban road traffic is not always effective; (2) traffic flow exceeding road capacity is wasteful transport, and traffic demand beyond the capacity of road capacity is an unreasonable demand for customers; (3) the explanation that the traffic congestion should apply the comprehensive theory of traffic engineering and resource economics; and (4) the wasteful transport theory and method may be one of the methods that can be applied to alleviate traffic congestion.

Piecewise continuous solutions of nonlinear pseudoparabolic equations in two space dimensions*

1992 ◽  
Vol 121 (3-4) ◽  
pp. 203-217 ◽  
Author(s):  
Dao-Qing Dai ◽  
Wei Lin
Keyword(s):  
Lipschitz Constant ◽  
Complex Function ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Lipschitz Continuous ◽  
Two Space Dimensions ◽  
Image Position ◽  
Initial Boundary Value ◽  
Pseudoparabolic Equations ◽  
Nonlinear Pseudoparabolic Equation

SynopsisAn initial boundary value problem of Riemann type is solved for the nonlinear pseudoparabolic equation with two space variablesThe complex functionHis measurable on ℂ ×I × ℂ5, withIbeing an interval of the real line ℝ, Lipschitz continuous with respect to the last five variables, with the Lipschitz constant for the last variable being strictly less than one (ellipticity condition). No smallness assumption is needed in the argument.

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