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.

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.

scholarly journals Fundamental Diagram Estimation Based on Random Probe Pairs on Sub-Segments

2021 ◽  
Vol 33 (5) ◽  
pp. 717-730
Author(s):  
Xiaoli Deng ◽  
Yao Hu ◽  
Qian Hu
Keyword(s):  
Wave Speed ◽  
Traffic Monitoring ◽  
Flow Speed ◽  
Urban Traffic ◽  
Free Flow ◽  
Fundamental Diagram ◽  
Traffic State ◽  
Expectation Maximisation ◽  
Free Flow Speed ◽  
Backward Wave

A new statistical algorithm is proposed in this paper with the aim of estimating fundamental diagram (FD) in actual traffic and dividing the traffic state. Traditional methods mainly focus on sensor data, but this paper takes random probe pairs as research objects. First, a mathematical method is proposed by using probe pairs data and the jam density to determine the FD on a stationary segment. Second, we applied it to the near-stationary probe traffic state set through linear regression and expectation maximisation iterative algorithm, estimating the free flow speed and the backward wave speed and dividing the traffic state based on the 95% confidence interval of the estimated FD. Finally, simulation and empirical analyses are used to verify the new algorithm. The simulation analysis results show that the estimation error corresponding to the free flow speed and the backward wave speed are 1.0668 km/h and 0.0002 km/h respectively. The empirical analysis calculates the maximum capacity of the road and divides the traffic into three states (free flow state, breakdown state, and congested state), which demonstrates the accuracy and practicability of the research in this paper, and provides a reference for urban traffic monitoring and government decision-making.

Empirical Assessment and Modeling of Traffic-induced Air Pollution

2021 ◽  
pp. 036119812110237
Author(s):  
Zhongyang Lu ◽  
Andy H. F. Chow ◽  
Jacky Leung ◽  
Haydn Kwok ◽  
Sammy Cheung
Keyword(s):  
Air Pollution ◽  
Hong Kong ◽  
Road Network ◽  
Historical Data ◽  
Flow Speed ◽  
Traffic Flows ◽  
Real World Data ◽  
Empirical Assessment ◽  
Air Quality Monitoring Stations ◽  
Transport Management

Congestion and traffic-induced air pollution are associated with population growth and economic development. Compared with congestion, there are relatively few studies on modeling and assessment of traffic-induced pollution. This paper presents an empirical assessment and analysis of traffic-induced air pollution with real-world data collected from the Hong Kong Strategic Road Network. The study employed historical data of traffic flows, speeds, and emission of air pollutants collated by the Hong Kong Transport Department and Environmental Protection Department. This paper first reveals the correlation between traffic flows, speeds, and corresponding induced pollutants including nitrogen oxides (NO2, NOX) and carbon monoxide (CO). To gain further statistical insight, a regression analysis was conducted on the flow–speed–emission relationship at three air quality monitoring stations, which revealed the significance of various factors on this relationship. This study contributes to green transport management and urban sustainability.

Local Mass Conservation and Velocity Splitting in PV-Based Balanced Models. Part II: Numerical Results

2007 ◽  
Vol 64 (6) ◽  
pp. 1794-1810 ◽  
Author(s):  
Ali R. Mohebalhojeh ◽  
Michael E. McIntyre
Keyword(s):  
Potential Vorticity ◽  
Wave Speed ◽  
Invariant Manifolds ◽  
Mass Conservation ◽  
Flow Speed ◽  
Local Mass ◽  
Potential Vorticity Inversion ◽  
Divergence Equation ◽  
Local Mass Conservation ◽  
Derivatives Of

The effects of enforcing local mass conservation on the accuracy of non-Hamiltonian potential-vorticity- based balanced models (PBMs) are examined numerically for a set of chaotic shallow-water f-plane vortical flows in a doubly periodic square domain. The flows are spawned by an unstable jet and all have domain-maximum Froude and Rossby numbers Fr ∼0.5 and Ro ∼1, far from the usual asymptotic limits Ro → 0, Fr → 0, with Fr defined in the standard way as flow speed over gravity wave speed. The PBMs considered are the plain and hyperbalance PBMs defined in Part I. More precisely, they are the plain-δδ, plain-γγ, and plain-δγ PBMs and the corresponding hyperbalance PBMs, of various orders, where “order” is related to the number of time derivatives of the divergence equation used in defining balance and potential-vorticity inversion. For brevity the corresponding hyperbalance PBMs are called the hyper-δδ, hyper-γγ, and hyper-δγ PBMs, respectively. As proved in Part I, except for the leading-order plain-γγ each plain PBM violates local mass conservation. Each hyperbalance PBM results from enforcing local mass conservation on the corresponding plain PBM. The process of thus deriving a hyperbalance PBM from a plain PBM is referred to for brevity as plain-to-hyper conversion. The question is whether such conversion degrades the accuracy, as conjectured by McIntyre and Norton. Cumulative accuracy is tested by running each PBM alongside a suitably initialized primitive equation (PE) model for up to 30 days, corresponding to many vortex rotations. The accuracy is sensitively measured by the smallness of the ratio ϵ = ||QPBM − QPE||2/||QPE||2, where QPBM and QPE denote the potential vorticity fields of the PBM and the PEs, respectively, and || ||2 is the L2 norm. At 30 days the most accurate PBMs have ϵ ≈ 10−2 with PV fields hardly distinguishable visually from those of the PEs, even down to tiny details. Most accurate is defined by minimizing ϵ over all orders and truncation types δδ, γγ, and δγ. Contrary to McIntyre and Norton’s conjecture, the minimal ϵ values did not differ systematically or significantly between plain and hyperbalance PBMs. The smallness of ϵ suggests that the slow manifolds defined by the balance relations of the most accurate PBMs, both plain and hyperbalance, are astonishingly close to being invariant manifolds of the PEs, at least throughout those parts of phase space for which Ro ≲ 1 and Fr ≲ 0.5. As another way of quantifying the departures from such invariance, that is, of quantifying the fuzziness of the PEs’ slow quasimanifold, initialization experiments starting at days 1, 2, . . . 10 were carried out in which attention was focused on the amplitudes of inertia–gravity waves representing the imbalance arising in 1-day PE runs. With balance defined by the most accurate PBMs, and imbalance by departures therefrom, the results of the initialization experiments suggest a negative correlation between early imbalance and late cumulative error ϵ. In such near-optimal conditions the imbalance seems to be acting like weak background noise producing an effect analogous to so-called stochastic resonance, in that a slight increase in noise level brings PE behavior closer to the balanced behavior defined by the most accurate PBMs when measured cumulatively over 30 days.

LIGHT REGULATION SYSTEMS IMPROVEMENT ANALYSIS TO FORECAST THE TRANSPORT FLOWS IN ALMATY

2021 ◽  
Vol 116 (1) ◽  
pp. 299-304
Author(s):  
Assel Aliyadynovna Sailau
Keyword(s):  
Environmental Pollution ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Light Regulation ◽  
Transport Network ◽  
Traffic Flows ◽  
Traffic Light ◽  
Traffic Lights ◽  
The Road ◽  
Transport Telematics

The number of vehicles on the roads of Almaty, Kazakhstan is growing from year to year. This brings about an increasing intensity and density of traffic flows in the streets which leads to congestion, decreasing speed of the traffic flow, increasing environmental pollution caused by car emissions, and which can potentially lead to the road traffic accidents (RTA), including fatalities. While the number of injuries grows up mainly due to drivers’ non-compliance with the speed limit, the environmental pollution is caused by longer traffic jams. Therefore, to reduce the level of road traffic injuries and emissions into the environment it is necessary to ensure the uniform movement of traffic flows in cities. Currently, one of the effective ways to do it is the use of transport telematics systems, in particular, control systems for road signs, road boards and traffic lights. The paper presents an analysis of existing systems and methods of traffic light regulation. The  analyses of the systems and methods are based on the use of homogeneous data, that is the data on standard parameters of traffic flows. The need in collecting and analyzing additional semi-structured data on the factors that have a significant impact on the traffic flows parameters in cities is shown as well. The work is dedicated to solving the problem of analysis and forecast of traffic flows in the city of Almaty, Kazakhstan. GPS data on the location of individual vehicles is used as the initial data for solving this problem. By projecting the obtained information onto the graph of the city's transport network, as well as using additional filtering, it is possible to obtain an estimate of individual parameters of traffic flows. These parameters are used for short-term forecast of the changes in the city's transport network.

Application of Moving Car Observer Method for Measuring Free Flow Speed on Two-lane Highways

2014 ◽  
Vol 69 (6) ◽  
Author(s):  
Othman Che Puan ◽  
Muttaka Na’iya Ibrahim ◽  
Usman Tasiu Abdurrahman
Keyword(s):  
Field Measurement ◽  
Flow Speed ◽  
Operating Conditions ◽  
Free Flow ◽  
Geometric Features ◽  
Highway Capacity ◽  
Highway Capacity Manual ◽  
Free Flow Speed ◽  
The Subject ◽  
Low Traffic

There exists a need to evaluate the performance indicator that reflects the current level of service (LOS) of the subject facility to justify any decision making on expenditures to be made for improving the performance level of a road facility. Free-flow speed (FFS) is one of the key parameters associated with LOS assessment for two-lane highways. Application of a more realistic approach for assessing road’s performance indicators would result in better estimates which could in turn suggest the most appropriate decision to be made (for situations where upgrading is needed); especially, in terms of finance, materials and human resources. FFS is the driver’s desired speed at low traffic volume condition and in the absence of traffic control devices. Its estimation is significant in the analysis of two-lane highways through which average travel speed (ATS); an LOS indicator for the subject road class is determined. The Highway Capacity Manual (HCM) 2010 offers an indirect method for field estimation of FSS based on the highway operating conditions in terms of base-free-flow-speed (BFFS). It is however, recommended by the same manual that direct field FSS measurement approach is most preferred. The Malaysian Highway Capacity Manual (MHCM) established a model for estimating FFS based on BFFS, the geometric features of the highway and proportion of motorcycles in the traffic stream. Estimating FFS based on BFFS is regarded as an indirect approach which is only resorted to, if direct field measurement proved difficult or not feasible. This paper presents the application of moving car observer (MCO) method for direct field measurement of FFS. Data for the study were collected on six segments of two-lane highways with varying geometric features. FFS estimates from MCO method were compared with those based on MHCM model. Findings from the study revealed that FFS values from MCO method seem to be consistently lower than those based on MHCM model. To ascertain the extent of the difference between the FFS values from the two approaches, student t-statistics was used. The t-statistics revealed a P–value of less than 0.05 (P < 0.05) which implies that there is a statistically significant difference between the two sets of data. Since MCO method was conducted under low traffic flow (most desired condition for field observation), it can be suggested that MCO estimates of FFS represent the actual scenario. A relationship was therefore developed between the estimates from the two methods. Thus, if the MHCM model is to be applied, the measured value needs to be adjusted based on the relationship developed between the two approaches.

scholarly journals Large amplitude, short wave peristalsis and its implications for transport

2015 ◽  
Author(s):  
Lindsay D Waldrop ◽  
Laura A. Miller
Keyword(s):  
Fluid Flow ◽  
Large Amplitude ◽  
Compression Wave ◽  
Wave Speed ◽  
Flow Direction ◽  
Short Wave ◽  
Flow Speed ◽  
Biological Pumps ◽  
Flow Speeds ◽  
Flow Compression

Valveless, tubular pumps are widespread in the animal kingdom, but the mechanism by which these pumps generate fluid flow are often in dispute. Where the pumping mechanism of many organs was once described as peristalsis, other mechanisms, such as dynamic suction pumping, have been suggested as possible alternative mechanisms. Peristalsis is often evaluated using criteria established in a technical definition for mechanical pumps, but this definition is based on a small-amplitude, long-wave approximation which biological pumps often violate. In this study, we use a direct numerical simulation of large-amplitude, short-wave peristalsis to investigate the relationships between fluid flow, compression frequency, compression wave speed, and tube occlusion. We also explore how the flows produced differ from the criteria outlined in the technical definition of peristalsis. We find that many of the technical criteria are violated by our model: fluid flow speeds produced by peristalsis are greater than the speeds of the compression wave; fluid flow is pulsatile; and flow speed have a non-linear relationship with compression frequency when compression wave speed is held constant. We suggest that the technical definition is inappropriate for evaluating peristalsis as a pumping mechanism for biological pumps because they too frequently violate the assumptions inherent in these criteria. Instead, we recommend that a simpler, more inclusive definition be used for assessing peristalsis as a pumping mechanism based on the presence of non-stationary compression sites that propagate uni-directionally along a tube without the need for a structurally fixed flow direction.

scholarly journals An Efficient Scheduling of Flyover at Grade Intersection under Mixed Traffic Environment

2021 ◽  
Vol 9 (VI) ◽  
pp. 824-833
Author(s):  
Shradha S. Zanjad
Keyword(s):  
Queue Length ◽  
Fixed Time ◽  
Flow Speed ◽  
Free Flow ◽  
Mixed Traffic ◽  
Time Control ◽  
Traffic Environment ◽  
Free Flow Speed ◽  
Big Cities

A flyover is a bridge constructed along an intersecting highway over an at-grade intersection. It allows two –direction traffic to flow at free flow speed on the bridge. The flyover is one of the methods for solving traffic problems at at-grade junctions on highways including capacity, congestion, long delay and queue length. Traffic signalization at the upgraded intersection often uses the same fixed time control plans, even after the installation of a flyover over the intersection. Most of the flyovers in India are constructed at the junctions on highway bypasses of big cities. The present work deals with a efficient scheduling of flyover at the grade intersection under the mixed traffic environment. From the results and the modeling carried out in the “SIDRA Intersection” software different points are observed. The present work consists of the Proposed Intersection at Rajkamal Square, Amravati.

scholarly journals ANALISIS KAPASITAS DAN KINERJA LALU LINTAS PADA RUAS JALAN JENDERAL SUDIRMAN JAKARTA

2021 ◽  
Vol 4 (1) ◽  
pp. 95
Author(s):  
Sarah Haryati ◽  
Najid Najid
Keyword(s):  
Flow Speed ◽  
Traffic Volume ◽  
Capital City ◽  
Free Flow ◽  
Degree Of Saturation ◽  
Level Of Service ◽  
Traffic Jam ◽  
Traffic Capacity ◽  
Traffic Behavior

Jakarta as the capital city of Indonesia is the center of economy, culture, and politics. Jenderal Sudirman street always crowded with passing vehicles, traffic snarls up everyday. The causes of these traffic jam is an increase the number of vehicles and cause a change in traffic behavior. Theoretically there is a fudamental relationship between flow, speed, & density, so the purpose of these research are to analyze and evaluate performance of traffic capacity in various conditions based on Manual Kapasitas Jalan Indonesia 1997 and Greenshields model. Conclusion of the analysis are, after compared with traffic volume, capacity and speed based on MKJI are 3.127,6 pcu/hour and 55,7 km/hour, but the capacity of the model are selected because it’s largest, for sudirman – thamrin it’s 8.272,5 pcu/hour, and for thamrin – sudirman it’s 8.067,9 pcu/hour, While the calculation of free flow for sudirman – thamrin it’s 41.2 km/hour the lowest occurs in  evening, and for thamrin – sudirman it’s 43,9 km/hour the lowest occurs in  afternoon. The largest capacity it’s used for the next analysis, the next analysis are calculating degree of saturation and level of service, the result  shows that the roads are at C and D.ABSTRAKJakarta ibu kota negara Indonesia merupakan pusat ekonomi, budaya, dan politik. Sebuah jalan di Jakarta yaitu Jenderal Sudirman selalu dipadati kendaraan. Lalu lintas di Jalan Jenderal Sudirman setiap hari mengalami kemacetan penyebabnya adalah peningkatan jumlah kendaraan di dalam kota dan menyebabkan perubahan perilaku lalu lintas, secara teoritis terdapat hubungan yang mendasar antara arus, kecepatan, dan kepadatan. Tujuan penelitian ini adalah untuk menganalisis, mengevaluasi kinerja dan kapasitas lalu lintas di berbagai macam kondisi, tentu berdasarkan pedoman Manual Kapasitas Jalan Indonesia dan kapasitas model Greenshields. Dari hasil analisis hasil perhitungan kapasitas dan kecepatan arus bebas berdasarkan MKJI sebesar 3.127,6 smp/jam dan 55,7 km/jam setelah dibandingkan dengan volume lalu lintas dipilih kapasitas model yang terbesar yaitu sebesar 8.272,5 smp/jam pada sudirman - thamrin & 8.067,9 smp/jam pada thamrin - sudirman, dan hasil perhitungan kecepatan arus bebas terendah sebesar 41,2 km/jam di sore hari untuk sudirman - thamrin, sebaliknya thamrin - sudirman terendah sebesar 43,9 km/jam di siang hari. Gunakan kapasitas yang terpilih tersebut untuk analisis berikutnya yaitu perhitungan ratio perbandingan arus dan kapasitas (DS) dan tingkat pelayanan yan berada pada tingkat pelayanan huruf C dan D di kedua arahnya.

scholarly journals The Effect of Congestion Pricing Scheme on the Generalized Cost and Speed of a Motorcycle

2016 ◽  
Vol 15 (1) ◽  
pp. 95-106
Author(s):  
Gito SUGIYANTO
Keyword(s):  
Traffic Congestion ◽  
Demand Management ◽  
Congestion Pricing ◽  
Flow Speed ◽  
Free Flow ◽  
Vehicle Speed ◽  
Traffic Jams ◽  
Pricing Scheme ◽  
Free Flow Speed ◽  
Generalized Cost

Traffic congestion is one of the significant transport problems in many cities in developing countries. Increased economic growth and motorization have created more traffic congestion. The application of transportation demand management like congestion pricing can reduce congestion, pollution and increase road safety. The aim of this research is to estimate the congestion pricing of motorcycles and the effect of a congestion pricing scheme on the generalized cost and speed of a motorcycle. The amount of congestion pricing is the difference between actual generalized cost in traffic jams and in free-flow speed conditions. The analysis approach using 3 components of generalized costs of motorcycle: vehicle operating, travel time and externality cost (pollution cost). The approach to analyze the pollution cost is marginal-health cost and fuel consumption in traffic jams and free-flow speed conditions. The value of time based on Gross Regional Domestic Product per capita in Yogyakarta City in October 2012. The simulation to estimate the effect of congestion pricing using Equilibre Multimodal, Multimodal Equilibrium-2 (EMME-2) software. The results of this study show that while the free-flow speed of a motorcycle to the city of Yogyakarta is 42.42 km/h, with corresponding generalized cost of IDR1098 per trip, the actual speed in traffic jams is 10.77 km/h producing a generalized cost of IDR2767 per trip, giving a congestion pricing for a motorcycle of IDR1669 per trip. Based on the simulation by using EMME-2, the effect of congestion pricing will increase on vehicle speed by 0.72 to 8.11 %. The highest increase of vehicle speed occurred in Malioboro Street at 2.26 km/h, while the largest decrease occurred in Mayor Suryotomo Street at north-south direction at 1.07 km/h. Another effect of this application for motorcycles users will decrease the generalized cost by 1.09 to 6.63 %.

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