Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

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Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

Sustainability ◽

10.3390/su10114182 ◽

2018 ◽

Vol 10 (11) ◽

pp. 4182 ◽

Cited By ~ 1

Author(s):

Shixu Liu ◽

Hao Yan ◽

Said Easa ◽

Lidan Guo ◽

Yingnuo Tang

Keyword(s):

Traffic Flow ◽

Network Traffic ◽

Numerical Experiments ◽

Dynamic Theory ◽

Evolutionary Model ◽

Dynamic Evolution ◽

Traffic Flows ◽

Route Network ◽

Analysis Of Stability ◽

Route Cost

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

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Analyzing Spatial Community Pattern of Network Traffic Flow and Its Variations across Time Based on Taxi GPS Trajectories

Applied Sciences ◽

10.3390/app9102054 ◽

2019 ◽

Vol 9 (10) ◽

pp. 2054 ◽

Cited By ~ 2

Author(s):

Wenhao Yu ◽

Menglin Guan ◽

Zhanlong Chen

Keyword(s):

Traffic Flow ◽

Transport System ◽

Urban Space ◽

Network Traffic ◽

Spatial Databases ◽

Spatial Dynamics ◽

Transport Systems ◽

Traffic Flows ◽

Trajectory Data ◽

Beijing City

The transport system is a critical component of the urban environment in terms of its connectivity, aggregation, and dynamic functions. The transport system can be considered a complex system due to the massive traffic flows generated by the spatial interactions between land uses. Benefiting from the recent development of location-aware sensing technologies, large volumes of traffic flow data (e.g., taxi trajectory data) have been increasingly collected in spatial databases, which provides new opportunities to interpret transport systems in cities. This paper aims to analyze network traffic flow from the perspective of the properties of spatial connectivity, spatial aggregation, and spatial dynamics. To this end, we propose a three level framework to mine intra-city vehicle trajectory data. More specifically, the first step was to construct the network traffic flow, with nodes and edges representing the partitioned regions and associated traffic flows, respectively. We then detected community structures of network traffic flow based on their structural and traffic volume properties. Finally, we analyzed the variations of those communities across time for the dynamic transport system. Through experiments in Beijing city, we found that the method is effective in interpreting the mechanisms of urban space, and can provide references for administrative divisions.

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MATHEMATICAL MODELLING OF NETWORK TRAFFIC FLOW

Transport ◽

10.3846/1648-4142.2009.24.333-338 ◽

2009 ◽

Vol 24 (4) ◽

pp. 333-338 ◽

Cited By ~ 28

Author(s):

Raimundas Junevičius ◽

Marijonas Bogdevičius

Keyword(s):

Traffic Flow ◽

Network Traffic ◽

Flow Model ◽

Flow Speed ◽

Complex Model ◽

Traffic Flows ◽

Flow Models ◽

Traffic Flow Models ◽

Single Complex ◽

Made In

The article describes mathematical models of traffic flows to initiate different traffic flow processes. Separate elements of traffic flow models are made in a way to be connected together to get a single complex model. A model of straight road with different boundary conditions is presented as a separate part of the network traffic flow model. First testing is conducted in case the final point of the whole modelled traffic line is closed and no output from that point is possible. The second test is performed when a constant value of traffic flow speed and traffic flow rate is entered. Mathematical simulation is carried out and the obtained results are listed.

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TripRes

ACM Transactions on Multimedia Computing Communications and Applications ◽

10.1145/3401979 ◽

2021 ◽

Vol 17 (2) ◽

pp. 1-21

Author(s):

Xiaolong Xu ◽

Zijie Fang ◽

Lianyong Qi ◽

Xuyun Zhang ◽

Qiang He ◽

...

Keyword(s):

Traffic Flow ◽

Discrete Distribution ◽

Resource Provisioning ◽

Path Selection ◽

Urban Traffic ◽

Traffic Flows ◽

Multimedia Services ◽

Traffic Flow Prediction ◽

The City ◽

Multimedia Surveillance

The Internet of Vehicles (IoV) connects vehicles, roadside units (RSUs) and other intelligent objects, enabling data sharing among them, thereby improving the efficiency of urban traffic and safety. Currently, collections of multimedia content, generated by multimedia surveillance equipment, vehicles, and so on, are transmitted to edge servers for implementation, because edge computing is a formidable paradigm for accommodating multimedia services with low-latency resource provisioning. However, the uneven or discrete distribution of the traffic flow covered by edge servers negatively affects the service performance (e.g., overload and underload) of edge servers in multimedia IoV systems. Therefore, how to accurately schedule and dynamically reserve proper numbers of resources for multimedia services in edge servers is still challenging. To address this challenge, a traffic flow prediction driven resource reservation method, called TripRes, is developed in this article. Specifically, the city map is divided into different regions, and the edge servers in a region are treated as a “big edge server” to simplify the complex distribution of edge servers. Then, future traffic flows are predicted using the deep spatiotemporal residual network (ST-ResNet), and future traffic flows are used to estimate the amount of multimedia services each region needs to offload to the edge servers. With the number of services to be offloaded in each region, their offloading destinations are determined through latency-sensitive transmission path selection. Finally, the performance of TripRes is evaluated using real-world big data with over 100M multimedia surveillance records from RSUs in Nanjing China.

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