Research on urban public traffic network with multi-weights based on single bus transfer junction

https://doi.org/10.1016/j.physa.2015.05.087Get rights and content

Highlights

  • Constructs urban traffic network models with multi-weights.

  • Splits the complex network with multi-weights into single weighted complex networks.

  • Study the global synchronization of the new network model with multi-weights.

  • Analytical and simulated results are given to the public traffic network balance.

Abstract

Regarding single bus transfer junction as a research object, this paper constructs the urban traffic network models with multi-weights taking different bus lines in bus transfer junction as the network nodes, that is, the urban traffic network with multi-weights is given different properties weights at every edge. According to the method of network split, the complex network with multi-weights is split into several different single weighted complex networks. Then, we study the global synchronization of the new network model by changing congestion degrees, transfers coefficient and passenger flow density between different bus lines. Finally, analytical and simulated results are given to show the impact of different properties weights to the public traffic network balance.

Introduction

Recently, there has been increasing research interest in the complex dynamical networks and its synchronization  [1], [2], [3], [4], [5], [6], [7], [8], [9]. Some effective methods have been proposed to investigate the stability of the synchronous state of complex networks. In Ref.  [4], Zhang et al. present a concept of xk-leading asymptotically stable, and study the synchronization in complex networks with adaptive coupling. In Ref.  [5], Huang studies the global synchronization in coupled oscillator networks, proposes an adaptive weighted network and shows that such a simple and quite general scheme is able to tip oscillator networks towards collective synchronization.

In recent papers many researchers have studied the synchronization of weighted complex networks with single weight  [5], [10], [11], [12], [13]. However, synchronization stability of complex networks with multi-weights has not yet been analytically investigated. It is well known that we can describe many real-world networks in complex network with multi-weights. The multi-weights networks where nodes are connected by more than one weight exist everywhere, such as human connection networks, transportation networks, communications networks, etc. For example, people can connect each other by mail, telephone, MSN, e-mail, and so on, suppose every contact information are different weights, so human connection network is a complex network with multi-weights. According to the method of network split, splits the complex network with multi-weights into several different complex networks with single weight. There must be a lot of different characteristics between complex dynamical networks with multi-weights and complex dynamical networks with single weight, therefore the complex dynamical networks with multi-weights need to be modeled.

In recent years, as scholars probe deeper into complex network, its application in public traffic network has been given much attention  [14], [15], [16], [17], [18], [19], [20], [21]. Much recent research suggest that the public traffic network just focus on networking static characteristics, for example, the degree distribution of the vertex, average shortest paths and clustering coefficient and so on, and rarely extend into the dynamic characteristic, such as the growth of edges and nodes, the change of passenger flow, human schedule, and their impact to the whole public traffic network.

Motivated by the above discussions, this paper aims to handle the problem of public traffic network form a new visual field of complex dynamical networks with multi-weights. On the basis of traditional weighting network, this paper gives a new multi-weights complex network model, and every edge of this model has one or several different properties weights. According to the method of network split, we split the multi-weights complex network into several different single weighted complex networks, and study its global synchronization. By the proposed network model and space R modeling approach, taking bus lines as the network nodes, we establish a new public traffic network model with multi-weights, and give different properties weights between two public traffic lines in every edge. Then the new network model is split into several different single weight networks and its global synchronization is studied based on the Lyapunov stability theory combined with adaptive control. At last, analyzes the impact of congestion degrees, transfers coefficient and passenger flow density between different bus lines on the new complex public traffic network to its synchronous ability. Then the public traffic network balance is discussed, and these give a theoretical basis for people to research bus dispatching and bus lines optimization.

The rest of the paper is organized as follows. In Section  2, the model of complex network with multi-weights and its split is presented. In Section  2, the synchronization criterion of complex network with multi-weights is designed. In Section  3, a new urban public traffic network model is designed. In Section  4, numerical simulations are given to demonstrate the relationship between complex networks and public traffic network. Conclusion is given in Section  5.

Section snippets

The model of complex network with multi-weights and its split

The way to split the complex network with multi-weights is that the network weights with different natures are split into different sub-networks. Consider a multi-weights complex networks consisting of N nodes and l weights (gij1,gij2,,gijl) at the network edge between the node i and j, and gijl is the lth weight. Noticing the different natures of the l weights, the weights with same nature and N nodes compose a sub-network. So via the theory of network split, the complex network with

The establishment of urban public traffic network model

From the public traffic stops networks, public traffic roads networks and the public traffic transfer networks point of view, one can establish three public traffic network models  [22], [23], [24], [25].

  • (1)

    Public traffic stops networks. Using the space L modeling method, and taking bus stops as the network nodes, the two bus stops have edge if they are adjacent in a bus line.

  • (2)

    Public traffic transfer networks. Using the space P modeling method, and taking bus stops as the network nodes, the two

Numerical simulations

Wu et al. draws the conclusions that passenger flow of urban public traffic fulfills the nonlinear behavior in paper  [26]. By analyzing the global public traffic network, we know that urban public traffic network has the characteristics of BA scale-free networks  [27]. Suppose that passenger flow fulfills Lorenz chaotic system and H1=H2=H3=diag(1,1,1), thus, the dynamical equations for each node i=1,2,,7, can be described by: (ẋi1ẋi2ẋi3)=(10(xi2xi1)28xi1xi2xi1xi3xi1xi28/3xi3)+(Mi1Mi2Mi3

Conclusions

Studying the urban public transport network need not only to investigate the structure of the urban traffic network topology itself, but more important to consider the characteristics of urban traffic, analysis the influence of network structure to the passenger flow on urban public traffic network and the frequency of depart, etc.

In real life, many problems can be described by complex network with multi-weights. Considering the single bus transfer junction, this paper establishes a new public

Acknowledgments

The authors express their gratitude to the referee for valuable comments on the first version of the paper. The authors also gratefully acknowledge support from the National Natural Science Foundation of China (No. 61164003, No. 61364001), Key Project of Chinese Ministry of Education (No. 212180), the Fundamental Research Funds for the Universities of Gansu Province (No. 620023), the Natural Science Foundation of Gansu Province (No. 1310RJZA028), and Lanzhou Jiaotong University Yong Scientific

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