Discrete Dynamics in Nature and Society

Volume 2015, Article ID 328320, 8 pages

http://dx.doi.org/10.1155/2015/328320

## Evaluation of Bus Networks in China: From Topology and Transfer Perspectives

^{1}School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China^{2}Civil and Environmental Engineering, University of Washington, Seattle, WA 98195-2700, USA^{3}Department of Geography, University of Cambridge, Cambridge CB2 3EN, UK

Received 11 December 2014; Revised 27 February 2015; Accepted 4 March 2015

Academic Editor: Ricardo López-Ruiz

Copyright © 2015 Hui Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

With the development of the public transportation, bus network becomes complicated and hard to evaluate. Transfer time is a vital indicator to evaluate bus network. This paper proposed a method to calculate transfer times using Space P. Four bus networks in China have been studied in this paper. Some static properties based on graph theory and complex theory are used to evaluate bus topological structure. Moreover, a bus network evolution model to reduce transfer time is proposed by adding lines. The adding method includes four types among nodes with random choice, large transfer time, degree, and small degree. The results show that adding lines with nodes of small degree is most effective comparing with the other three types.

#### 1. Introduction

Bus network plays more and more significant role in alleviating the increasingly heavy traffic congestion in metropolis due to urban sprawl and population explosion. During the last two decades, there are many researches on transportation systems using complex networks theory such as subway networks [1–3], aviation networks [4, 5], marine networks [6], street networks [7–9], railway networks [10, 11], highway networks [12], and commuting networks [13]. Many studies focus on some static properties of transit networks such as degree distribution, the average shortest path distance, and cluster [14–17].

Complex network theory is a useful tool to analyze network topological structures. It has been successfully applied in many fields including power grid networks [18, 19], scientific collaboration networks [20–22], WWW [23, 24], and protein networks [25–27] in attempt to understand the relationship between topological properties and performances. The topological structure and dynamics are two aspects of a complex system and they interact with each other [28, 29]. An eminent topological structure can always bring high-performance dynamics. Although there are many researches on the analysis of bus topological structure, seldom research focuses on the transfer issues. In bus network, transfer is such a very important factor that it cannot be negligible. Because of time-consuming and inconvenience, transfer has become a barrier to hinder passengers from using bus network. How to reduce transfer times has become a priority problem to resolve for transit network designer and planner.

As a complex network, bus network has its unique traits. Lines play an important role in constituting a bus network; it is necessary to understand the effect of each line. To evaluate the topological structures of bus networks, this paper uses several indicators based on graph theory and complex theory and proposes two indicators concerning transfers. An effective method to calculate the average transfer time considering traffic demand has been proposed using Space P. Moreover, the role of each line playing in transfer times of the whole network has been studied. In the end, four types to reduce total transfer time have been given by adding lines.

This paper focuses on the transfer issues of bus network and aims to find an efficient way to reduce transfer times. The rest of paper is organized as follows. Section 2 describes bus network representation. Statistic properties are given in Section 3. Section 4 gives the two transfer-related indicators. The evolution of bus network transfer is introduced in Section 5.

#### 2. The Approaches of Describing Bus Network

In this paper, we use three forms of matrices to represent the bus network: line-station matrix, weighted adjacent matrix, and adjacent matrix under Space P. Line-station matrix is a basic form to express bus network, where each row stands for a line and each column stands for a station. Take Figure 1(a) for example; there are three rows in the matrix: 1-2-3-4-5, 6-2-3-7-8, and 9-4-7-10. The weighted adjacent matrix is widely used to present networks in graph theory. Here, it is used to calculate some indicators of bus network. We represent networks as , where is the set of nodes and is the set of edges. is described by the adjacent matrix ; is the weight of edge between nodes and . If there is no edge between nodes and , . When the weight equals 1, it is the common adjacent matrix. In this paper, there are two weights to be used, which are the section length and the number of overlapped section. Another useful matrix to display bus network is adjacent matrix under Space P. In this matrix, nodes which belong to a line connect with each other (see Figure 1(b)).