Effective vector variance in modeling Malaysia highway traffic network

Abstract

Highway traffic networks consist of in-coming vehicles to a toll plaza and out-coming vehicles from a toll plaza. The current practice to analyse a network is by using social network analysis (SNA) with the following three steps: (i) the network is considered as an undirected weighted complete graph (UWCG), (ii) the important information in the network is filtered using minimal spanning tree (MST), and (iii) the topological properties of each node is investigated using certain centrality measures. However, highway networks are complex and need a better method to analyse it. In this thesis, the Projek Lebuhraya Usahasama Berhad (PLUS) highway network is represented as a weighted directed network (WDN). The PLUS highway traffic network from 63 toll plazas in Peninsular Malaysia is studied to understand the in-coming and out-coming weights of traffic burden. Here, the weights of traffic burden refer to the in-coming and out-coming vehicles between two toll plazas. This study represents the complex PLUS highway traffic network as a non-symmetric matrix with positive finite element. The important information contain in the network are extracted using a unique and more robust method known as Forest. It is found that PLUS highway network produces only one MST in a network. This differs from other complex networks such as stock markets which typically produce more than one MST in a network. This study also investigates the dynamicity amongst PLUS highway toll plazas, which has not been discussed in other highway network studies. Using regression analysis on log return of traffic burden, it is found that Bukit Tambun Utara and Bukit Tambun Selatan are the two most dynamic toll plazas. In addition, the topological properties of network in this study use four types of centrality measures which are degree, betweenness, closeness and eigenvector. The performance of the toll plazas in the network can also be summarized based on an overall centrality measure using Principle Component Analysis. This approach is able to identify the most important toll plaza in the network. For instance, Sungei Besi toll plaza is found to be the most important toll plaza from the years 2009 until 2013 for in-coming traffic burden. However, this method could not identify the performance of the toll plazas based on the importance of their centrality measures. This is because it does not take into account, the multivariate dispersion of the centrality measures and thus cannot identify the most important centrality measure. An existing measure of multivariate dispersion is using effective variance (EV) based on the geometric mean of all eigenvalues. In this study, a new approach called effective vector variance (EVV) based on the arithmetic mean of all eigenvalues is used together with EV to identify the most important centrality measure. It is found that the most important centrality measure containing only one type of centrality measure is betweenness, the important centrality measure containing two types of centrality measures is betweenness and eigenvector, and the most important centrality measure containing three types of centrality measures is degree, betweenness and eigenvector. The results from this study can be used by the management of PLUS highway to improve its current system and operation.