Hub Identification of the Metro Manila Road Network Using Pagerank Paper Identification Number: AYRF15-015 Jacob CHAN1, Kardi TEKNOMO2
Total Page：16
File Type：pdf, Size：1020Kb
“Transportation for A Better Life: Harnessing Finance for Safety and Equity in AEC August 21, 2015, Bangkok, Thailand Hub Identification of the Metro Manila Road Network Using PageRank Paper Identification Number: AYRF15-015 Jacob CHAN1, Kardi TEKNOMO2 1Department of Information Systems and Computer Science, School of Science and Engineering Ateneo de Manila University, Loyola Heights, Quezon City, Philippines 1108 Telephone +632-426-6001, Fax. +632-4261214 E-mail: [email protected] 2Department of Information Systems and Computer Science, School of Science and Engineering Ateneo de Manila University, Loyola Heights, Quezon City, Philippines 1108 Telephone +632-426-6001, Fax. +632-4261214 E-mail: [email protected] Abstract We attempt to identify the different node hubs of a road network using PageRank for preparation for possible random terrorist attacks. The robustness of a road network against such attack is crucial to be studied because it may cripple its connectivity by simply shutting down these hubs. We show the important hubs in a road network based on network structure and propose a model for robustness analysis. By identifying important hubs in a road network, possible preparation schemes may be done earlier to mitigate random terrorist attacks, including defense reinforcement and transportation security. A case study of the Metro Manila road network is also presented. The case study shows that the most important hubs in the Metro Manila road network are near airports, piers, major highways and expressways. Keywords: PageRank, Terrorist Attack, Robustness 1. Introduction Table 1 Comparative analysis of different Roads are important access points because methodologies on network robustness indices connects different places like cities, districts, and Author Method Strength Weakness landmarks. Studying road networks is important because disrupting at least one road can affect the Scott, Network Better than Cannot handle et.al [14] Robustness V/C model isolated nodes connectivity of a road network, the safety of the Index people, and the accessibility of each road [1]. Wakaba- Cost-Benefit Useful Useful for Studying the robustness of a network is a yashi Analysis with reliability limited and Fang different index networks only relatively new research area. Generally, network [20] indices robustness is defined as the ability of a system to Tampère Dynamic Realistic Incomplete operate correctly under a wide range of change in , et.al Traffic methodology operational conditions, and to fail gracefully under [16] Assignment these conditions by tolerating sudden changes Knoop, Incidence Good Not good for et.al [8] Impact correlation freeways caused by different scenarios [6,10]. However, in transportation studies, road network robustness is de Vulnerability Good Computation Olivera, and vulnerability time the ability of the system to keep a certain capacity et.al [3] Congestion indicators level to handle traffic situations under abnormal Indicators conditions. Table 1 shows a wide-ranging overview Murray, Multi- Scenario Biased of several road network robustness indices and et.al [12] methodology identification measures and is compared to one another based on their approach, strengths, and weaknesses. However, the indices used in analyzing road robustness did not consider random attacks on the network, specifically man-made disasters like terrorist attacks. Terrorist attacks pose different issues not found in natural disasters because they II “Transportation for A Better Life: Harnessing Finance for Safety and Equity in AEC August 21, 2015, Bangkok, Thailand are difficult to protect for law enforcement agencies connected. Tarjan’s algorithm has a runtime of O [19]. Furthermore, aggressors are motivated, and (|V| + |E|), where |V| represents the number of thus exploit schedules in order to get around patrol nodes in the network, while |E| represents the schedules from law enforcement agencies. As a number of links. However, the runtime of the result, these agencies randomize their scheduling algorithm was reduced to O(|V|) using a binary techniques. However, these agencies need to protect decision technique [5]. thousands of vehicles from terrorist attacks, which pose different risks like threat, vulnerability, and 2.3. Terrorist Attacks and Robustness consequence [21]. Natural disasters like earthquakes and landslides have been used to find possible evacuation routes In this paper, we propose a model that uses and assess road networks before such disasters PageRank to identify the most important hubs in a happen [7,13]. However, planned disasters like road network, where each hub has a certain level of terrorist attacks pose different issues because unlike importance. Knowing these hubs may contribute to natural disasters, they are less uniform due to their awareness of safety during terrorist attacks. In unpredictability [9]. Furthermore, transportation Section 2, we discuss the important terms used for networks and public transits are the primary target the study, as well as different literature on road of most terrorist attacks because it an easy and robustness analysis. Section 3 deals with how our accessible way to take lives, cause damage, spread model was designed. We present a case study in the fear, and impact local, regional, and national Metro Manila road network in Section 4. Finally, in economies [4]. Section 5, we discuss the conclusions we have from our case study, as well as possible future works Willis, et.al [21] estimated the risks involved in regarding road network analysis. terrorist attacks through quantification. He used threat, vulnerability, and consequences, and 2. Literature Review multiplied it to get an estimation of terrorism risks, In this section, we define the terminologies used for which are probabilistic. Threat is the probability our research to better understand our proposed that a target will be attacked at a certain time in a model. We also present research on terrorist attacks certain way. Vulnerability is probability that an and its effects on transportation networks, as well attack results in damages, given that an attack as the concept of PageRank and its variants. occurs. Lastly, consequence is the magnitude of damage given a specific attack type. 2.1. Road Networks A road network is a weighted directed graph where 2.4. PageRank links represent actual roads, and nodes represent PageRank is a technique used to determine the intersections and corners. The weight of each link importance of nodes in a network, and is applied in represents the distance of the link from one source search engines like Google [2]. A website node in a node to a destination node. Each link can only be web network is considered important when traversed in one direction only, depending on where referenced by other websites. The more that the the destination node the link is directed. Road website is cited, the more likely that it is important. networks differ from another in terms of network In short, PageRank measures the inflow of the topology and link distances. Road networks can be nodes and ranks each node based on the number of represented in several ways, including images from inflowing links. geographical information systems and adjacency matrices. For transportation networks, a method called NodeRank [11] was created based on the PageRank 2.2. Network Connectivity algorithm. Three standards were used to measure In graph theory, a strongly connected network is a the degree of importance of each node, namely the property where each node is reachable from any topology, weights of each link, and importance of node, regardless of weight or distance. Tarjan [17] other vertices it connects to. Part of traffic flow proposed an algorithm that finds the strongly information can be acquired using this technique. connected components in a graph using depth-first Using this technique can also assist in traffic search. A graph is divided into sub-graphs, where system analysis, safety evaluation, and optimization. each component in each sub-network is strongly II “Transportation for A Better Life: Harnessing Finance for Safety and Equity in AEC August 21, 2015, Bangkok, Thailand 3. Methodology Δϕ Δλ d = 2r sin-1 (√sin2 ( ) + cos ϕ cos ϕ sin2 ( )) (2) We divided our network structure into two major ij 2 1 2 2 parts. The first part is cleaning the data with Tarjan’s algorithm. We then identified the most The value of Δϕ and Δλ represent the change in significant nodes called hubs using PageRank. latitude and longitude values of the node pair, Finally, we used our model in a case study of the respectively. The resulting distance is put in row i Metro Manila road network, and studied and and column j of matrix D to indicate a link between Current Metro Manila Road Network 121.3 analyzed our results. node i and node j. However, the value of the dij is 0 121.25 if no link exists between node i and node j. 121.2 3.2. Data Cleaning 121.15 Once the distance values have been computed for 121.1 each element in matrix D, we cleaned our data with Longitude 121.05 Tarjan’s algorithm [17]. The network was divided into smaller groups known as sub-networks that 121 represented the strongly connected nodes in the 120.95 network. The sub-network with the most number of 120.9 strongly connected components was retained in the network, while the sub-networks with less number 120.85 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 Fig. 1 Metro ManilaLattitude Road Network of strongly connected nodes were considered weaker sub-networks, and were immediately 3.1. Distance Calculation removed from the network. We considered the We collected a road network data and mapped it as strongly connected nodes and links because they nodes and links using a distance matrix D, which would greatly affect the connectivity and topology has n rows and n columns, where n respresents the of the entire network. The largest strongly number of nodes.