A Simulation Study for Emergency/Disaster Management by Applying Complex Networks Theory

Transcription

1 A Smulaton Study for Emergency/Dsaster Management by Applyng Complex Networks Theory L Jn 1, Wang Jong 2 *, Da Yang 3, Wu Huapng 4 and Dong We 5 1,4 Earthquake Admnstraton of Guangdong Provnce Key Laboratory of Earthquake Montorng and Dsaster Mtgaton Technology, CEAKey Laboratory of Earthquake early Warnng and Safety Dagnoss of Maor Proect, Guangdong, Chna 2 School of Electrcal Engneerng, North Chna Unversty of Water Resources and Electrc Power, ZhengZhou , Chna 3 School of Economcs and Management, Southwest Jaotong Unversty, ChengDu, Chna 5 Deparment of nformaton Systems, USTC-CtyU Jont Advanced Research Centre, Chna * kfwd@ncwu.edu.cn ABSTRACT Earthquakes, hurrcanes, floodng and terrorst attacks pose a severe threat to our socety. What s more, when such a dsaster happens, t can spread n a wde range wth ubqutous presence of a large-scale networked system. Therefore, the emergency/dsaster management faces new challenges that the decson-makers have extra dffcultes n percevng the dsaster dynamc spreadng processes under ths networked envronment. Ths study tres to use the complex networks theory to tackle ths complexty and the result shows the theory s a promsng approach to support dsaster/emergency management by focusng on smulaton experments of small world networks and scale free networks. The theory can be used to capture and descrbe the evoluton mechansm, evoluton dscplne and overall behavor of a networked system. In partcular, the complex networks theory s very strong at analyzng the complexty and dynamcal changes of a networked system, whch can mprove the stuaton awareness after a dsaster has occurred and help perceve ts dynamc process, whch s very mportant for hgh-qualty decson makng. In addton, ths study also shows the use of the complex networks theory can buld a vsualzed process to track the dynamc spreadng of a dsaster n a networked system. Keywords:.Dsaster Management, Emergency Management, Complex Networks Theory, Small World Network, Scale Free Network. 1. Introducton Dsasters have a serous mpact on human socety, and despte the development of scence and technology, they stll cause heavy casualtes. On one hand, dsasters usually occur unexpectedly and effectve emergency/dsaster management s very crtcal needs hgh-qualty decson makng. Ths requres the decson-makers to well perceve the nature of a dsaster, gather relevant nformaton, make the rght udgment, and then generate an approprate acton plan. On the other hand, the real world s a networked one that s composed of many network systems, such as water supply networks, gas supply networks, power supply networks, road networks and communcaton networks. All these network systems are very complex and a so-called domno or avalanche effect feature s commonly shared among dsastrous events. A strong ntal event trggers a falure avalanche, whch spreads n a cascade-lke manner wthn a network and fnally has an mpact on large parts of the system. For example, the maor power blackout on August 14, 2003, whch lasted up to 4 days n varous parts of eastern USA, not only caused severe traffc congestons, but also affected many other crtcal nfrastructures. Ths avalanche effect makes the decson makng process for emergency/dsaster management very complex and dffcult because the decson-makers hardly perceve the phenomenon about how the dsaster spreads n a complex networked system. JournalofAppledResearchandTechnology 223

2 ASmulatonStudyforEmergency/DsasterManagementbyApplyngComplexNetworksTheory, LJnetal./ Effectvely understandng and percevng a dsaster s very mportant for emergency/dsaster management. In ths paper, the complex networks theory s appled to help perceve the dsaster spreadng (the avalanche effect) n a networked system by adoptng a smulaton approach. Because of the capacty and capablty to deal wth hgh complexty of systems and execute a wde range of analyses under dfferent envronment, smulaton experments are a useful tool and can be used n many felds. For example, Munoz- Pacheco and Tlelo-Cuautle [1] conducted a smulaton study to show the usefulness of the proposed synthesze 2D chaotc systems, Vargas- Martnez and Garza-Castafnon [2] made a smulaton experments to exam the usefulness of Pattern Search Optmzaton and ANNs on mprovng the performance of the fault-tolerant control (FTC) scheme. The study focuses on some crtcal lfelne systems, such as, water supply networks, gas supply networks, power supply networks, road networks and communcaton networks. The rest of ths paper s organzed as follows: n Secton 2 a bref lterature revew on emergency/dsaster management and complex networks theory s presented. A complex networks theory-based model that s used n ths study s ntroduced n Secton 3 and two smulaton experments and the assocated results are presented and dscussed n Secton 4. Fnally, a summary and a concluson are gven n Secton Lteratures Revew In a real-tme stuaton, the response to a natural dsaster or terrorst attack, creates a very crtcal, threatenng decson-makng context that must be consstently dealt wth n a tmely manner. The characterstcs that make dsaster respondng scenaros very complex nclude: hgh levels of uncertanty [3], compressed tmelnes [4], sgnfcant lack of nformaton [5], dffculty n assessng nformaton qualty [6]. Meanwhle, emergency/dsaster management encounters new challenges under the complex network envronment because of the avalanche effect. It s mportant to note that a large number of systems can be seen as a complex network whose nodes represent system components and whle the lnks ndcate the nteractons between those components. Over the last decade, the study of large-scale networked systems spannng has grown enormously[7], [8]. Network scence, as emergng research feld, has brought an nterdscplnary vew to the study of complex networks. Studes on these large-scale real networks have produced many new concepts and measures attemptng to characterze the structure of networks[9], [10]. A seres of unfyng prncples and statstcal dstrbutons related to dfferent propertes of real networks have been dentfed from those studes. The complex network theory can be used n many felds: nformaton systems[11], marketng[12], and desgn problem[13]. The complex network study can have a good help for the emergency decson makng wth a understandng of the stuaton awareness [14], whch s consdered ndspensable for decson makng n the context of a real-tme, complex and dynamcs envronment. Wth the ubqutous presence of large-scale networked systems and the study of complex networks, the complex networks theory can be well appled n emergency or dsaster management. Three famous network models are wdely used to examne complex systems, random network, small world network and scale free network, and a large amount of real networks have a hgh degree of smlarty wth small world network and scale free network. One of the foremost dscoveres n the complex networks theory s the exstence of smallworld property n many real networks. The Small-world property [9] refers to the fact that despte ther large sze most networks have relatvely short paths between any of ther two nodes. It s ponted out n many cases real networks exhbt a scale free (or power law) degree dstrbuton [15]. Therefore, n ths study, we lmt our smulaton scope to the small world network and scale free network for a better match to the real networked systems. In order to measure the avalanche effect of a complex networked system, a number of mportant models have been dscussed n the lterature and many valuable results have been found. [16] propose a model for cascadng falures n complex networks and ther fndngs showed that the 224 Vol.12,Aprl214

3 ASmulatonStudyforEmergency/DsasterManagementbyApplyngComplexNetworksTheory, LJnetal./ breakdown of a sngle node s suffcent to collapse the effcency of the entre system f the node s among the ones wth the largest load. [17] present a dynamc spreadng of the falures model n networked systems wth the recovery process n the network. [18] and [19] follow ths dea by takng dfferent nodes or strateges nto consderaton. In addton, many cascadng falure models have also been proposed, such as the sand ple model [20], [21], the ORNL-PSerc-Alaska (OPA) model [22] to study blackout dynamcs n the power transmsson grd. In partcular, the CASCADE model [23] s used to examne power transmsson system crtcal loadng and power tals n probablty dstrbutons of blackout sze, etc. 3. The Model In ths study the model s proposed by (Wang, Rong et al. 2008) s adopted to descrbe the complexty of emergency/dsaster management and vsualze the network-specfc spreadng process of a dsaster. Inspred by ths process of cascadng falures, the model s proposed as follow. (1).For smplcty, ntal load L of each node n the network s a functon of ts degree k and defned as: L ak (1) Where a and are tunable parameters n our study, whch control the strength of the ntal load of the node. (2).The load at the broken node s redstrbuted to ts neghborng node, accordng to the preferental probablty: ak ak m m k km m (2) where represents the set of all neghborng nodes of the broken node Accordng to the rule of (2), the addtonal load L receved by the node s proportonal to ts ntal load,.e., L k L km m (3) Meanwhle, each node n the network has a capacty threshold, whch s the maxmum flow that the node can transmt. Snce the node capacty on real-lfe networks s generally lmted by cost, t s natural to assume that the capacty C of the node s proportonal to ts ntal load for smplcty: C T L,,,,..., N. (4) where the constant T (>1) s the tolerance parameter characterzng the tolerance of the network. Because every node has a lmted capacty to handle the load, so for the node, f, L L C then the node wll be broken and nduce further the redstrbuton of the load L L and potentally further other nodes breakng. 4. Smulaton and Results 4.1 Buldng a Networked System In ths study, two networked systems are bult: a small world network and a scale free network. The algorthm for constructng the small world network s as follow: Step 1: Constructng a regular graph that has N nodes and s a nearest-neghbor couplng network. These nodes form a rng and each node connect wth K/2 nodes around ts rght and left, where K s an even number. Step 2: Randomly reconnectng the regular graph s edges wth the probablty P. That s, keepng one node of the target edge, and randomly selectng a node from the network as the other node of the edge, and every two nodes have ust one edge and every node can not be connected wth tself. The algorthm for constructng the scale free network as follow: JournalofAppledResearchandTechnology 225

4 ASmulatonStudyforEmergency/DsasterManagementbyApplyngComplexNetworksTheory, LJnetal./ Step 1: constructng a network wth m0 nodes, ths network can have no edges or be fully connected or randomly connected. Step 2: Brngng n one new node every tme, and connectng ths node wth m nodes from ths network, where m m0 The probablty for the new node connectng wth an exsted node can be expressed as k k 4.2 Attack Strateges, where k s the degree for node. Albert (2000) took two attack strateges nto consderaton for complex networks: one s falure strategy and the other s selectve attack strategy. To many real networks, such as water supply networks, gas supply networks, power supply networks, road networks and communcaton networks, an abrupt dsaster ncludes falure of nature dsasters and falure of terrorst attacks. A nature dsaster s a falure of operaton and, the destroyed nodes are selected randomly. A terrorst attack s a selectve attack and, the destroyed nodes are selected by the mportance of the node. In our study, we examne the selectve attack strategy and ntend to measure the dynamcs process of a network when t s attacked by destroyng mportant nodes, whch s mportant for emergency or dsaster management to better understand and perceve the dsaster s avalanche effect. A smulaton study s conducted to smulate such a selectve attack strategy and examne ts dynamc process. Two groups of experments are ncluded n ths study. One s to adopt the selectve attack strategy n a small world network and the other one s to adopt t n a scale free network. For these two networks, the fnal node number equals 30, whch s an approprate node number for develop a good vsualzaton effect snce the network becomes more complex and lower vsualze when the number of the node s large. The degree of the node s used to measure the mportance of the node, that s, a node wth hgher degree s more mportant. Ths actually reflects the stuaton of real networks. For example, people always consder a power staton connected wth many wres as an mportant node n the real power supply network. At the same tme, some other researchers also adopt ths rule, such as(tan, WU et al. 2006). Addtonally, the experments also show the changes of some statstcal propertes of a network when t s beng attacked, such as the degree dstrbuton, the probablty of the node degree. 4.3 Smulaton Results Fg.1 s the smulaton result for small world network that has nne sub-fgures to form a 3 by 3 matrx. The three sub-fgures n the frst row provde a dynamcal process of the network evoluton, the frst sub-fgure shows the network stuaton before an attack, the second sub-fgure shows one ntermedate stuaton of the dynamcal process when ths network s beng attacked, and the thrd sub-fgure shows the fnal stuaton of ths network when the dynamcal process has been over. Ths three fgures offer an ntutve effect about the changes of the small world network. As we know ths dynamcal process can mprove dsaster/emergency managers stuaton awareness ablty and, ths stuaton awareness s vtal for better understandng the dsaster and makng hgh-qualty decson, especally n a short tme when a dsaster has happened. The second row and thrd row present the changes of statstcal propertes of ths network. The three sub-fgures n the second row show the changes of node degree dstrbuton of the small world network. The frst sub-fgure shows the node degree dstrbuton before ths network s attacked, the second one shows the dstrbuton at one condton when t s beng attacked, and the last one shows the fnal dstrbuton. The three subfgures n the last row show the changes for node degree probablty before, when and after ths network s attacked. These changes of the statstcal propertes provde some detals of nformaton about the dynamcal process of the network evoluton. One can easly obtan the nformaton about whch node s destroyed at any tme of ths dynamcal process and how many nodes survve and the fnal connecton nformaton the network after ths process s over. 226 Vol.12,Aprl214

5 ASmulatonStudyforEmergency/DsasterManagementbyApplyngComplexNetworksTheory, LJnetal./ Fgure 1. The smulaton result for small world network. For example, t can be seen that the node 1, 2, 3, 4, 5, 8, 10 and 11 are destroyed and the node 15, 16 and 28 have the same maxmum degree and the value s 5 from the second sub-fgure of the second row. One also get the nformaton that there are ust eght nodes and the degree are 3, 2, 2, 2, 3, 4, 2 and 2 for ths eght nodes, respectvely. Fg.2 presents the smulaton results for the scale free network. It s constructed based on the same prncples adopted for Fg. 1. The frst row shows the dynamcal process of the scale free network evoluton, the second row provdes changes of node degree dstrbuton, and the thrd row offers the changes for probablty of node degree. The scale free network has the power law property for degree dstrbuton, and the frst sub-fgure n the second row shows ths property. One can get one mportant result from second row: the network always shows the power law property at any tme when ths network s attacked. Ths smulaton also can offer useful nformaton when the avalanche effect occurred whch can ncrease the effectveness of dsaster/emergency decson makng. Ths smulaton fts partcularly the stuaton when real networks own the power law property. JournalofAppledResearchandTechnology 227

6 ASmulatonStudyforEmergency/DsasterManagementbyApplyngComplexNetworksTheory, LJnetal./ Fgure 2. The smulaton results for scale free network 5. Conclusons In ths study we nvestgate the effect of complex networks theory to be used n dsaster/emergency management, especally for graspng and percevng some key characterstcs of a dsaster, whch s very mportant for decson makng n a short tme. Ths work s a novel attempt for enhancement of dsaster/emergency management. Based on the smulaton, one can conclude that the complex networks theory can help understand the dsaster by offerng vsualzed dynamcal process for the avalanche effect when a target network s beng attacked by destroyng the mportant nodes. One can obtan the useful nformaton such as whch node s destroyed at any tme of the dynamcal process, the degree dstrbuton and node degree probablty changes at any tme. One can also conclude that t s possble to apply complex networks theory to dsaster/emergency management, because complex networks theory can be used to capture and descrbe the evoluton mechansm, evoluton dscplne and overall behavor of the networks. Addtonally, we dscovery an mportant result from the smulaton: the scale free network always shows the power law property at any tme when the network s attacked. To summarze, the smulaton results shows that the complex networks theory s a powerful tool for formng stuaton awareness and percevng the spreadng of a dsaster. However, more experments should be conducted n the future study n order to further understand the complexty and other key features of a dsaster. References [1]-Munoz-Pacheco, J.M. and E. Tlelo-Cuautle, Automatc synthess of 2D-n-scrolls chaotc systems by behavoral modelng. Journal of Appled Research and Technology, (1): p Vol.12,Aprl214

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