A New Models for Emergency Evacuation under the Disaster Condition

People must face many disasters every day, which cause losses in property and human lives. It is significant how to establish the emergency evacuation model and for high density population in large areas according to the actual situation of their emergency evacuation. This paper put forward a Multi-levels Emergency Evacuation Model (MEE) based on the collective evacuation for high density of population in large areas under the earthquake condition in China, which firstly find the best ways from the multi-gathering points(Origins) in the disaster area to multi-settling points(Destinations )in the safe area based on the road impedance such as the traffic, road speed limit and pavement damage to weight the evacuation ability of road network, and secondly determine the evacuation auto numbers on the every routes which is at the target to deliver all the evacuating people from the Origins to Destinations in the shortest time. The experiment area is Dezhou city in Shandong province of China, and an emergency evacuation platform was put up according to the multilevel emergency evacuation model using Google map API and C# as development platform, and the result show us that MEE is promised to be a new methods for emergency evacuation.


INTRODUCTION
The disasters were recurrent around the world during the last several years.Taking some cases for example, on May 12, 2008, the grievous earthquake struck Wenchuan County, Sichuan province in southwestern China that has taken 70, 000 people away, made 370, 000 wounded and more than 10, 000 disappeared or so.The day on April 14, 2010, the quake which hit 7.1 on the Richter scale happened in Yushu county, Qinghai province with 2, 220 people dead and 70 missing.The more terrible is the 9.0 magnitude earthquake in the eastern waters of Honshu island that resulted in 13498 deaths and 14734 disappearances on March 11, this year.They are not unique, but have their counterparts.On October 23, this year, 481 were deceased in eastern Van province of Turkey under the quake measuring 7.2.The awesome figures by quakes show that the recurrent earthquake disasters have a serious influence on social stability, development and public safety.So, coping with emergencies to safeguard the public lives and properties has being the cardinal issue of researchers all over the world.Model for emergency evacuation has to start with road network, with affecting the efficiency, and selecting evacuation path which transfers the stricken persons from hazardous area to secure area is the principal problem of constructing the model for emergency evacuation.From 1960s on, the researchers have proposed many emergency evacuation models for kinds of disasters: In the 1970s, Lewis(1985) proposed transportation planning for hurricane evacuations.In the next followed decade, the Virginia State of America advanced NETVACI (Antoine G et al, 1998).Cova (2003) put forward a network optimal flow model for lane based evacuation routing.Jernigan and Post.etc (2000)proposed macro-level evacuation modeling analysis system which is named evacuation travel demand forecasting system.Franzese and Han(2001) developed a computer-based incident management decision aid system.Zou and Yeh.etc (2005)proposed a simulation-based emergency evacuation system for ocean city Maryland under hurricane attacks.U. Petruccelli (2003)research the knowledge under earthquake evacuation.Yuan Yuan et al. (2008) established path select model for emergency evacuation.
Under the internal concrete condition of collective transition and the network from multi-gathering points to multi-settling points when severe disasters struck, this paper discusses the distribution of multi-gathering points in the hazardous area and multi-settling points in the secure area, the respective suffers density in the corresponding gathering points, the respective accommodation of the corresponding setting points and the number of government vehicles for evacuation according to the computer simulation, and analyses the spatial point matching, path selecting and vehicle allocating methods during the evacuation model construction process.This paper takes Shandong province in China as the experimental area, based on WEBGIS and GOOGLE MAP API with computer programming language, to build the earthquake emergency evacuation platform.

CAPACITY OF ROAD EVALUATING
There are two goals need achieved when we evacuate persons from the disaster area to the safe area on the situation of quakes, that is to say, efficiency and safety.The efficiency indicates transition all victims from gathering points to setting points as soon as possible, relate to the road grades, the speed limits, the road length and the traffic flow and so forth.The safety denotes in the evacuation process we should ensure the victims safe because when passing through a part of disaster zone that building collapses, road surface damages and landslides were caused by the quakes.The strongest transportation capacity is equivalent to the lowest impedance on the contrary.Integrating it with the spring bounce model in physics: F k ∆x, we propose one methods for structural objective function evaluation on road capacity, with the impedance as the criterion.

Objective function evaluation on road capacity
With the road impedance as the evaluation criterion, when it is a constant, the longer the road is, the stronger the impedance is, likewise, the two roads of the same length but different values of impedance, whose impedance is stronger with the longer length.The impedance is determined by two key factors: one is the transportation speed impedance determined by the road class, the speed limits, the road width and the traffic flow and so on, the other is the disaster impedance resulting from the road collapses and countercheck.According to the fore-mentioned theory, we can get the objective function evaluation on road capacity as follows: (1) Ti denotes the efficient transportation time of some path.Di denotes the damage degree of some path surface.
1 and 2 denote the coefficients in the object function which is decided by experts' experience and actual road condition.To make it easy, we assume 1 1, 2 1 in the after-mentioned experiment, that is, efficient transportation time and the weight of the damage degree of the relevant path are identical.

Objective function solution
According to the fore-mentioned theory we derive the object function in formula 1, and then solve the unknown quantity to get the summation P. Based on the past research and analysis on the road network data, many computation methods for road impedance have been proposed (Wang W.Q. and Zhou W et al. 2004;Zhuang Y. and Lv Sh., 2005), but we pick the model of calibration over again on the BPR function, rising in the research on traffic capacity, which is the key project in the ninth five-year plan, to formulate as below: Qi (pcu/h) denotes the road flow in the real time.Ci (pcu/h) denotes the road capacity.ti denotes the running time according to the designing speed.V0(km/h)denotes the average speed.Vd ( km/h ) denotes the designing speed depending on the road ranking.α1、 α2、 α3、 β denotes regression parameters and correction factor respectively, with the actual values in the literature (Wang W. and Deng W., et al. 2001).
The disaster impedance often has a close correlation with the disaster type, the geographical conditions and economic situation in the location.It's the letter's key point that evacuation on the condition of earthquake, so we use the following formulation which proposed by Xu Tianben and Lv Jianghui (2002) to compute the disaster impedance.

Di=Pbi×Si× Ei
(3) Pbi denotes the damage probability of the road.Si denotes the impedance degree of the same road.Ei denotes the corresponding exposure level.
Si=Hi/Di (4) Hi denotes the average height of buildings in the road.Di denotes the valid width of the correspondent road.
Ei=ki/Li (5) ki denotes the building density in the road.Li denotes the length of the road.

MODELING MULTI-HIERARCHY EMERGENCY EVACUATION
Modeling multi-hierarchy emergency evacuation is based on the road network data in the actual time, according to the road capacity evaluation criterion under the disaster, deriving from the fore-mentioned research, we can gain the support of the real-time and handled road network data, and then construct the multi-hierarchy evacuation model.We establish it according to the three levels.

Spatial points matching
The central mission of the model is to evacuate the people from the multi-gathering points in the disaster area to the multi-settling points in the secure area when disaster is striking.How to finish the evacuation from a certain gathering point to some setting points needs the points matching on the basis of the spatial property between the gathering point and setting point.This paper supposes that the epicenter locates a certain center of the experimental area, then designates the dangerous region, buffer zone and safe region by simulating quake magnitude, and picks multi-gathering points and multi-settling points in the corresponding zones.The points must satisfy certain criteria.The gathering points ought to be in the disaster region which is convenient to gathering people, where is no tall building, which is far away from the disaster origin and which is near to the traffic hub zone.The setting points ought to be in the safe region away from the dangerous area.We usually take hospitals, schools and squares as setting points in consideration of factors such as the relief materials conveyance, the real-time cure to victims and adopt ability for evacuation persons.As long as the points are fixed, we can match the multi-gathering points and the multi-settling points by spatial analysis.
(1) Spatial analysis and Voronoi diagram Spatial analysis is an analysis technology of spatial data based on the location and morphological feature of geographic object, with the goal of learning about the events in space, extracting and conveying spatial information.Spatial analysis includes spatial location, spatial distribution, spatial morphology, spatial distance, spatial orientation, topology, similarity and relevance amounting to five aspects.In this paper we mainly rely on the spatial location, spatial distribution, spatial orientation and topology of multi-gathering points and multi-settling points, and settle the matching problem according to the dissection trait of Voronoi diagram.
The Voronoi diagram (Franz A. and Rolf K., 1996) is correlative with discrete points, divided the plane into several region with only one point in it, which is the nearest assemble points to the only point.It is used for spatial dissection whose      .For each layer Hi∈ H, we compare Wi(v, e) with threshold ζi and make sure the current road data belongs to which layer.After all road data has compared with threshold, we will get four sets such as: Hi= {Vi, Ei, Wi}, i=1, 2, 3, 4. Searching the K optimal paths from gathering point to setting point based on following steps: Step1: Finding the nearest road to the current gathering point and compare the ability of road evacuation with threshold of each layer; Step2: Looking for the other collinear points with current gathering point and compare those points with threshold value to make sure they are located in which layer.Assume that the set of road nodes of collinear road section be represented as: N={n|ni∈ Ls, i 1, 2 … ….}.
Step3: Taking one node from the set N to begin the next step of path searching.
Step4: If the current road node is located in the highest layer then search the next section of road which is collinear with it.The end node of the current section of road as the current node, that is, to reuse the same method over and over again until the current node is collinear with settling point.
Step5: If we can't find the collinear node with current node in the current data layer, we need to find the mapping point of current node in the next layer and reuse Step 4 and Step 5 until to find all the successful way from all gathering points to all setting points.The concrete methods are shown in the figure below.

Vehicle Assignment
The traffic flow's assignment has a strong influence on the unblocked transportation of one road.When constructing the emergency evacuation platform, we put traffic flow's assignment into vehicle's assignment, considering the special situation of collective evacuation and special strategies of specific road section after the disaster happened.By searching paths and allocating node flow, we can get the population on each single road of the K optimal paths from certain gathering point (Origin) to certain setting points (destination).Supposed starting from gathering points to setting points, the number of population allocated to each evacuation path are Q 1 , Q 2 , Q 3 ...Q m .According to the computational formula of evacuation time, we can acquire the single evacuation time ET i (the single evacuation time of the path numbered i) of each path.Assumed that there are m optimal evacuation paths, the single evacuation time of each path can be expressed as ET 1 , ET 2 , ET 3 ...ET m .Objective function of vehicle assignment was established aiming at seeking overall optimal.

Establishing objective function of vehicle assignment:
While the evacuation time of single path is approximate to mean value of the finished evacuation time of all the emergency evacuation paths, we can treat it as overall optimal, that's when the value of the objective function F above is infinite close to zero.The amount of vehicles for each optimal path is the best result.In practical application, we obtain the number of vehicles allocated for each path by setting F as zero.

Solving objective function:
Supposed there are m paths from all the gathering points to all the setting points, the single evacuation time of each path in all the m paths is ET i .Assumed that the number of people certain vehicle can carry is a, so the number of vehicles allocated for each path is N m , the total amount of the vehicles is N. n i means there are n road sections on evacuation path numbered i. t ij indicates the single evacuation time of road section j on path i.

EXPERIMENT
We chose Dezhou city, Shangdong province as the experimental area to set up emergency evacuation model platform.Assume that a point in Dezhou city as the center of the earthquake.Setting up emergency evacuation model platform under the condition of earthquake.

Establishing real-time database
Flexible emergency evacuation model can provide scientific and reasonable evacuation strategy for policy makers in accordance with categories, severity and area of disasters and also need real-time dynamic so as to adapt to constant disasters while some disasters happen.To make the latest data be used by platform, we chose to use real-time database system (Y.Kim and S.H.Son, 1996;Jan.L, 2008.)Usually, real-time information only guarantees to realize relative real-time dynamic in the shortest period as soon as possible.Real-time database mainly stores the real-time road network data and disaster data.When platform uses these data, it needs to be pretreated.Data pretreatment includes road network traffic capacity monitoring in a period, disaster degree monitoring, network topology construction and experimental gathering dot and setting dot selection.Real-time database framework is as follows: Figure 5.The conceptual graphs of Real-time data base

Road capacity assessment of the experimental zone
Road capacity assessment is determined by real time road data and the type of disaster of the experimental zone.From literature [11] we can get each parameter and according to the objective function of road network capacity assessment which has explained in the earlier paragraph to get the capacity of each section of road.Assume that the road network of whole experimental zone as a undirected graph: G={V, E, W}, V={v1, v2, v3……..}, E={e1, e2, e3……}, W={w1, w2, w3……..}.And we store the value of road capacity to set W and correspond with the set V and E.
We can get the topological information table (tab.4 and tab.5) of road data after finish the building of topological of road network of the experimental zone.Table 5. Road network table The information of road sections is described by relational table.Start Point and End Point record the two point information of one road section.And we use ID number to record the road section."Length" record the length information of each road section; "Transportation Time" record the evacuation time of each road section; "Weight" record the capacity of each road section under the disaster condition; the node information is recorded in the Node relational table.In this table we use ID number to record the nodes number and utilize "XCoord" and "YCoord "to record the coordinates for all nodes of the road network.According to the ID number in the Node table and the information of "Start Point" and "End Point" in the Road network relational table, we can connect two tables easily.

The multi-gathering points and multi-settling points selection and the internal mechanisms of points matching
The multi-gathering points and multi-settling points are determined by the real disaster situation of experimental zone.According to the real situation of Shang Dong province De Zhou city and to analog the situation of disaster, we choose four gathering points according to (Current J.M. and Schilling D., 1990;Fang L. and He J.M., 2003;Chang Y.L. and Wang W., 2005): S1, S2, S3, S4 and eleven setting points : T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T11.According to the above mentioned method, we can build the road network hierarchical diagram to overly on the weighted Voronoi diagram which is established by the special position of gathering points and setting points.The principle of two layer overlying is described as follows (fig.6).Then we need to store the gathering points and the setting points matching information to the real time data base.

Experiment
Based on the establishing method of emergency evacuation model in this paper and connected with the Web GIS technology and Google Map API technology, we use C# program language to establish the emergency evacuation plot which be called as : traffic network emergency decision support system of cross area.Follow the function buttons which are provided by the traffic network emergency decision support system of cross area, we can get the position of all the gathering points and setting points, and input the real data which include amount of stayers in gathering points, the adopt capacity of setting points, the position of disaster happening and the range of disaster.Meanwhile we can set the relevant parameters such as the amount of vehicles to get the final evacuation scenario as follows (fig.7).We assume that the population of the area is 25000, and the government has 1000 vehicles to evacuate.According to shown in the figures: we can get the following final distribution form:

SUMMERY
Frequent occurrences of natural disasters in recent years have caused concern about studying the emergency evacuation model.Based on examining the system of emergency evacuation and predicting the happening of disaster, to minimize damage and avoid loss of life is of great importance for safeguarding and seeking social stability and promoting common development.In this paper we propose several new methods for building emergency evacuation model which include using weighted Voronoi diagram to get the matching of multi-gathering points and multi-settling points, applying hierarchical road data to optimize path searching method, establishing vehicle assignment model in the base of the global optimization.Those approaches are not only used for collective evacuation in china when an earthquake occurs but also be adopted for other disaster in through updates the real time data base.And how to develop and optimize those methods to promote the further development of emergency evacuation model is still a challenge.
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Figure
Figure 4. Detailed network

Figure 6 .
Figure 6.Real point matching diagram

Figure 7 .
Figure 7.The route planning and vehicles assignment Result

Table 1 .
Spa space adjacency of the multi-ga an see from the ent points here points here: s here: T4, T

Table 4 .
Node table