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Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220

Contents lists available at SciVerse ScienceDirect

Process Safety and Environmental Protection

journa l h om ep age: www.elsev ier .com/ locate /ps ep

mergency response plans optimization for unexpectednvironmental pollution incidents using an open spacemergency evacuation model

ianfeng Lia, Sandra M.Y. Leeb,∗, Wenmao Liua

School of Environment, Tsinghua University, Beijing 100084, PR ChinaSchool of Architecture, Tsinghua University, Beijing 100084, PR China

a b s t r a c t

The objective of this research is to model the crowd evacuation process providing dynamic spatial–temporal distri-

bution information, which can minimize the human exposure risk (death or casualties) on the population implied

by a specific evacuation policy when he or she was exposed to adverse effects under accidents. An open space

evacuation model based on the stochastic Markov process was introduced here to estimate the spatial–temporal

distribution of the evacuees during evacuation covering the estimation of affected areas, space discretization, nodes

and links creation, etc. Then, according to the solution of the Markov process providing the expected distribution of

the evacuees in the nodes of the area as a function of time and the dose–response relationship, the people’s health

effects (e.g., death, several kinds of injuries, etc.) suffered in the evacuation process can be calculated, so that the

accident’s health consequence can be determined. Finally, different emergency response policies can be evaluated

with corresponding health consequence, so that the emergency policy can be optimized.

© 2012 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Heavy gas diffusion; Numerical simulation; Crowd evacuation; Emergency rescue; Stochastic Markov model

of different approaches have been used. Most of the research

. Introduction

mergency response plan (ERP) has commonly been used inisk reduction action everywhere. In the context of an ERP inn area affected by accidents or disasters, the effectivenessf a protective action for the population must be evaluated.n the case of evacuation in particular, the decision maker

ust take into consideration many multiple organizational,echnical, scientific and psychological issues. One of the mostmportant factors influencing such decisions is the health con-equences (fatalities or casualties) on the population impliedy a specific evacuation policy. A simple minded, almost intu-tive approach, suggests that the larger the area of evacuationhe lower the health consequences. This policy is not optimumn all-possible situations and probably is sub optimum in all-ractical cases. This is usually owe to the fact that the larger

he area of evacuation the slower the evacuation progress.

∗ Corresponding author at: Room 504, School of Architecture, Tsinghuaax: +86 10 62795220.

E-mail address: 999forever@sina.com.cn (W. Liu).Received 3 August 2011; Received in revised form 10 May 2012; Accept

957-5820/$ – see front matter © 2012 The Institution of Chemical Engittp://dx.doi.org/10.1016/j.psep.2012.05.005

Most of the times there is not enough warning time to evacu-ate large areas. Furthermore, decision makers are reluctant toorder evacuation of smaller or larger areas in the early stagesof an accident evolution. The rightness of decisions is closelyrelated to his/her positions, performance and promotions. Ifdecision-making is improper, accountability mechanisms willtake effects and endanger his/her political career. For thesereasons it is important to be able to calculate health conse-quences by taking into consideration the movement of thepopulation in case of evacuation.

Over the last two decades there has been considerableinterest in modeling evacuation for a well-defined zone andevent scenario, like the evacuation of a low lying coastalzone that may be subject to a hurricane surge. To analyzean evacuation scenario for a well-defined footprint, a number

Park, Haidian District, Beijing, PR China. Tel.: +86 10 62795220;

ed 14 May 2012

has been concentrated on two distinct problems, evacuation

neers. Published by Elsevier B.V. All rights reserved.

214 Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220

of buildings and evacuation of large areas, like entire cities orcoastal plains.

Some of the earliest research on building evacuation wasdone by Chamlet et al. (1982). Their paper describes threemodels they developed to analyze clearing time, bottlenecklocations, and general performance of a building in the eventof an evacuation. The most important of these models is thedynamic model that represents the evacuation of a buildingas it evolves over time (Chamlet et al., 1982). As an alter-native to network flow models inspired by Chamlet et al.(1982), researchers have also modeled building evacuationusing simulation. For example, Feinberg and Johnson (1997)present a simulation procedure called ‘FIRESCAP’ that empha-sizes behavioral characteristics of individuals in modeling anevacuation. They stress the importance of behavioral aspectssuch as cooperativeness, competitiveness and social con-structs such as a pairs (e.g. married couples) or individuals.Their simulation model uses these behavioral characteristicsas stochastic variables in a Monte Carlo sampling frameworkto create graphical snapshots of the evacuation evolving overtime.

Evacuation modeling applied to large areas has involvedthe use of similar approaches. An excellent review of evac-uation modeling applied to large areas can be found inSouthworth (1991). Simulation has been the preferred toolof choice. Examples include OREMS, MASSVAC, and TEVACS.The Oak Ridge Evacuation Modeling System (OREMS) is anexcellent example of a simulation model designed to ana-lyze possible evacuation scenarios of large areas, where theroad network involves major linkages like primary arterialsand highways. Demands are based upon small areas or trans-portation analysis zones. The principal objective is to estimateclearing times and identify bottlenecks. MASSVAC is a sim-ulation model designed for the analysis and evaluation ofevacuation plans for urban areas threatened by natural dis-asters (Hobeika and Jamei, 1985). It is capable of simulatingthe flow on highway networks and identifying the availableefficient routes from a hazard area to the nearest shelters andcalculating the evacuation time for the network. Hobeika andChangkyun (1998) have extended MASVAC by integrating auser equilibrium (UE) assignment algorithm into MASSVAC.Han (1990) also developed a simulation model, called TEVACS,to analyze large-scale evacuation. This model was config-ured to specifically address the evacuation of large cities inTaiwan.

The related work in evacuation with health consideration,as well as, the minimization of the associated socioeconomicimpacts of the emergency plan is the well-deserved one(Georgiadou et al., 2007).

Related research on evacuation using simulation includesthat of Seagle et al. (1985), MacGregor Smith (1991), Hara(1978), Hobeika and Jamei (1985) and Thompson and Marchant(1995).

The paper consists of four sections. Section 2 describesthe basic features of the stochastic Markov model for theestimation of the spatial population distribution duringevacuation. This section includes also some applicationsand a sensitivity analysis of the main parameters of themodel. Section 3 presents the dose–response function tocalculate health effects in the case of accidents. Section4 presents the use of the evacuation model in the calcu-lation of health effects in the case of accidents. Finally,

Section 5 offers a summary and the conclusion of thiswork.

2. Stochastic Markov traffic flow model

2.1. Core model description

In transportation and evacuation modeling a graph represen-tation of an area (i.e. network represented by nodes and links)has been used extensively (Rogers et al., 1990).

The area of interest is divided into a number of sub-areas ofarbitrary shape and size. Here, the area of interest is dividedin N discrete nodes. A node represents a geographic area ofvariable size and shape, i.e. it may represent an area includingone or more building blocks. Each node is characterized by theinitial population and the number of vehicles participating inthe evacuation procedure. The nodes are connected betweeneach other by links.

A link might represent even a single road between twobuilding blocks. However, if the node corresponds to morethan one building block, then the link represents the capabilityof connection between two adjacent nodes.

Several discrete actions are then defined such as contin-uation of normal activities or a protective action such asevacuation, sheltering in large buildings, sheltering in houses,etc. An emergency response policy (ERP) is defined when anaction has been defined at each and every node of the area.The optimum or most preferred ERP is to be selected out ofthis decision space (Sinkko et al., 2004).

The model simulates the movement of the population fromone node to another, as a random process, where the nextnode (and the corresponding link to it) is randomly chosen bythe evacuees. The probabilities rate [˛ij(t)] governing the choicedepends, however, on the traffic-related characteristics of thenodes and the links among them.

Here, we suppose the probability rate [˛ij(t)] depends onthe travel time between nodes (i) and (j), i.e. the probabilityof an individual to choose between two different destinationsis greater for the destination corresponding to a shorter traveltime which is assumed known to the evacuee or it is somehowsuggested to the evacuee by appropriate traffic controls. Incases in which there is no congestion, the travel time betweennode (i) and node (j) depends on the existing road connectionsand capacities between them, as well as on the speeds of evac-uees or their vehicles used for the evacuation. Therefore, [˛ij(t)]is given by the following equation (if i /= j):

[˛ij(t)] = U

dij(1)

where U is the average speed of evacuees or their vehicles,depending on their type (cars, buses, heavy vehicles, etc.); anddij is the length of the link from node (i) to node (j). In cases inwhich node (i) is not connected with node (j) (either temporar-ily or permanently), or if there are constraints, then, [˛ij(t)] isequal to zero.

2.2. Model adjustment

According to the historic experiences, the main parametersaffecting the road congestion and consequently the probabil-ity of population movement during evacuation are:

• Evacuee’s preference factors according to its final destina-tion (e.g. location of friends) or the type of vehicle used.

• Risk factors such as the toxic plume direction.• Travel ‘costs’ to each destination (travel time or distance).

Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220 215

•

•

w

((((

22ocsd

|

H

ttd

a

iii

2tnteci

2Ntt

Table 1 – The velocity of different evacuation types.

Type Predefined speed Value adopted

Walk About 5 km/h Uwalk 75 m/minRunning About 10 km/h Urun 150 m/minBicycle About 30 km/h Ubike 500 m/minAuto About 90 km/h Uvehicle 1500 m/min

nt

Available traffic data for a specific area sometimes called‘myopic’ view of the traffic conditions (i.e. vehicles choosetheir way among available roads by taking into account thecurrent congestion in each one).

Identification of bottlenecks that would constrain the flowof traffic and assessment of the effectiveness of differentevacuation strategies, etc.

The main factors that influence the evacuation processere described as following:

1) with/without road system;2) with/without vehicles used in evacuation;3) traffic jam;4) weather conditions.

.2.1. Road network

.2.1.1. Evacuation without road network. As for the rural arear plane or medial shallow incised mountainous region, therowd evacuation will occur without the support of roadystem. The difference of altitude between the source andestination was:

dij| =√

(xj − xi)2 + (yj − yi)

2 + (zj − zi)2,

ere, the coordinate of i is (xi, yi, zi); j (xj, yj, zj).The physical energy consumption which resulted from the

errain would influence the final choice of route selection. So,he coefficient for the velocity adjustment would be intro-uced into the formula.

Eq. (1) was modified as:

ij(t) = U · CoefficientU√(xj − xi)

2 + (yj − yi)2 + (zj − zi)

2(2)

More to this point, the problem of traffic jam did not exitn this case. Further, the routes selection behaviors also var-ed from different areas culturally, which would be considerednto in the model.

.2.1.2. Evacuation through road network. In this situation,he travel time depends on the level of congestion betweenodes. The average speed of vehicles, depending on theirype (cars, buses, heavy vehicles, etc.), as well as on consid-rations such as construction works, road accidents, weatheronditions (rain, snow, ice, fog), on the average number ofntersections, etc.

.2.2. Evacuation using vehiclesowadays, with the economics incessant growth in China,

he emergency evacuation using vehicles is prevailing underhe leadership of local government. So, the influence from the⎧⎪⎪⎛ U · Coefficie

aij(t) =

⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

⎝ car U√(xj − xi)

2 + (yj − yi)2 + (z

−i

usage of vehicles in evacuation must take into account.First, the vehicle becomes the mobile unit:

Num Vehiclei(t = 0) = Num Evacueei

Ave Capa Vehicle(3)

where Num Vehiclei(t = 0), the number of vehicles participat-ing in the evacuation procedure being in node (i) at time zero;Num Evacueei, the number of evacuees being in node (i) attime zero; Ave Capa Vehicle, the average number of personsper vehicle; i, variable for nodes; t, variable for time.

Evacuees can be residents, workers, visitors in the area, etc.The total number of people participating in the evacuation is

Total Num Evacuee =N∑

i=1

Num Evacueei, (i = 1, . . . , N) (4)

The total number of vehicle participating in the evacuationis

Total Num Vehicle =N∑

i=1

Num Vehiclei(t = 0) (5)

Second, the increase in mobility:Walking speed of most people is about 0.85–1.1 m/s, i.e.

about 60–75 cm for each step, no more than 6 km/h; if runningis used, the speed will be 8–12 km/h; also as for bicycle move-ment, the speed 30 km/h, for automobile, that is 60–100 km/h,depending on the type of vehicle (car, bus, buses, etc.).

Here, Table 1 shows the velocity used in this paper.

2.2.3. Traffic jamAccording to Eq. (5), the travel time is calculated by con-sidering free movement of vehicles. However, the traveltime depends also on the level of congestion betweennodes. In particular, [˛ij(t)] increases when the levels ofcongestion in node (i) and node (j) decrease, and viseversa.

The transition probability rate depends not only on the(time dependent) level of congestion of its alternative desti-nations, but also on the level of congestion of the node whichoccupies at the current time step. In order to simulate thiseffect instead of Eq. (5), the following expression is used forthe calculation of [˛ij(t)]:

j − zi)2

⎞⎠ [1 − resisti(t)][1 − resistj(t)], i /= j

N∑ /= j,j=1

aij(t), i = j

⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭

(6)

216 Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220

Fig. 1 – Level of congestion.

ehicl)

Fig. 2 – Densely populated area after discretization. Note: �node; hazardous facility; © evacuation area (2.4 km

velocity of vehicle here defined as 150 m/min which can be

The function resisti(t) corresponds to the level of congestionin node (i) and it is estimated as follows:

resisti(t) =

⎧⎪⎨⎪⎩

Rmax, Num Vehiclei(t) ≥ cMi

Rmax

[1 − exp

(− Num Vehiclei(t)

Mi − Num Vehiclei(t)

)], Num V

where Num Vehiclei(t), the number of vehicles participatingin the evacuation in node (i) at time t; Rmax,c are parame-ters affecting the behavior of the model, Rmax < 1, c < 1; Mi, themaximum capacity corresponding to node (i); i,j, source anddestination node.

According to Eq. (7), the congestion function of every node(i) increases exponentially with Num Vehiclei(t), reaching itsmaximum value [rmax] when the node is considered over con-gested, i.e. the number of vehicles in the roads approaches themaximum capacity [Mi]. A graphical example for the variationof the function resisti(t) is presented in Fig. 1 as a function ofthe population density in that node Num Vehiclei(t). The threecurved lines correspond to different maximum capacities [Mi]of the node, though in all cases [rmax] 0.9 (Lan and Davis, 1999;Carey and McCartney, 2004).

2.2.4. Weather conditionsFor example, rain during evacuation reduces speeds up to10% and capacity 10–20% (due to the increase of the distancebetween vehicles) (Southworth, 1991; Hu, 2004).

2.2.5. A stochastic evacuation model based on MarkovmodelA stochastic evacuation model based on Markov model issolved numerically by discretizing the time of transitions asfollows:

x(n + 1) = x(n)P(n) (8)

where x(n) is a N × N vector with elements xi(n); xi(n) is theprobability that a vehicle participating in the evacuation is innode (i) in the interval �tn, between times tn and tn + �tn{n =1, 2, . . . , T}; Pn is a N × N matrix with elements pij(n); pij(n) isthe transition probability of an individual from node (i) at

time tn = n·�t to node (j) at time tn+1 = (n + 1) · �t, 0 ≤ pij(n) ≤ 1,

ei(t) < cMi

⎫⎪⎬⎪⎭ (7

radius).

∑N

i,j=1pij(n) = 1; n is the current time step {n = 1, 2, . . . , T}; T isthe total number of time steps considered T = Total Time/�t;

and Total Time is the total time considered for the evacuationsimulation.

The transition probability pij(n) is given by

pij(n) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

aij(t)∑N

i /= j,j=1aij(t)

[1 − exp

(−

N∑i /= j,j=1

aij(t) · �t

)]], i /= j

exp

(−

N∑i /= j,j=1

aij(t) · �t

), i = j

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

(9)

2.3. Sensitivity analysis of the model

Main parameters affecting the road congestion and con-sequently the probability of population movement duringevacuation are: the population density (P); the maximumcapacity of the roads (M); and the speed of vehicles (V). Ananalysis of the sensitivity of the evacuation clearance timeto these parameters has been performed with the followingresults.

In order to introduce all the factors mentioned above, theemergency evacuation scenario was designed as following:

Step 1: exposure zone discretizationThe diameter of exposure zone was 2.4 km with spatial grid150 m × 150 m. Spatial discretization resulted in 256 (16 × 16)grids (see Fig. 2). The coordinate of grid i and j ranges from−8 to 8, i.e. the center grid is labeled by (0,0). Accordingly,272 (17 × 16) links representing the capability of connectionbetween two adjacent nodes were built.Step 2: initialization of input vectorProvided that there are 256 × 12 = 3072 evacuees and capacityof each vehicle is 3, 256 × 4 vehicles are needed for evacua-tion. Then, Num Vehiclei(0) = 4; also Mi is defined as 6. The

used to estimate the time consumption of movement. So, the

Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220 217

;

Veh)

initial vector is a line matrix like this:

Ri(t = 0, step = 0) = Num Vehichei(0) × [1, 1, . . . , 1], 1 ≤ i ≤ 256

where i, j represent a node; n, m is the subscript of nodes;step = N is time step.Step 3: construction of transition probability matrix

(1)

8∑n,m=−8

Pnm = 1, (Pnm ≥ 0);

(2) R(2) = R(1) × P;Step 4: solution to matrixBased on the homogeneousness of meshing and the zeroaltitude difference assumption, the reduced model is:

resisti(N) =

⎧⎪⎨⎪⎩

Rmax, Num Vehiclei(N) ≥ cMi

Rmax

[1 − exp

(− Num Vehiclei(N)

Mi − Num Vehiclei(N)

)], Num

aij(t = N ∗ �t, step = N)

=

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

(Ucar

dij

)[1 − resisti(N)][1 − resistj(N)], i /= j

begineqnarray∗12pt] −256∑

i /= j,j=1

aij(N), i = j

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

(11)

Pi,j is formulated as following:

pij(N) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

aij(N)∑256

i /= j,j=1aij(N)

[1 − exp

(−

256∑i /= j,j=1

aij(N)

)], i /= j

exp

(−

256∑i /= j,j=1

aij(N)

), i = j

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

(12)

Step 5: clearance rulesFor the sake of fully clearance, the rules can be defined asfollowing:(1) In the initial vector, Ri(t = 0, step = 0) will be assigned.(2) When step /= 0, Ri(step /= 0) at the top and bottom will be

zero after each step, i.e. the vehicle has been evacuatedout of the exposure zone.

Step 6: discussionSensitivity analysis illustrates the evacuation clearance timeof the population of the area within 2.4 km radius aroundthe hazardous facility by vehicles. It is assumed that onlythe individuals occupying the nodes included in this areawill participate in the evacuation. Here, when the defaultsparameters are used, the clearance time is 20 min (P1) till theleft population is less than 72.(1) Three different population densities (P2 = 0.5P1, P3 = 2P1)

for a given maximum capacity [Mi] for every node havebeen considered. As it is shown in this illustration, theeffect of the population density on the evacuation clear-ance time is very important. For small population density(P2) the evacuation clearance time decreases to approx-imately 17 min, relatively to the evacuation clearancetime of 20 min (P1). On the other hand, if the populationdensity increases (P3), then only 62% of the populationwill have left the area at the same time, and the totalclearance time increases to 22 min.

(2) Similarly, the effect of the maximum capacity of the

roads on the evacuation clearance time must be takeninto consideration. Here, sensitivity analysis corresponds

iclei(t) < cMi

⎫⎪⎬⎪⎭ (10

to three different cases for maximum capacities, i.e.M2 = 2M1,M3 = 0.5M1, for a given population density (P1).Experiments indicate if maximum capacity shortens toM1, the clearance time increased to 25 min. It is alsoshown that, as the maximum capacity of the roadsdecreases, the evacuation clearance time increases sig-nificantly.

(3) Finally, the evolution of the evacuation is tested forthree different values of U (U2 = 2U1,U3 = 0.2U1) forthe base case population density (P1) and maximumcapacity (M1) of the nodes. It is obvious that theevacuation clearance time decreases significantly when

the speed of vehicles increase and vice versa(TU2=5 min,TU1 = 105 min).

3. Evaluation of health consequences

One of the most important criterions in ERP assessment isto minimize the consequences caused by the accident. Herethe stochastic Markov model was used to evaluate the popu-lation distribution that changes with time, so that people’shealth consequences can be estimated. In this article, poi-son gas leakage was selected as an example to assess healthconsequences of the accident.

Given a specific accident (considering the amount andtype of hazardous material, the accident’s type and its char-acteristics, the environmental characteristics including thewind speed and direction, etc.), a spatial and temporal pro-file of the extreme condition, corresponding to each point inthe area as a function of time, can be calculated by usingappropriate models (Papazoglou et al., 1992). According to theaccident’s type (toxic release, fire, explosion), these profilesmight correspond to the concentration of a toxic substance,to the intensity of heat radiation or to the size of overpressure(Papazoglou et al., 1992; TNO, 1997).

An individual’s absorption dose at node (i) in interval�tn(tn < t < tn + �tn, n = 1, . . . , T) was assumed as a constant,which can be calculated using the non-linear relationship oftoxic load and exposure concentration and time. It can beshown as follows:

Di(tn) = C˛i �tn (13)

where Ci—the gas concentration at node (i), which is cal-culated by use of gas diffusion models; ˛—toxic load indexassociated with types of gases; �tn—exposure time.

Absorption dose (DT) of individual can be calculatedthrough the following two-step:

First, the individual’s average absorption dose [D(tn)] at timetn(n = 1, . . . , T) can be obtained through averaging out all nodesin the study area:

D(tn) =N∑

xi(tn)C˛i �tn (14)

i=1

218 Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220

Fig. 3 – Accident descriptions.

where xi(tn)—the probability that the individual appears atnode (i) at time tn, that can be calculated with the Markovmodel described in the second part.

Then the overall average dose received by an individual inthe process of the evacuation is:

DT =T∑

n=1

D(tn) (15)

Conditional probability PD of various consequences(including death, various injuries, etc.) caused by individual’sexposure to dose D, can be obtained according to correspond-ing “probability variable”:

PD = 1√2�

∫ Y−5

−∞exp

(−u2

2

)du (16)

In practice, the Eq. (16) can also be transformed from prob-ability variable to percentage with the following equation:

PD = 50[

1 + Y − 5|Y − 5| erf

( |Y − 5|√2

)](17)

where erf is error function; Y is probability variable, it can begiven as follows:

Y = k1 + k2 ln(DT) (18)

k1, k2 are constants depending on types of accidents.Let N0 be the number of people exposed to a dose D. Then,

the average expected number of people related to the respec-tive consequence Nc is:

Nc = N0 · PD (19)

By comparing the Nc under various emergency strategies,the ERP can be assessed.

4. Effect of dose variability on thecalculated health consequences

The following case showed a more exhaustive explanation ofhow the integrated model is used in the simulation itself.

Here, we assumed that there is a densely populated areawith many large, medium and small enterprises, some ofwhich (including oil refineries, chemical plants, etc.) use alarge number of hazardous substances. To reduce injuries ofthe accident, it is necessary to develop emergency responsepolicies (ERP) and take protective actions including evacuationwhen accidents happened.

The dose estimated by Eqs. (15) and (16) is of course theaverage dose that an individual subject to the evacuation pol-icy will receive. Actually, different individuals follow differentevacuation routes, each one corresponding to a different valueof received dose.

As a result, the moving population will receive a dose span-ning a range of values each with an associated probability. Inthis case, the probability of a specific consequence (e.g. death,several types of injury) of a given dose is provided through theequation:

∫ ( )

p(PD) = f (D) · g

PD

D· dD (20)

where f(D) is the probability density function (pdf) of thereceived dose (D), and g(PD/D) is the conditional probabilityof consequence PD (causalities or death) for a given dose D,and is estimated by Eq. (16).

This densely populated area was divided into 441 dis-crete nodes with the same size, as shown in Fig. 3. Vehicleswere assumed to move only in the direction away from thedangerous source. Initial number of vehicles and maximumcapacity of each node was distributed according to the regionalresponse operation center. The average evacuees per vehiclewas assumed 3, the average speed (U) of evacuation vehicleswas 10 km/h, c and rmax was 0.8 and 0.9 respectively. Four cor-ners of the study area were selected as evacuation exits, sothat the evacuees can stay away from the dangerous source,as can be seen in Fig. 3.

The hazardous source in Fig. 3 was assumed to have a liquidchlorine tank leak; the leakage amount was 500 kg. Two ERPswere considered. Radius of evacuation scope of ERP1 and ERP2was 1 km and 1.9 km respectively.

4.1. Calculation of population distribution

On the basis of the Markov model described in the second part,the population changing with time within the region can becalculated with C# programming language.

Remaining population within the evacuation regionchanged as a function of time, as can be seen in Fig. 4.

Evacuation scope of ERP1 was smaller, people had feweroptions during the evacuation, therefore, at the beginning ofthe evacuation, there would be congestion and evacuationspeed was slow. The relatively flat curve in the beginningof Fig. 4(a) reflected this problem. With the continuation ofevacuation, people moved to nodes having lower level of con-gestion and the evacuation speed were gradually accelerated.

Evacuation scope of ERP2 was bigger; people had moreoptions during the evacuation, so the probability of congestioncan be reduced.

4.2. Assessment of health consequences

To simplify the calculation process, Ci in Eq. (13) was calculatedusing box model in accordance with the initial concentrationof chlorine. Here, ̨ is 2, k1 is −8.29, and k2 is 0.92. According tothe Eqs. (13)–(19), with the results of the Markov model, health

consequences under different ERPs can be calculated.

Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220 219

Fig. 4 – Remaining population in the evacuation region. (a) ERP1, (b) ERP2.

sHb

e

Calculation results are as follows:

PD1 = 15.02%, Nc1 = 5648

PD2 = 15.96%, Nc2 = 18, 218

Clear time of ERP1 was shorter, so people’s various con-equences due to exposure to the chlorine were smaller.owever, its evacuation efficiency was lower, especially at theeginning of the evacuation.

ERP2 had a longer clear time, people had a longer timexposed to chlorine and it is more possible to produce a variety

of consequences as the cumulative effect. Nevertheless, theevacuation was more efficient, and there was less congestion.

5. Discussion

According to the background, in the real world, evacuees’spatial distribution as a function of time is necessary inorder to evaluate every alternative emergency response policyaccording to the corresponding health consequences of the

population. So, the basic idea is to link the stochastic Markovevacuation model with the dose–response function.

220 Process Safety and Environmental Protection 9 1 ( 2 0 1 3 ) 213–220

A stochastic non-homogeneous Markov evacuation modelwas presented to provide the spatial distribution of the pop-ulation during evacuation in the area of interest, by takinginto account its density and its initial location, the roadconnections and capacities, the effect of road congestionas well as the type of vehicles used for the evacuationprocedure.

The dose–response function can provide the evaluation ofhealth consequences as a function of time in which evac-uees’ were subjected to the poisoning effect that caused thedeath or casualties. More specifically, the area under evac-uation is divided in sub-areas called nodes and evacueesby a stochastic non-homogeneous Markov evacuation modelthat is the first step are transferring from one sub-area toanother through the existing road network represented bylinks.

As far as the health consequences of the popula-tion are concerned, it was shown that the emergencyresponse policy minimizing the expected number of fatal-ities might not be the one that maximizes the evacuationarea, depending on the time interval considered and onthe level of congestion of the roads due to the evacuees’movement.

6. Conclusions

One of the most important factors to assess ERPs is thepossible health consequences (death or casualties) underthe guidance of that ERP. And that is the guideline of thispaper.

Here, we select health consequences (death or injury) asour reference indexes to study the effectiveness of differentERPs, and help decision-makers make correct decisions inan emergency situation. That is, minimization of health con-sequences is used as determination standard to assess andoptimize the ERP. The solution of Markov model provides astochastic temporal variation of the population density in thearea under evacuation which in turn can be used in the estima-tion of health consequences when a major industrial accidentoccurs.

The proposed model can be solved in the pre-planningstage, if the use of models with different initial distributionof the population, natural disasters and industrial accidentsto provide useful information for decision-making, such aswhether to evacuate some areas, the need to increase trans-portation network capacity, or the need for residents to buildshelters for asylum, their numbers and how to select the loca-tion.

Also, in real-time command stage after the disaster, ifthere is enough warning time, the model can be usedto help decision-makers to conduct real-time emergencyrescue decision-making. The ERP can be adjusted dynam-ically and real-timely, of course, this cannot be separated

from the support of site information and transmissiontechnology.

Acknowledgments

The study is financially supported by financially supportedby the Critical National Natural Science Foundation of China(20937002/B07 and 20100480016) and The National Natural Sci-ence Foundation for the Youth (No. 41105099).

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