# Study on Evacuation Evaluation in Subway Fire Based on Pedestrian Simulation Technology

Authors: Yanyan Chen; Yiwen Cai; Pingpu Li; Guanghou Zhang
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

In order to improve the ability to evacuate from subway fire in subway’s planning, design, operation, and maintenance stages, a simulation model of pedestrians’ evacuation process in subway fire was established based on Legion and FDS software. It can truly reflect the dynamic effects of the fire environment on subway station evacuation. Then dynamic evaluation indicators systems were established from the point of survival index, security risk index, effectiveness index, and orderliness index. In order to help decision makers to identify the most appropriate plan, matter-element analysis (MEA) was used to rate different plans. At last a case study of Songjiazhuang (SJZ) station was provided to test the effectiveness and practicability of the evaluation method.


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## Body

## 1. Introduction

The subway, as one of urban public transportation means, due to the large capacity, land saving, and so forth, is becoming an effective tool to alleviate urban traffic congestion. But subway is a place where the disasters and accidents happened easily owing to its characteristics of being complex, close, agglomerate, and so on. Of all these disasters, fire is the most serious. Therefore, it is necessary to evaluate different pedestrians’ evacuation plans facing with different fire conditions in subway’s planning, design, operation, and maintenance stages. Because of the particularity of fire accident, the drilling method has many shortcomings such as big-cost, time-consuming, and more participants. And in the planning and design stages, it is difficult to evaluate and optimize the fire evacuation facility and pedestrians’ evacuation plan.With the development of computer technology, simulation technology of subway fire has become a way of high-feasibility, low-cost, and good-effect. Based on the reasonable parameter calibration, the simulation model can truly reflect the status of subway fire and record the data of pedestrians’ speed, acceleration, density, coordinate, and other traffic behavior. It provides a strong support for the quantitative evaluation of fire evacuation situation and has been widely used in all areas [1–5].There have been many researches [6–8] about evaluation of fire evacuation in subway station at home and abroad. However, the evaluation systems have a lot of shortages in different degrees. Firstly, there are still some qualitative indicators in exiting evaluation system. Setting value of these indicators needs to be finished by experts. Thus, qualitative indicators are limited to the experience of the experts or decision makers and the values might be not objective and convictive. Secondly, quantitative indicators are not reasonable enough to be selected and quantified. And they cannot reflect pedestrians’ behavior dynamically in the evacuation process. Thus, the evacuation situation cannot be reflected accurately. At present, qualitative description or basic comparison of simulation results is still the main application method of pedestrian simulation tools. The simulation evaluation method is not versatile because of lacking of standard dynamic evaluation indicators system and procedure.In this paper, a model of pedestrians’ evacuation process in subway fire is established based on Legion and FDS simulation software, and a dynamic evaluation indicators system is also established. A case is used to verify its effectiveness and practicability.


## 2. The Evacuation Evaluation in Subway Fire

### 2.1. Pedestrian Simulation Technology: Legion and FDS

The multiagent pedestrian model is the heart of the Legion simulation tool which uses the “minimum cost” [9] as the basic principles. Field investigation and data preparation are the basic work for pedestrian simulation modeling. Therefore, the parameters in Table 1 should be calibrated in building a simulation model.Table 1
Details of parameters.
Parameters
Details
Facility layout
Stairs, escalators, ramps, brake machine, etc.
Pedestrian characteristics
Age ratio, culture degree, sex ratio, etc.
Demand
The number of pedestrians, distribution
Pedestrian behavior
Along the wall, clustering behavior, panic behavior
Regions
Walking region, waiting region, isolation region, danger zone
Environment calibration
Speed reduction, path choice, life characteristicsLegion can record detailed track of each individual pedestrian and can accurately calculate the individual traffic behavior parameters and macroscopic traffic flow characteristics of pedestrian. The status of pedestrian traffic system can be reflected by maps, charts, and tables. Detailed output parameters can be found in Table2.Table 2
Output parameters of Legion.
Output format
Output parameters
MapChartTable
Ingress and egressOccupancyFlowSpeedEntity and space densityJourney timeSocial costInconvenience and frustration discomfort and dissatisfactionFire dynamics simulator (FDS) is the computational fluid dynamics simulation software in the fire, which was developed by the US national institute of standards technology. FDS can solve continuity equation, momentum equation, energy equation, and stress convergence equation with large eddy simulation (LES) model. Then the spatial distribution of temperature, pressure, gas composition, visibility, and so forth can be got [10]. FDS was validated by a lot of engineering experiments, and it is recognized by the international fire engineering.


### 2.2. The Process of Simulation Evaluation

The simulation is a method to simulate the complicated traffic phenomenon by computer technology and to display the real-time traffic situation based on the forecasting. Then the work of analysis, evaluation, and optimization can be started. The process of pedestrians’ evacuation evaluation in subway fire based on the simulation technology is shown in Figure1.Figure 1
The process of pedestrians’ evacuation evaluation based on the simulation technology.


## 2.1. Pedestrian Simulation Technology: Legion and FDS

The multiagent pedestrian model is the heart of the Legion simulation tool which uses the “minimum cost” [9] as the basic principles. Field investigation and data preparation are the basic work for pedestrian simulation modeling. Therefore, the parameters in Table 1 should be calibrated in building a simulation model.Table 1
Details of parameters.
Parameters
Details
Facility layout
Stairs, escalators, ramps, brake machine, etc.
Pedestrian characteristics
Age ratio, culture degree, sex ratio, etc.
Demand
The number of pedestrians, distribution
Pedestrian behavior
Along the wall, clustering behavior, panic behavior
Regions
Walking region, waiting region, isolation region, danger zone
Environment calibration
Speed reduction, path choice, life characteristicsLegion can record detailed track of each individual pedestrian and can accurately calculate the individual traffic behavior parameters and macroscopic traffic flow characteristics of pedestrian. The status of pedestrian traffic system can be reflected by maps, charts, and tables. Detailed output parameters can be found in Table2.Table 2
Output parameters of Legion.
Output format
Output parameters
MapChartTable
Ingress and egressOccupancyFlowSpeedEntity and space densityJourney timeSocial costInconvenience and frustration discomfort and dissatisfactionFire dynamics simulator (FDS) is the computational fluid dynamics simulation software in the fire, which was developed by the US national institute of standards technology. FDS can solve continuity equation, momentum equation, energy equation, and stress convergence equation with large eddy simulation (LES) model. Then the spatial distribution of temperature, pressure, gas composition, visibility, and so forth can be got [10]. FDS was validated by a lot of engineering experiments, and it is recognized by the international fire engineering.


## 2.2. The Process of Simulation Evaluation

The simulation is a method to simulate the complicated traffic phenomenon by computer technology and to display the real-time traffic situation based on the forecasting. Then the work of analysis, evaluation, and optimization can be started. The process of pedestrians’ evacuation evaluation in subway fire based on the simulation technology is shown in Figure1.Figure 1
The process of pedestrians’ evacuation evaluation based on the simulation technology.


## 3. Pedestrian Evacuation Evaluation Indicators System in Subway Fire

### 3.1. Indicators System and Quantification of Indexes

It is vital to ensure that pedestrians’ evacuation in subway fire is effective and safe. The evaluation of subway fire evacuation is used to investigate the merits degree of survival index, security risk index, effectiveness index, and orderliness index under different conditions such as facility layout and evacuation plan. The dynamic pedestrians’ evacuation evaluation indicators system in subway fire based on the output parameters of Legion is shown in Figure2.Figure 2
Pedestrians’ evacuation evaluation indicators system in subway fire.


#### 3.1.1. Survival Index

Survival index reflects the survival probability directly in the evacuation process. It can be described as two aspects: one is survival ratio and the other one is survival reliability.(
1) Survival Ratio
u
11. The index reflects pedestrians’ survival situation in the evacuation process:(1)u11=qQ×100%.In the type,q stands for the amount of evacuation pedestrians; Q is the total amount of pedestrians.(
2) Survival Reliability
u
12. Due to the randomness of pedestrians’ evacuation process, there will exist distance between deterministic methods to describe the evacuation process and actual situation. So this paper uses survival reliability index to describe pedestrians’ evacuation process.In the process, if available safe evacuation time (ASET) is longer than required safe evacuation time (RSET), pedestrians will be safe. That is,(2)ASET-RSET>0.According to the above criterion, the limit state equation for pedestrians’ safe evacuation can be constructed:(3)Z=TA-TR>0.TA stands for ASET and TR stands for RSET. The unit is “s.” TA is mainly affected by the fire situation; it can be got by FDS in all regions. TR can be got by Legion and obeys the normal distribution according to existing research [11].Obviously,Z obeys the normal distribution, and its mean μz and standard deviation σz are as follows:(4)μZ=TA-μTR,σZ=σTR.μTR and σTR are TR’s mean and standard deviation. The reliability index of safe evacuation (β) can be indicated as follows:(5)β=μZσZ.Then,u12 can be described as follows:(6)μ12=PZ>0=ϕβ.In the type,ϕ(·) is standard normal distribution function.


#### 3.1.2. Security Risk Index

In pedestrians’ evacuation process, some high density and serious conflicting regions are often high probability of accidents. There is security risk that should be avoided.(
1) Effect of High Density Region
u
21. This index reflects the effect of high density. It can be considered that regions under “D” service level are high density [12]. The formula takes time of duration and affected passenger flow into account:(7)u21=∑i=1e∑j=1milij·vijTt·qt.In the type,e is the number of high density regions, mi is the number of high density time periods in region i, lij is the length of time period j in region i and the unit is “s,” vij is the number of passengers during time period j in region i, Tt is total simulation time and the unit is “s,” and qt is the total passengers in all simulation regions.(
2) Effect of Conflicting Points
u
22. This index represents the proportion of passengers who go through the conflicting points:(8)u22=∑i=1nqiqt.In the type,qi stands for the number of affected passengers in conflicting point i, qt stands for the total passengers during the simulation time, and n is the number of conflicting points.


#### 3.1.3. Effectiveness Index

Effectiveness refers to the execution efficiency in pedestrians’ evacuation process.(
1) Average Evacuation Time
u
31. For passengers, evacuation time can reflect evacuation efficiency intuitively:(9)u31=∑i=1qttiqt.In the type,ti stands for the evacuation time of passenger i and the unit is “s” and qt stands for the total passengers during the simulation time.(
2) The Number of Evacuation Passengers in Unit Time
u
32. According to “Design Specifications for Subway,” the longest evacuation time is not more than 6 minutes in subway station. The number of evacuation passengers in unit time can also reflect evacuation efficiency. The formula is as follows:(10)u32=QTT≤6Q6T>6.In the type,Q stands for the number of evacuation passengers in 6 minutes; T stands for the whole evacuation time.


#### 3.1.4. Orderliness Index

Orderliness mainly reflects the order of pedestrians’ evacuation process. Good order can ensure safety and comfort.(
1) Round Coefficient
u
41. This index reflects the convenience of pedestrians’ evacuation in integrated transport hub:(11)u41=∑i=1r∑j=1swij∑k=1OijlijkOij·Sij.In the type,r is the total number of starting points, s is the total number of terminal points, Oij is the number of passengers from starting point i to terminal point j, Sij stands for the shortest distance from i to j and the unit is “m,” and lijk stands for the actual working distance of passenger k from origin i to destination j. wij is weight of i to j. Considering the passenger flow of each OD pair, wij can be calculated based on entropy weight coefficient method. Based on information theory [13], the entropy of OD pair ij is(12)Hij=-1ln⁡n∑l=1nhijlln⁡hijl,hijl=oijl∑l=1noijl,where n is the number of fire evacuation plans.The weight of OD pairij is(13)wij=(1-Hij)(r×s-∑i=1r∑j=1sHij).(
2) The Diversity of Speed
u
42. The index reflects orderliness of evacuation process directly. The formula is as follows:(14)u42=∑i=1nvi-v¯2n.In the type,vi is evacuation speed of period i, n is the number of simulation time periods, and v- is the average speed during the whole simulation.


### 3.2. Matter-Element Evaluation Algorithm

Many algorithms can be used to sort the best plan such as cosine function, linear assignment, fuzzy logic, and matter-element algorithm [14–16]. This paper uses matter-element analysis to calculate the value of decision-making of each plan. The main theories of this algorithm are the definition of matter-element, extension mathematics, and the matter-element transformation theory [17–20]. It has been widely used in evaluation fields. In this paper, a specific matter-element algorithm is established based on the dynamic evaluation indicators system.


#### 3.2.1. Normalization of Decision-Making Matrix

It is assumed that there aren fire evacuation plans in subway station noted to S={S1,S2,…,Sn}. The index set of second grade is P={P1,P2,…,Pn}. Then the decision-making matrix of plan Si with matter-element algorithm can be written as follows:(15)Yi=AiP1yi1P2yi2⋮⋮Pmyimω1ω2⋮ωm,i=1,2,…,n.Each index has different units and needed to be normalized. To define index setP+={indexes of bigger better} and to define P-={indexes of smaller better}, then normalization process can be represented as follows:(16)rij=yij-min⁡1≤i≤nyijmax⁡1≤i≤nyij-min⁡1≤i≤nyij,i=1,2,…,n,j∈P+,rij=max⁡1≤i≤nyij-yijmax⁡1≤i≤nyij-min⁡1≤i≤nyij,i=1,2,…,n,j∈P-.The normalized matter-element algorithm matrix of planSi can be represented as follows:(17)Ri=AiP1ri1P2ri2⋮⋮Pmrimω1ω2⋮ωm,i=1,2,…,n.


#### 3.2.2. The Best and Worst Matrix

To define(18)rj+=max⁡1≤i≤n⁡rij,j∈P+min⁡1≤i≤nrij,j∈P-,rj-=min⁡1≤i≤nrij,j∈P-max⁡1≤i≤n⁡rij,j∈P+,then the best and worst matrix can be represented as follows:(19)R+=AiP1r1+P2r2+⋮⋮Pmrm+ω1ω2⋮ωm,R-=AiP1r1-P2r2-⋮⋮Pmrm-ω1ω2⋮ωm.


#### 3.2.3. Weights Calculation

In this paper, APN method is used to calculate the weight of each index [21, 22].


#### 3.2.4. The Distance and Relative Closeness

To defineSi+ as the distance from plan Si  (i=1,2,…,n) to the best plan and Si- as the distance to the worst plan(20)Si+=∑j=1mωj2rij-R+2,Si-=∑j=1mωj2rij-R-2,then the relative closeness of planSi  (i=1,2,…,n) to the best plan is ei:(21)ei=Si-Si++Si-.In the type,ei is the value of decision-making of plan Si and 0<ei<1. When ei is bigger, Si+ is closer to 0 and the evacuation plan is better.


## 3.1. Indicators System and Quantification of Indexes

It is vital to ensure that pedestrians’ evacuation in subway fire is effective and safe. The evaluation of subway fire evacuation is used to investigate the merits degree of survival index, security risk index, effectiveness index, and orderliness index under different conditions such as facility layout and evacuation plan. The dynamic pedestrians’ evacuation evaluation indicators system in subway fire based on the output parameters of Legion is shown in Figure2.Figure 2
Pedestrians’ evacuation evaluation indicators system in subway fire.


### 3.1.1. Survival Index

Survival index reflects the survival probability directly in the evacuation process. It can be described as two aspects: one is survival ratio and the other one is survival reliability.(
1) Survival Ratio
u
11. The index reflects pedestrians’ survival situation in the evacuation process:(1)u11=qQ×100%.In the type,q stands for the amount of evacuation pedestrians; Q is the total amount of pedestrians.(
2) Survival Reliability
u
12. Due to the randomness of pedestrians’ evacuation process, there will exist distance between deterministic methods to describe the evacuation process and actual situation. So this paper uses survival reliability index to describe pedestrians’ evacuation process.In the process, if available safe evacuation time (ASET) is longer than required safe evacuation time (RSET), pedestrians will be safe. That is,(2)ASET-RSET>0.According to the above criterion, the limit state equation for pedestrians’ safe evacuation can be constructed:(3)Z=TA-TR>0.TA stands for ASET and TR stands for RSET. The unit is “s.” TA is mainly affected by the fire situation; it can be got by FDS in all regions. TR can be got by Legion and obeys the normal distribution according to existing research [11].Obviously,Z obeys the normal distribution, and its mean μz and standard deviation σz are as follows:(4)μZ=TA-μTR,σZ=σTR.μTR and σTR are TR’s mean and standard deviation. The reliability index of safe evacuation (β) can be indicated as follows:(5)β=μZσZ.Then,u12 can be described as follows:(6)μ12=PZ>0=ϕβ.In the type,ϕ(·) is standard normal distribution function.


### 3.1.2. Security Risk Index

In pedestrians’ evacuation process, some high density and serious conflicting regions are often high probability of accidents. There is security risk that should be avoided.(
1) Effect of High Density Region
u
21. This index reflects the effect of high density. It can be considered that regions under “D” service level are high density [12]. The formula takes time of duration and affected passenger flow into account:(7)u21=∑i=1e∑j=1milij·vijTt·qt.In the type,e is the number of high density regions, mi is the number of high density time periods in region i, lij is the length of time period j in region i and the unit is “s,” vij is the number of passengers during time period j in region i, Tt is total simulation time and the unit is “s,” and qt is the total passengers in all simulation regions.(
2) Effect of Conflicting Points
u
22. This index represents the proportion of passengers who go through the conflicting points:(8)u22=∑i=1nqiqt.In the type,qi stands for the number of affected passengers in conflicting point i, qt stands for the total passengers during the simulation time, and n is the number of conflicting points.


### 3.1.3. Effectiveness Index

Effectiveness refers to the execution efficiency in pedestrians’ evacuation process.(
1) Average Evacuation Time
u
31. For passengers, evacuation time can reflect evacuation efficiency intuitively:(9)u31=∑i=1qttiqt.In the type,ti stands for the evacuation time of passenger i and the unit is “s” and qt stands for the total passengers during the simulation time.(
2) The Number of Evacuation Passengers in Unit Time
u
32. According to “Design Specifications for Subway,” the longest evacuation time is not more than 6 minutes in subway station. The number of evacuation passengers in unit time can also reflect evacuation efficiency. The formula is as follows:(10)u32=QTT≤6Q6T>6.In the type,Q stands for the number of evacuation passengers in 6 minutes; T stands for the whole evacuation time.


### 3.1.4. Orderliness Index

Orderliness mainly reflects the order of pedestrians’ evacuation process. Good order can ensure safety and comfort.(
1) Round Coefficient
u
41. This index reflects the convenience of pedestrians’ evacuation in integrated transport hub:(11)u41=∑i=1r∑j=1swij∑k=1OijlijkOij·Sij.In the type,r is the total number of starting points, s is the total number of terminal points, Oij is the number of passengers from starting point i to terminal point j, Sij stands for the shortest distance from i to j and the unit is “m,” and lijk stands for the actual working distance of passenger k from origin i to destination j. wij is weight of i to j. Considering the passenger flow of each OD pair, wij can be calculated based on entropy weight coefficient method. Based on information theory [13], the entropy of OD pair ij is(12)Hij=-1ln⁡n∑l=1nhijlln⁡hijl,hijl=oijl∑l=1noijl,where n is the number of fire evacuation plans.The weight of OD pairij is(13)wij=(1-Hij)(r×s-∑i=1r∑j=1sHij).(
2) The Diversity of Speed
u
42. The index reflects orderliness of evacuation process directly. The formula is as follows:(14)u42=∑i=1nvi-v¯2n.In the type,vi is evacuation speed of period i, n is the number of simulation time periods, and v- is the average speed during the whole simulation.


## 3.1.1. Survival Index

Survival index reflects the survival probability directly in the evacuation process. It can be described as two aspects: one is survival ratio and the other one is survival reliability.(
1) Survival Ratio
u
11. The index reflects pedestrians’ survival situation in the evacuation process:(1)u11=qQ×100%.In the type,q stands for the amount of evacuation pedestrians; Q is the total amount of pedestrians.(
2) Survival Reliability
u
12. Due to the randomness of pedestrians’ evacuation process, there will exist distance between deterministic methods to describe the evacuation process and actual situation. So this paper uses survival reliability index to describe pedestrians’ evacuation process.In the process, if available safe evacuation time (ASET) is longer than required safe evacuation time (RSET), pedestrians will be safe. That is,(2)ASET-RSET>0.According to the above criterion, the limit state equation for pedestrians’ safe evacuation can be constructed:(3)Z=TA-TR>0.TA stands for ASET and TR stands for RSET. The unit is “s.” TA is mainly affected by the fire situation; it can be got by FDS in all regions. TR can be got by Legion and obeys the normal distribution according to existing research [11].Obviously,Z obeys the normal distribution, and its mean μz and standard deviation σz are as follows:(4)μZ=TA-μTR,σZ=σTR.μTR and σTR are TR’s mean and standard deviation. The reliability index of safe evacuation (β) can be indicated as follows:(5)β=μZσZ.Then,u12 can be described as follows:(6)μ12=PZ>0=ϕβ.In the type,ϕ(·) is standard normal distribution function.


## 3.1.2. Security Risk Index

In pedestrians’ evacuation process, some high density and serious conflicting regions are often high probability of accidents. There is security risk that should be avoided.(
1) Effect of High Density Region
u
21. This index reflects the effect of high density. It can be considered that regions under “D” service level are high density [12]. The formula takes time of duration and affected passenger flow into account:(7)u21=∑i=1e∑j=1milij·vijTt·qt.In the type,e is the number of high density regions, mi is the number of high density time periods in region i, lij is the length of time period j in region i and the unit is “s,” vij is the number of passengers during time period j in region i, Tt is total simulation time and the unit is “s,” and qt is the total passengers in all simulation regions.(
2) Effect of Conflicting Points
u
22. This index represents the proportion of passengers who go through the conflicting points:(8)u22=∑i=1nqiqt.In the type,qi stands for the number of affected passengers in conflicting point i, qt stands for the total passengers during the simulation time, and n is the number of conflicting points.


## 3.1.3. Effectiveness Index

Effectiveness refers to the execution efficiency in pedestrians’ evacuation process.(
1) Average Evacuation Time
u
31. For passengers, evacuation time can reflect evacuation efficiency intuitively:(9)u31=∑i=1qttiqt.In the type,ti stands for the evacuation time of passenger i and the unit is “s” and qt stands for the total passengers during the simulation time.(
2) The Number of Evacuation Passengers in Unit Time
u
32. According to “Design Specifications for Subway,” the longest evacuation time is not more than 6 minutes in subway station. The number of evacuation passengers in unit time can also reflect evacuation efficiency. The formula is as follows:(10)u32=QTT≤6Q6T>6.In the type,Q stands for the number of evacuation passengers in 6 minutes; T stands for the whole evacuation time.


## 3.1.4. Orderliness Index

Orderliness mainly reflects the order of pedestrians’ evacuation process. Good order can ensure safety and comfort.(
1) Round Coefficient
u
41. This index reflects the convenience of pedestrians’ evacuation in integrated transport hub:(11)u41=∑i=1r∑j=1swij∑k=1OijlijkOij·Sij.In the type,r is the total number of starting points, s is the total number of terminal points, Oij is the number of passengers from starting point i to terminal point j, Sij stands for the shortest distance from i to j and the unit is “m,” and lijk stands for the actual working distance of passenger k from origin i to destination j. wij is weight of i to j. Considering the passenger flow of each OD pair, wij can be calculated based on entropy weight coefficient method. Based on information theory [13], the entropy of OD pair ij is(12)Hij=-1ln⁡n∑l=1nhijlln⁡hijl,hijl=oijl∑l=1noijl,where n is the number of fire evacuation plans.The weight of OD pairij is(13)wij=(1-Hij)(r×s-∑i=1r∑j=1sHij).(
2) The Diversity of Speed
u
42. The index reflects orderliness of evacuation process directly. The formula is as follows:(14)u42=∑i=1nvi-v¯2n.In the type,vi is evacuation speed of period i, n is the number of simulation time periods, and v- is the average speed during the whole simulation.


## 3.2. Matter-Element Evaluation Algorithm

Many algorithms can be used to sort the best plan such as cosine function, linear assignment, fuzzy logic, and matter-element algorithm [14–16]. This paper uses matter-element analysis to calculate the value of decision-making of each plan. The main theories of this algorithm are the definition of matter-element, extension mathematics, and the matter-element transformation theory [17–20]. It has been widely used in evaluation fields. In this paper, a specific matter-element algorithm is established based on the dynamic evaluation indicators system.


### 3.2.1. Normalization of Decision-Making Matrix

It is assumed that there aren fire evacuation plans in subway station noted to S={S1,S2,…,Sn}. The index set of second grade is P={P1,P2,…,Pn}. Then the decision-making matrix of plan Si with matter-element algorithm can be written as follows:(15)Yi=AiP1yi1P2yi2⋮⋮Pmyimω1ω2⋮ωm,i=1,2,…,n.Each index has different units and needed to be normalized. To define index setP+={indexes of bigger better} and to define P-={indexes of smaller better}, then normalization process can be represented as follows:(16)rij=yij-min⁡1≤i≤nyijmax⁡1≤i≤nyij-min⁡1≤i≤nyij,i=1,2,…,n,j∈P+,rij=max⁡1≤i≤nyij-yijmax⁡1≤i≤nyij-min⁡1≤i≤nyij,i=1,2,…,n,j∈P-.The normalized matter-element algorithm matrix of planSi can be represented as follows:(17)Ri=AiP1ri1P2ri2⋮⋮Pmrimω1ω2⋮ωm,i=1,2,…,n.


### 3.2.2. The Best and Worst Matrix

To define(18)rj+=max⁡1≤i≤n⁡rij,j∈P+min⁡1≤i≤nrij,j∈P-,rj-=min⁡1≤i≤nrij,j∈P-max⁡1≤i≤n⁡rij,j∈P+,then the best and worst matrix can be represented as follows:(19)R+=AiP1r1+P2r2+⋮⋮Pmrm+ω1ω2⋮ωm,R-=AiP1r1-P2r2-⋮⋮Pmrm-ω1ω2⋮ωm.


### 3.2.3. Weights Calculation

In this paper, APN method is used to calculate the weight of each index [21, 22].


### 3.2.4. The Distance and Relative Closeness

To defineSi+ as the distance from plan Si  (i=1,2,…,n) to the best plan and Si- as the distance to the worst plan(20)Si+=∑j=1mωj2rij-R+2,Si-=∑j=1mωj2rij-R-2,then the relative closeness of planSi  (i=1,2,…,n) to the best plan is ei:(21)ei=Si-Si++Si-.In the type,ei is the value of decision-making of plan Si and 0<ei<1. When ei is bigger, Si+ is closer to 0 and the evacuation plan is better.


## 3.2.1. Normalization of Decision-Making Matrix

It is assumed that there aren fire evacuation plans in subway station noted to S={S1,S2,…,Sn}. The index set of second grade is P={P1,P2,…,Pn}. Then the decision-making matrix of plan Si with matter-element algorithm can be written as follows:(15)Yi=AiP1yi1P2yi2⋮⋮Pmyimω1ω2⋮ωm,i=1,2,…,n.Each index has different units and needed to be normalized. To define index setP+={indexes of bigger better} and to define P-={indexes of smaller better}, then normalization process can be represented as follows:(16)rij=yij-min⁡1≤i≤nyijmax⁡1≤i≤nyij-min⁡1≤i≤nyij,i=1,2,…,n,j∈P+,rij=max⁡1≤i≤nyij-yijmax⁡1≤i≤nyij-min⁡1≤i≤nyij,i=1,2,…,n,j∈P-.The normalized matter-element algorithm matrix of planSi can be represented as follows:(17)Ri=AiP1ri1P2ri2⋮⋮Pmrimω1ω2⋮ωm,i=1,2,…,n.


## 3.2.2. The Best and Worst Matrix

To define(18)rj+=max⁡1≤i≤n⁡rij,j∈P+min⁡1≤i≤nrij,j∈P-,rj-=min⁡1≤i≤nrij,j∈P-max⁡1≤i≤n⁡rij,j∈P+,then the best and worst matrix can be represented as follows:(19)R+=AiP1r1+P2r2+⋮⋮Pmrm+ω1ω2⋮ωm,R-=AiP1r1-P2r2-⋮⋮Pmrm-ω1ω2⋮ωm.


## 3.2.3. Weights Calculation

In this paper, APN method is used to calculate the weight of each index [21, 22].


## 3.2.4. The Distance and Relative Closeness

To defineSi+ as the distance from plan Si  (i=1,2,…,n) to the best plan and Si- as the distance to the worst plan(20)Si+=∑j=1mωj2rij-R+2,Si-=∑j=1mωj2rij-R-2,then the relative closeness of planSi  (i=1,2,…,n) to the best plan is ei:(21)ei=Si-Si++Si-.In the type,ei is the value of decision-making of plan Si and 0<ei<1. When ei is bigger, Si+ is closer to 0 and the evacuation plan is better.


## 4. Test Results

### 4.1. Simulation Model

In order to test the practicability of evacuation evaluation system in subway fire, the paper chooses Songjiazhuang (SJZ) station as an example. SJZ is a transfer station of line 10, line 5, and line Yizhuang. It is predicted that the peak hour traffic of SJZ will reach 66800 in 2016. There is no doubt that it will be one of the most large-scale subway stations in Asia. Therefore it is particularly important to evaluate the fire evacuation plans of SJZ.


#### 4.1.1. Data Preparation

Data preparation is the basic work for pedestrian simulation modeling. The number of passengers in subway platform and subway hall is shown in Table3 through field investigation.Table 3
The number of passengers for evacuation.
Places
Arriving person
Waiting person
Subway platform
Line 10 up
1200
300
Line 10 down
1200
300
Line 5
700
300
Line Yizhuang
700
300
Subway hall
—
450


#### 4.1.2. Fire Environment

In order to reflect the evacuation conditions of different fire scenes in subway, in this paper, two different scenarios are simulated. Exhaust mode settings are shown in Table4 and the distribution of fire product in platform is shown in Figure 3.Table 4
Exhaust mode settings in different fire scenes.
Fire scenes
Exhaust smoke level
Exhaust smoke model
Remark
Fire of platform
180
Exhaust smoke of platform
All of the shield doors open for auxiliary exhausting smoke
Fire of hall
180
Exhaust smoke of hall
All of the shield doors open for auxiliary exhausting smokeFigure 3
Fire product distributed in platform.


#### 4.1.3. Speed Calibration of Fire Environment

Equivalent velocity is the movement speed in fire environment. The paper considered the impact of mainly fire products on personnel evacuation separately:(22)v=v0·fKs,ρ,T=v0·f1Ksf1ρf1T,where v is equivalent velocity, v0 is pedestrian normal velocity, f1(Ks) is visibility influence coefficient, f1(ρ) is toxic gas concentration influence coefficient, and f1(T) is temperature influence coefficient.(
1) The Effect of Visibility on Pedestrian Speed. The relationship between people’ walking speed and smoke obscuration coefficient when people were exposed to the irritating and nonirritating smoke is shown in Figure 4 by experiment [23].Figure 4
The walking speed in irritating and nonirritating smoke.(
2) The Effect of Toxic Gas on Pedestrian Speed. The effect of toxic gas on evacuation pedestrian is velocity-decrease. Milke had got the data by experiment about the effect of different concentrations of CO on pedestrian in fire [24] shown in Table 5.Table 5
Different concentrations of CO impact on pedestrian in fire.
Co (%)
Exposure time (min)
Cumulative dose (%min)
Personnel velocity decrease (m/s)
>0.1
1
>0.1
0.05
2
>0.2
0.1
n
>0.1n
0.05n
>0.15
1
>0.15
0.1
2
>0.3
0.2
n
>0.15n
0.1n
>0.2
1
>0.2
0.15
2
>0.4
0.3
n
>0.2n
0.15n
>0.25
Person faint or death, being unable to move(
3) The Effect of Temperature on Pedestrian Speed. According to the predecessors’ research data, the influence coefficient of flue gas temperature on personnel movement speed can be concluded as follows: (23)f3T=1(T0<Ts≤Tσ1)(vmax⁡-1.2)Ts-Tσ1/Tσ2-Tσ12v0+1(Tσ1<Ts≤Tσ2)vmax⁡1.21-Ts-Tσ2Tdeal-Tσ22Tσ2<Ts≤Tdeal,where Ts is the temperature in the fire, v0 is pedestrians normal velocity, vmax⁡ is maximum speed to escape, generally taking 5 m/s, Tσ1 is the temperature when people feel uncomfortable, generally taking 30°C, Tσ2 is the temperature that harm a person, generally taking 60°C, and Tσ2 is the temperature that cause death, generally taking 120°C.


#### 4.1.4. Pedestrian Survival Condition Calibration

All kinds of fire products occurring in the process of fire have a great threat to pedestrians’ life. The third edition ofFire handbook in China gives human tolerance limits to different fire products (Table 6).Table 6
Human tolerance limits to fire products.
Content
Human tolerance limits
Radiation heat flux
2.5 kw/m2
Gas temperature
When the smoke layer height >2 m, 180°C
When <2 m for 30 min, 60°C
Visibility
When the smoke layer height <2 m, 0.1 m (10 cm)
Toxic gas
CO concentration achieves 0.25%


#### 4.1.5. Evacuation Routes Calibration

Plan 1. According to the layout of metro station and passenger flow forecast, the mode of passenger evacuation from the nearest exit is shown in Figure 5.Figure 5
The evacuation route of plan 1.Plan 2. Because of the uneven distribution of passengers in the platform, it is suggested that part of passengers is guided to other exits which are not nearest to them. The specific measures are shown in Figure 6, guiding 300 passengers in line 10 platform to exits in line 5 and line Yizhuang platform.Figure 6
The evacuation route of plan 2.


### 4.2. Results of Evaluation

Based on the output data of simulation model, the value of the evaluation indexes of two evacuation plans in two scenes can be calculated, as shown in Table7.Table 7
The value of evaluation indexes of two plans in two scenes.
Evaluation indexes
Subway platform on fire
Subway hall on fire
Plan 1 (S1)
Plan 2 (S2)
Plan 1 (S1)
Plan 2 (S2)
u
11
99.35
99.57
99.82
99.88
u
12
0.943
0.942
0.969
0.966
u
21
0.763
0.783
0.782
0.773
u
22
0.639
0.623
0.659
0.624
u
31
278
221
271
216
u
32
678
741
691
761
u
41
1.36
1.32
1.33
1.21
u
42
0.18
0.14
0.16
0.13The value of decision-making of different plans can be calculated by the matter-element algorithms, as shown in Table8.Table 8
The value of decision-making of different scenes.
The value of decision-making
Subway platform on fire
Subway hall on fire
Plan 1 (S1)
Plan 2 (S2)
Plan 1 (S1)
Plan 2 (S2)
e
i
0.198
0.366
0.730
0.896From the results, when the platform is on fire,e2>e1. It shows that S2 is better than S1. When the hall is on fire, e2>e1. It also shows that S2 is better than S1. According to the value of decision-making in two scenes, it is known that the fire evacuation effect in hall is better than in platform regardless of plans.


### 4.3. Analysis of Simulation Results

From the value of evaluation indexes of two plans shown in Table7, we know the following.(1)
More people can escape in plan 2 and the others will die in line 10 platform from the simulation process. Figure7 shows the relationship between the number of people present in the subway and the evaluation time of two plans. It is obvious that the escape speed of plan 2 is faster than plan 1.(2)
The comparison of security risk shows the effect of high density passenger and the number of conflicts is less in plan 2. It is proved that the evacuation organization of plan 2 is more reasonable.(3)
The comparison of effectiveness index shows the average evacuation time of plan 2 is less, although part of people did not evacuate from the nearest exits.(4)
The comparison of orderliness index shows the diversity of speed is smaller, so the evacuation flow is more uniform and orderly in plan 2.Figure 7
The relationship between the number of people present in the subway and the evaluation time.
(a)
Plan 1
(b)
Plan 2


### 4.4. Simulation Conclusion and Optimization

(1)
Because of the uneven distribution of passengers in subway, the plan that all pedestrians evacuate from the nearest exits is not the best. Guiding a certain number of passengers to other exits may be more suitable.
(2)
The evacuation time of pedestrians in line 10 platform is the longest from the simulation process; it is suggested that the new emergency stair or channel of line 10 platform should be added.


## 4.1. Simulation Model

In order to test the practicability of evacuation evaluation system in subway fire, the paper chooses Songjiazhuang (SJZ) station as an example. SJZ is a transfer station of line 10, line 5, and line Yizhuang. It is predicted that the peak hour traffic of SJZ will reach 66800 in 2016. There is no doubt that it will be one of the most large-scale subway stations in Asia. Therefore it is particularly important to evaluate the fire evacuation plans of SJZ.


### 4.1.1. Data Preparation

Data preparation is the basic work for pedestrian simulation modeling. The number of passengers in subway platform and subway hall is shown in Table3 through field investigation.Table 3
The number of passengers for evacuation.
Places
Arriving person
Waiting person
Subway platform
Line 10 up
1200
300
Line 10 down
1200
300
Line 5
700
300
Line Yizhuang
700
300
Subway hall
—
450


### 4.1.2. Fire Environment

In order to reflect the evacuation conditions of different fire scenes in subway, in this paper, two different scenarios are simulated. Exhaust mode settings are shown in Table4 and the distribution of fire product in platform is shown in Figure 3.Table 4
Exhaust mode settings in different fire scenes.
Fire scenes
Exhaust smoke level
Exhaust smoke model
Remark
Fire of platform
180
Exhaust smoke of platform
All of the shield doors open for auxiliary exhausting smoke
Fire of hall
180
Exhaust smoke of hall
All of the shield doors open for auxiliary exhausting smokeFigure 3
Fire product distributed in platform.


### 4.1.3. Speed Calibration of Fire Environment

Equivalent velocity is the movement speed in fire environment. The paper considered the impact of mainly fire products on personnel evacuation separately:(22)v=v0·fKs,ρ,T=v0·f1Ksf1ρf1T,where v is equivalent velocity, v0 is pedestrian normal velocity, f1(Ks) is visibility influence coefficient, f1(ρ) is toxic gas concentration influence coefficient, and f1(T) is temperature influence coefficient.(
1) The Effect of Visibility on Pedestrian Speed. The relationship between people’ walking speed and smoke obscuration coefficient when people were exposed to the irritating and nonirritating smoke is shown in Figure 4 by experiment [23].Figure 4
The walking speed in irritating and nonirritating smoke.(
2) The Effect of Toxic Gas on Pedestrian Speed. The effect of toxic gas on evacuation pedestrian is velocity-decrease. Milke had got the data by experiment about the effect of different concentrations of CO on pedestrian in fire [24] shown in Table 5.Table 5
Different concentrations of CO impact on pedestrian in fire.
Co (%)
Exposure time (min)
Cumulative dose (%min)
Personnel velocity decrease (m/s)
>0.1
1
>0.1
0.05
2
>0.2
0.1
n
>0.1n
0.05n
>0.15
1
>0.15
0.1
2
>0.3
0.2
n
>0.15n
0.1n
>0.2
1
>0.2
0.15
2
>0.4
0.3
n
>0.2n
0.15n
>0.25
Person faint or death, being unable to move(
3) The Effect of Temperature on Pedestrian Speed. According to the predecessors’ research data, the influence coefficient of flue gas temperature on personnel movement speed can be concluded as follows: (23)f3T=1(T0<Ts≤Tσ1)(vmax⁡-1.2)Ts-Tσ1/Tσ2-Tσ12v0+1(Tσ1<Ts≤Tσ2)vmax⁡1.21-Ts-Tσ2Tdeal-Tσ22Tσ2<Ts≤Tdeal,where Ts is the temperature in the fire, v0 is pedestrians normal velocity, vmax⁡ is maximum speed to escape, generally taking 5 m/s, Tσ1 is the temperature when people feel uncomfortable, generally taking 30°C, Tσ2 is the temperature that harm a person, generally taking 60°C, and Tσ2 is the temperature that cause death, generally taking 120°C.


### 4.1.4. Pedestrian Survival Condition Calibration

All kinds of fire products occurring in the process of fire have a great threat to pedestrians’ life. The third edition ofFire handbook in China gives human tolerance limits to different fire products (Table 6).Table 6
Human tolerance limits to fire products.
Content
Human tolerance limits
Radiation heat flux
2.5 kw/m2
Gas temperature
When the smoke layer height >2 m, 180°C
When <2 m for 30 min, 60°C
Visibility
When the smoke layer height <2 m, 0.1 m (10 cm)
Toxic gas
CO concentration achieves 0.25%


### 4.1.5. Evacuation Routes Calibration

Plan 1. According to the layout of metro station and passenger flow forecast, the mode of passenger evacuation from the nearest exit is shown in Figure 5.Figure 5
The evacuation route of plan 1.Plan 2. Because of the uneven distribution of passengers in the platform, it is suggested that part of passengers is guided to other exits which are not nearest to them. The specific measures are shown in Figure 6, guiding 300 passengers in line 10 platform to exits in line 5 and line Yizhuang platform.Figure 6
The evacuation route of plan 2.


## 4.1.1. Data Preparation

Data preparation is the basic work for pedestrian simulation modeling. The number of passengers in subway platform and subway hall is shown in Table3 through field investigation.Table 3
The number of passengers for evacuation.
Places
Arriving person
Waiting person
Subway platform
Line 10 up
1200
300
Line 10 down
1200
300
Line 5
700
300
Line Yizhuang
700
300
Subway hall
—
450


## 4.1.2. Fire Environment

In order to reflect the evacuation conditions of different fire scenes in subway, in this paper, two different scenarios are simulated. Exhaust mode settings are shown in Table4 and the distribution of fire product in platform is shown in Figure 3.Table 4
Exhaust mode settings in different fire scenes.
Fire scenes
Exhaust smoke level
Exhaust smoke model
Remark
Fire of platform
180
Exhaust smoke of platform
All of the shield doors open for auxiliary exhausting smoke
Fire of hall
180
Exhaust smoke of hall
All of the shield doors open for auxiliary exhausting smokeFigure 3
Fire product distributed in platform.


## 4.1.3. Speed Calibration of Fire Environment

Equivalent velocity is the movement speed in fire environment. The paper considered the impact of mainly fire products on personnel evacuation separately:(22)v=v0·fKs,ρ,T=v0·f1Ksf1ρf1T,where v is equivalent velocity, v0 is pedestrian normal velocity, f1(Ks) is visibility influence coefficient, f1(ρ) is toxic gas concentration influence coefficient, and f1(T) is temperature influence coefficient.(
1) The Effect of Visibility on Pedestrian Speed. The relationship between people’ walking speed and smoke obscuration coefficient when people were exposed to the irritating and nonirritating smoke is shown in Figure 4 by experiment [23].Figure 4
The walking speed in irritating and nonirritating smoke.(
2) The Effect of Toxic Gas on Pedestrian Speed. The effect of toxic gas on evacuation pedestrian is velocity-decrease. Milke had got the data by experiment about the effect of different concentrations of CO on pedestrian in fire [24] shown in Table 5.Table 5
Different concentrations of CO impact on pedestrian in fire.
Co (%)
Exposure time (min)
Cumulative dose (%min)
Personnel velocity decrease (m/s)
>0.1
1
>0.1
0.05
2
>0.2
0.1
n
>0.1n
0.05n
>0.15
1
>0.15
0.1
2
>0.3
0.2
n
>0.15n
0.1n
>0.2
1
>0.2
0.15
2
>0.4
0.3
n
>0.2n
0.15n
>0.25
Person faint or death, being unable to move(
3) The Effect of Temperature on Pedestrian Speed. According to the predecessors’ research data, the influence coefficient of flue gas temperature on personnel movement speed can be concluded as follows: (23)f3T=1(T0<Ts≤Tσ1)(vmax⁡-1.2)Ts-Tσ1/Tσ2-Tσ12v0+1(Tσ1<Ts≤Tσ2)vmax⁡1.21-Ts-Tσ2Tdeal-Tσ22Tσ2<Ts≤Tdeal,where Ts is the temperature in the fire, v0 is pedestrians normal velocity, vmax⁡ is maximum speed to escape, generally taking 5 m/s, Tσ1 is the temperature when people feel uncomfortable, generally taking 30°C, Tσ2 is the temperature that harm a person, generally taking 60°C, and Tσ2 is the temperature that cause death, generally taking 120°C.


## 4.1.4. Pedestrian Survival Condition Calibration

All kinds of fire products occurring in the process of fire have a great threat to pedestrians’ life. The third edition ofFire handbook in China gives human tolerance limits to different fire products (Table 6).Table 6
Human tolerance limits to fire products.
Content
Human tolerance limits
Radiation heat flux
2.5 kw/m2
Gas temperature
When the smoke layer height >2 m, 180°C
When <2 m for 30 min, 60°C
Visibility
When the smoke layer height <2 m, 0.1 m (10 cm)
Toxic gas
CO concentration achieves 0.25%


## 4.1.5. Evacuation Routes Calibration

Plan 1. According to the layout of metro station and passenger flow forecast, the mode of passenger evacuation from the nearest exit is shown in Figure 5.Figure 5
The evacuation route of plan 1.Plan 2. Because of the uneven distribution of passengers in the platform, it is suggested that part of passengers is guided to other exits which are not nearest to them. The specific measures are shown in Figure 6, guiding 300 passengers in line 10 platform to exits in line 5 and line Yizhuang platform.Figure 6
The evacuation route of plan 2.


## 4.2. Results of Evaluation

Based on the output data of simulation model, the value of the evaluation indexes of two evacuation plans in two scenes can be calculated, as shown in Table7.Table 7
The value of evaluation indexes of two plans in two scenes.
Evaluation indexes
Subway platform on fire
Subway hall on fire
Plan 1 (S1)
Plan 2 (S2)
Plan 1 (S1)
Plan 2 (S2)
u
11
99.35
99.57
99.82
99.88
u
12
0.943
0.942
0.969
0.966
u
21
0.763
0.783
0.782
0.773
u
22
0.639
0.623
0.659
0.624
u
31
278
221
271
216
u
32
678
741
691
761
u
41
1.36
1.32
1.33
1.21
u
42
0.18
0.14
0.16
0.13The value of decision-making of different plans can be calculated by the matter-element algorithms, as shown in Table8.Table 8
The value of decision-making of different scenes.
The value of decision-making
Subway platform on fire
Subway hall on fire
Plan 1 (S1)
Plan 2 (S2)
Plan 1 (S1)
Plan 2 (S2)
e
i
0.198
0.366
0.730
0.896From the results, when the platform is on fire,e2>e1. It shows that S2 is better than S1. When the hall is on fire, e2>e1. It also shows that S2 is better than S1. According to the value of decision-making in two scenes, it is known that the fire evacuation effect in hall is better than in platform regardless of plans.


## 4.3. Analysis of Simulation Results

From the value of evaluation indexes of two plans shown in Table7, we know the following.(1)
More people can escape in plan 2 and the others will die in line 10 platform from the simulation process. Figure7 shows the relationship between the number of people present in the subway and the evaluation time of two plans. It is obvious that the escape speed of plan 2 is faster than plan 1.(2)
The comparison of security risk shows the effect of high density passenger and the number of conflicts is less in plan 2. It is proved that the evacuation organization of plan 2 is more reasonable.(3)
The comparison of effectiveness index shows the average evacuation time of plan 2 is less, although part of people did not evacuate from the nearest exits.(4)
The comparison of orderliness index shows the diversity of speed is smaller, so the evacuation flow is more uniform and orderly in plan 2.Figure 7
The relationship between the number of people present in the subway and the evaluation time.
(a)
Plan 1
(b)
Plan 2


## 4.4. Simulation Conclusion and Optimization

(1)
Because of the uneven distribution of passengers in subway, the plan that all pedestrians evacuate from the nearest exits is not the best. Guiding a certain number of passengers to other exits may be more suitable.
(2)
The evacuation time of pedestrians in line 10 platform is the longest from the simulation process; it is suggested that the new emergency stair or channel of line 10 platform should be added.


## 5. Conclusion

With the continuous improvement of urban subway system in China, the ability of subway stations to prevent the disasters and accidents will face a huge challenge. In the practical application, a model of pedestrians’ evacuation process in subway fire and a dynamic evaluation indicators system are shown in this paper. The test results prove them to be applied and effective. The evaluation indicators system provides a new method to evaluate the facility layout and evacuation plan quantitatively. It also has a strong guiding significance for optimizing evacuation plan and improving the ability to prevent the disasters and accidents of subway stations.



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*Source: 357945-2015-03-23.xml*