Study on Emergency Response Process of Metro Emergency Based on Stochastic Petri Nets

Abstract

Stochastic Petri Nets (SPN) approach is used to model emergency response process of metro emergency in order to analyze the performance of emergency response process of metro emergency. With the method of “top down,” we establish the basic models of each stage of metro emergency, then according to the actual rescue process with each stage mode of public places and transitions to construct a SPN model of the emergency response process. According to the possible state set of SPN mode, an isomorphic Markov Chain is developed for measuring and evaluating the performance of emergency response process of metro emergency, and the efficacious of the model is justified through the case of Beijing metro emergency plan response process.

Introduction

The subway emergency response process is an important part in the subway emergency safety management due to the tightness of the subway space which brings many uncertain factors to the subway emergency and causes inconvenience to forecast the link busy degree and execution efficiency of emergency response. There are many scholars that have carried out a lot of research on the emergency response of metro emergency [1,2,3,4,5,6,7], and they mainly focus on subway emergency response mechanism and system structure but they ignore the quantitative analysis of emergency response process. The Petri nets modeling method is commendable to reflect the flow of personnel, materials, and other aspects of emergency response process of metro emergency. Fateh et al. [8] establish emergency evacuation process model based on Petri nets. Landry et al. [9] use Petri nets to establish the working flow model of the decision maker in the emergency management, and the simulation is carried out based on fuzzy rules. Sharmin et al. [10] study on the flood emergency management process based on Petri nets, and the feasibility of the model is verified by simulation. Zhong et al. [11] establish model of city emergency response system based on Petri nets, and illustrate the effectiveness of the mode by a simple example. However, in most of these studies analysis, the rationality and validity of emergency process are based on the basic Petri nets, which are not reflected by the time limit of the emergency response process.

In this paper, the SPN is selected to analyze emergency response process, and the isomorphic Markov chain is developed to calculate the stable probability of reachable markings. The time performance and operation efficiency of each link and the operation status of each stage in emergency response process are analyzed to provide the reference for the emergency management decision.

Analysis on Emergency Response Process of Metro Emergency

Subway emergency response process can be divided into four stages that early warning stage, decision-making stage, implementation stage, emergency recovery stage. There is certain relation between stages which constitute the emergency response system of metro.

Early Warning Stage Process

Early warning stage refers to the accident occurred after the subway, from the scene of the relevant personnel to the rescue department rushed to the scene of the accident process which consists of pre-handling, accident alarm, determine the level of information, and information submission, the detailed process is shown in Fig. 1. The relevant disposal of the early warning stage has provided information basis for decision-making stage.

Fig. 1

Process of early warning stage

Decision-Making Stage Process

The stage of emergency decision-making mainly includes alarm analysis, expert consultation, emergency plan analysis, and on-site information analysis; the detailed process is shown in Fig. 2. Emergency command group sent related personnel to the accident scene to investigate and analyze emergency development trend, organized experts to analyze type of the accident, influence range and emergency measures, analyzed emergency plan. Decision-making stage provides a guide for implementation stage.

Fig. 2

Process of decision-making stage

Implementation Stage Process

Implementation stage is under the command of the emergency leading group, carry out a series of rescue operations according to the emergency response plan. It mainly includes on-site disposal, resource scheduling, external coordination, and information classification; the detailed process is shown in Fig. 3. Implementation stage is the core of the whole emergency response, departments need to coordinate and cooperate to complete the rescue mission.

Fig. 3

Process of implementation stage

Emergency Recovery Stage Process

Emergency recovery stage mainly includes rehabilitation disposal, investigation, and evaluation. It is shown in Fig. 4. Through the recovery stage of the relevant disposal measures, the subway to resume normal operations, while the investigation of the accident assessment and summary, to provide reference for the future of the accident disposal.

Fig. 4

Process of emergency recovery stage

Metro Emergency Response Process SPN Model

Modeling Basic Principle

According to the basic principle of Petri net, make full use of the advantage of Petri net in process modeling [12], stochastic Petri nets is used to modeling the emergency response process of Metro Emergency in this paper. In the SPN model, the transitions represent the emergency response activities; the places represent data processing and storage. The dynamic properties of the SPN mode can reflect logical order and the generation, storage, transmission, and processing of information and resources of the various activities in the process of emergency response well. Specific principles are embodied as follows:

• (1) It is feasibility to model emergency process by using SPN to describe the process system, and the places represent information and other resources of the emergency process; the transition represents information production and transfer of the emergency process and describe the changes of information and other resources of emergency response process through assigning a delay time to the transition.

• (2) It is enforceability of emergency process based on SPN. The place contains a token which indicates that the place is active and when the associated transitions are fired, the token is transferred from the place to another place which means that information, resources, and so on from one state to the next state in the process of emergency response. After the data tracking and collection activities are added in the model, the system can be simulated.

• (3) It is evaluable of emergency process based on SPN. The response time and the operation efficiency of each link of the emergency response system can be evaluated by assigning the transition rate $\lambda$ in the model.

The SPN Model for Each Stage of Metro Emergency Response

Through detailed analysis of each stage of the emergency disposal of Metro Emergency, we can set up the early warning, decision-making, response action, and recovery stages of the SPN model.

Early Warning Stage SPN Mode

The SPN model of early warning stage is shown in Fig. 5. A token placed in place P₁ when an emergency event occurs. The related personnel alarm is enabled expressed by transition T₁, when one placed in P₁. The firing transition T₁ consumes the one token in place P₁ and produces one token in place P₂, representing that Operating Control Center (OCC) received alarm information. Others places P₃–P₆, respectively, represent preliminary handing information, emergency classified information, application for higher-level response procedures, emergency decision scheme information, and emergency summary report. The transitions T₂–T₇,respectively, represent preliminary handing, cancel alarm, OCC determine emergency classification level, application for higher-level response procedures, report to the superior emergency leadership organization, and start rescue programs. The transitions T₁–T₇ rates are, respectively, represented by $\lambda_{1} {-}\lambda_{7}$. The SPN model of early warning stage is shown in Fig. 5.

Fig. 5

Early warning stage SPN model

Decision-Making Stage SPN Mode

A token placed in place P₁ when the emergency classified level information is determined. Transitions T₁ and T₂ represent a conflict structure, and its firing is determined by token placed in place P₁. The firing transition T₁ consumes the one token in place P₁ and produces one token in place P_2, representing that emergency leadership organization received alarm information. The places P₃–P₁₇,respectively, represent emergency situation information, the result of emergency situation analysis, emergency plan information, preliminary emergency plan information, final emergency plan information, emergency plan revision information, expert database information, expert consultation information, final expert consultation information, expert consultation modify information, preliminary rescue plan, plan modify information, final rescue plan, and higher-level response information. The transitions T₃–T₁₁, respectively, represent that start alarm information analysis, on-site situation analysis, emergency plan analysis, call emergency plan, expert consultation, call expert consultation result, generate rescue plan, rescue plan evaluation, start rescue plan, and assist in higher-level response. The transitions T₁–T₁₁ rates are, respectively, represented by $\lambda_{1} {-}\lambda_{11}$. The SPN model of decision-making stage is shown in Fig. 6.

Fig. 6

Decision-making stage SPN model

Implementation Stage SPN Mode

A token placed in P1 when the rescue plan is determined. The firing transition T₁ consumes the one token in place P₁ and produces one token in place P₂, P₃, P₄, and P₅, respectively, represent that on-site disposal information, resource allocation information, accident coordination information, and accident information sorting information. The places P₆–P₁₂, respectively, represent that on-site disposal feedback information, resource allocation feedback information, accident coordination feedback information, accident information sorting feedback information, situation analysis information, higher-level response information, and emergency summary report. The transitions T₂–T₁₀, respectively, represent that on-site disposal, resource allocation, accident coordination, accident information sorting, situation analysis, modifying rescue plan, escalation of emergency, start post activities, and assist in higher-level response. The transitions T₁–T₉ rates are, respectively, represented by $\lambda_{1} {-}\lambda_{9}$. The SPN model of decision-making stage is shown in Fig. 7.

Fig. 7

Implementation stage SPN mode

Emergency Recovery Stage SPN Mode

There is not detailed to investigation and assessment of emergency process. A token placed in place P₁ when start post activities. The transition T₁ represents post-activities. The firing transition T₁ consumes the one token in place P₁ and produces one token in place P₂, P₃, respectively, represent that dealing with the aftermath information and investigation and evaluation information. The place P₄ represents emergency summary report. The transition T₂ represents emergency summary. The transitions T_1, T₂ rates are, respectively, represented by $\lambda_{1}$, $\lambda_{2}$. The SPN model of recovery stage is shown in Fig. 8.

Fig. 8

Emergency recovery stage SPN mode

The SPN Mode of Metro Emergency Response

According to the preamble of metro emergency response, the contents of each step of process analysis and modeling, fully integrated Petri net theory of information disposal, with SPN model of each stage of public transitions and places, we establish a comprehensive subway emergency disposal of the whole process of Petri net model, which shown in Fig. 9. The definitions of the places P_k and transitions T_k are listed in Table 1 and Table 2.

Fig. 9

Metro emergency response process SPN mode

Table 1 Definitions of places

Table 2 Definitions of transitions

The instantaneous transition T₂₆ is added in the input place P₃₀ and the output place P₃₀ to guarantee the continuous process of the network which the steady-state solution can be obtained, but count nothing actually. Transitions T₃–₄ and T₅–₆ represent a conflict structure. Transitions T₈–₁₀ and transitions T₁₆–₁₉ represent a simultaneous structure. There is loop structure in SPN model.

The SPN Mode Performance Analysis

Reachability Graph of SPN Mode

According to the SPN model shown in Fig. 9, from the initial state $S_{0}$ of the system, using the Petri net modeling tool, we can put all the state of the system and the relationship between the states. Reachability graph is shown in Fig. 10.

Fig. 10

Reachability graph

S_i represents the state of the system; S₄ represents the virtual state associated with the transition T₂₅. The reachability state of $S_{0}$ has 44. It can be determined that the model is live and bounded by reachable graph. Assign a relevant rate $\lambda_{i}$ of transition Ti on each arc that can obtain isomorphic Markov chain. There are 43 states in reachability graph. Initial marking is denoted by m ₀ = (1, 13, 14, 16), representing the tokens that are these places P₁, P₁₃, P₁₄, P₁₆ simultaneously. Assumed transitions T₁–T₂₅ rates associated with correspondence parameter $\lambda_{1} {-}\lambda_{25}$ and $x = (x_{1} ,x_{2} , \ldots \,x_{44} )$ are a set of steady-state probability of reachability states of Markov chain. We can obtain the steady-state probability based on correlation theorem of Markov chain [13], and calculate busy probability of places indicator and utilization indicator of transitions.

A Case Study of Beijing Metro

Any finite place, finite transition, marked stochastic Petri net are isomorphic to a one-dimensional discrete Markov process [14]. The performance of the average token number of places and the utilization of transitions are analyzed by steady-state marking probabilities of Markov chain.

In this paper, a simulation analysis of Beijing Metro Emergency Plan response process is developed. This emergency plan divide emergency response process into four stages such as early warning stage, decision-making stage, implementation stage, emergency recovery stage, and we can obtain SPN mode of this case based on metro emergency response process model in this paper. The Beijing metro emergency plan response process SPN model is shown in Fig. 11. The transitions of the decision-making stage is combined with the change of T14, and the transitions of emergency recover stage is merged into T24.

Fig. 11

Beijing metro emergency plan response process SPN model

According to the experience of Beijing subway emergency experience data, we can assign each transitions T_i corresponding rate parameter $\lambda_{i}$ which is shown in Table 3.

Table 3 Transitions rate

Solving the isomorphic Markov chain, we can obtain steady-state making probabilities shown in Table 4.

Table 4 Steady-state making probabilities

Calculate average token number of places and utilization of transition based on steady-state making probabilities shown in Tables 5 and 6.

Table 5 Average token number of place

Table 6 Utilization of transition

• (1) The average token number of places

It reflects the busy probability of the places. The average token number of places P23–P26 and P30 shown in Table 5 is significantly greater than other place, and in the process of emergency, information feedback and higher level of emergency response takes much longer compared to other links. Because in the process of emergency, emergency leading group of unified command departments launched rescue operations, which lead to multi departments rescue receiving feedback information, and in a short period of time of information for decision-making, this case easily lead to information blockage, in addition to catastrophic events, the emergency response to the need for a cross organizational, cross area of city level emergency response, easy to produce a plethora of information, which leads to the accumulation of information. Therefore in the rescue process and need to pay attention to all kinds of information sorting, the improvement of emergency decision-making mechanism and other sectors of society to emergency response, strengthening of Metro emergencies emergency drills which is a key of optimizing the process of emergency.

• (2) Utilization of transition

It reflects that the time is occupied by the activities in emergency response process. The utilization of Transition T1, T2, T4, T15–T20 from Table 6 is significantly higher than that of other changes high. In the process of emergency accident reporting, grade judgment, resource scheduling on-site, external coordination, the situation analysis activity for a longer period of time. Because the on-site disposal involves the multi-body, emergency command group coordination difficulty bigger, received too many accident information, decision required a longer period of time, in addition to meet emergency needs more resources, scheduling to step in place. Therefore, the emergency response organization should strengthen management, clear the duties of each department in emergencies, so as to enhance the various departments in the process of emergency coordination, enhance the efficiency of subway emergency disposal.

Conclusions

In this paper, a SPN model of metro emergency response process is constructed based on the stochastic Petri net. An isomorphic Markov chain constructed after the model is proved that it is active and bounded by constructing reachability graph. The average token number of places and the utilization of transitions are calculated based on Markov chain. According to the Beijing metro emergency plan response process, simulation analysis is carried out and we get busy probability of emergency response process of each link and the time of activities in emergency response process and we put forward suggestions to improve the emergency rescue efficiency. It plays a guided role to the information construction and improves the efficiency of multi department linkage of the metro emergency response.