Non-autonomous coloured Petri net-based methodology for the dispatching process of urban fire-fighting

qSupported by the National Science Fund for Distinguished Young Scholar of China (59825105).*Corresponding author. Fax: #86-21-6598-7989.E-mail address: [email protected] (X. Han).

Fire Safety Journal 35 (2000) 299}325

Non-autonomous coloured Petri net-basedmethodology for the dispatching process

of urban "re-"ghtingq

Han Xin*, Li Jie, Shen ZuyanTongji University, Shanghai Institute for Disaster Prevention and Relief 1239, Siping Road, Shanghai 200092,

People's Republic of China

Received 19 August 1999; received in revised form 19 June 2000; accepted 3 July 2000

Abstract

This paper presents the main features of our approach to the study of the dispatching processof urban "re-"ghting. A new non-autonomous coloured Petri net (NCPN) method is developedand a corresponding simulation experiment is also carried out towards the practical process.Based on an extensive analysis of the urban "re-"ghting process, the basic concept of discreteevent dynamic systems as well as Petri net theory is introduced. In this way, the NCPN methodis extended and applied to set up systematic simulation model. It enables the modelling andsimulation analysis for the dispatching process of the Shanghai 119 Command Center. Statist-ical analysis has also been completed involving the three aspects &&object, resource and activity''for 13563 "res which took place in the Shanghai Municipality from 1992 to 1997. It furnishesthe corresponding key parameters and key random variable models. Under a background ofthe practical dispatching process of "re-"ghting in the Shanghai Municipality, the relevantsimulation system is built up by means of software development. The simulation experimentsare made to analyze systematically the simulation environment and the model behaviour of thedispatching process. Various sorts of residential "re objects have been tested, in which theZhenru Fire Station is taken as the "re-"ghting force and residential "re cases are randomlygenerated in the simulation experiment ( 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction

Fighting against unwanted "res and improving "re safety has been one of theconstant themes in the development of the human society. In the new era of peace

0379-7112/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 3 7 9 - 7 1 1 2 ( 0 0 ) 0 0 0 3 9 - 4

and development, "re protection of the urban area has become an importanttheme. With the development of the economy and society, many new conditions,contradictions and problems of the urban area have risen, attracting more and moreconcern from the international community. Also with the development of science andtechnology, many new concepts and ideas for "re safety have emerged and aresupported by new scienti"c and technological achievements in various related "elds[1}4].

Urban "re is frequently disastrous. It can burn out large volumes of property andit endangers the life safety of people. Now, however, most studies focus onthe fundamental theory of "re protection. This embraces analysis and researchon the formation and spread of "re complemented by "re control measures forbuildings, adopting physics}chemistry, physics}machinery and economy}mathemat-ics methods [5}16]. The problem of controlling the urban "re disaster "eld is a majorchallenge with rapid development of the economic situation. It is evidenced by greater"re risk and more di$cult "re-"ghting conditions. Although there are some studiesdevoted to "re safety design as well as assessment and quanti"cation of "re risk[17}34], there is little theory and method of the dispatching process of urban"re-"ghting. Therefore, it is important to uncover this research according to actualsituations [35].

From the viewpoint of system control theory [36}43], it is essential to set upa model based on the real-time dispatching and decision controlling process of urban"re-"ghting forces. The emphasis on modelling and controlling is to help solve theproblem of quantitative decision making. It is commonly accepted that "re isa stochastic event. Therefore, "re-"ghting measures are subject to the "re environ-ment, such as occurrence time, position, weather condition, object combustion, etc.Even for the same "re object, the adopted "re-"ghting measures will be di!erent onthe basis of various surroundings, quality of "re-"ghting service as well as equipment.In this way, "ghting of urban "re is a very complicated dynamic process, includingevents from receiving "re calls to summing up of "re-"ghting. Based on this, thepurpose of a real-time dispatching process for "re-"ghting is to assign certain "rebrigades and emergency services to put out a "re according to information obtained.Therefore, its general aim is to minimize the whole period of "re-"ghting under thecondition of a given "re-"ghting resource.

In this paper, considering the discrete and stochastic nature of real-timedispatching for the "re-"ghting process and, based on theory of discrete eventdynamic system [44], we produce the non-autonomous coloured Petri net (NCPN)method to carry out simulation research for the dispatching process of urban "re-"ghting [45].

2. Analysis for the dispatching process of urban 5re-5ghting

The dispatching process of urban "re-"ghting is classi"ed into two stages namelydispatching of received "re calls and dispatching of the "re "eld. In this paper, theemphasis is put on the dispatching process of received "re calls.

300 X. Han et al. / Fire Safety Journal 35 (2000) 299}325

Fig. 1. Systematic diagram of the dispatching process for the Shanghai 119 Command Center.

2.1. The dispatching process of urban xre-xghting

Due to the randomness and #ashover nature of unwanted "re occurrence, the"re-"ghting process can be regarded as a very complicated dynamic procedurecomprising a series of stochastic events. The whole process is divided into severalbranch stages, including receiving "re calls, dispatching "re brigades, "re brigadesoutgoing, reconnoitering of the "re situation, organizing "re-"ghting, saving life,supplying water, ventilating smoke, evacuating and protecting property, breaking andremoving obstacles, communicating, putting out "re, summing up of "re-"ghting, etc.Although listed as a sequence, some of these activities are performed throughout thewhole process, such as dispatching and communicating. On the other hand, some ofthem are carried out almost concurrently, such as reconnoitering the "re situation,organizing "re-"ghting as well as saving life, etc.

The systematic diagram of the dispatching process for the Shanghai 119 CommandCenter is shown in Fig. 1.

As for the dispatching of urban "re-"ghting, a detailed plan of "re-"ghting shouldbe formulated according to the results of urban "re hazards analysis. This facilitatesthe operational e$ciency of any "re service. Due to the complexity of an actual "redisaster "eld, we are not able to grasp the real state of the "re location. Therefore, thekey point of successfully controlling a "re disaster "eld is dependent on the incompleteinformation got from the "re call and the comprehensive judgement as well as theexperience of "re-"ghting dispatchers.

2.2. Feature of dispatching process of urban xre-xghting

In accordance with control system theory [46], the dispatching process of urban"re-"ghting is characterized under:

X. Han et al. / Fire Safety Journal 35 (2000) 299}325 301

Non-determination: The "re occurrence is a stochastic event. Its occurring time,location, combustion object, weather condition as well as "re environment cannot beclearly known and there are other non-deterministic factors which will change withthe time and the actual "re "eld.

Complexity: The dispatching process system is very complicated: (a) there arenumbers of components which attach to di!erent levels of the system; (b) in the branchprocess structure, the corresponding performance parameter is multi-division, time-variant and random; (c) the information structure of the "re object and the dispatch-ing process is complex in form and there are lots of data to be handled withcomplicated arithmetic.

Demand for high performance: During the dispatching process of "re-"ghting, thetarget requirement should be satis"ed including the demand of real-time, rule-basedand optimal operation.

3. Non-autonomous coloured Petri net (NCPN)

Petri nets theory has been developed considerably since its origin by Petri in his1962 Ph.D. dissertation on the study of the communication protocols between thecomponents of a computer. The theory enables a discrete event dynamic system of anykind whatsoever to be modelled and presents many interesting characteristics. Espe-cially, it makes it possible to model and visualize behaviours comprising concurrency,synchronization and resource sharing. A brief introduction to Petri nets theory isgiven in the appendix.

In the past decades, numerous applications of Petri nets have been continuallyadded to by a number of research workers to enable more condensed descriptions,including time factor interventions [47]. In our research, a new non-autonomouscoloured Petri net (NCPN) method is developed to carry out simulation studies onthe urban "re-"ghting process.

3.1. Dexnition of non-autonomous coloured Petri net (NCPN)

A non-autonomous PN is adopted to model the operation of a system which islimited by external events and (or) time. The NCPN which is developed to simulatethe dispatching process of urban "re-"ghting should have capabilities of treating timedelay and randomness of the system. On the basis of timed-PN and coloured PN, weconstruct the methodology to include:

(1) All entities modelled by the PN are classi"ed in three aspects of object, resourceand activity.

(2) The factors of time and colour are simultaneously introduced to the PN. Hencethe capability of the PN in describing and simulating the practical system isenhanced and the structure of PN is also simpli"ed. Meanwhile, the resolvabilityof PN model is improved.


(3) Each directed arc of the PN is characterized by a colour function, highlighting thedynamic relationship between the colour that is associated with the transition andthe token colour of the corresponding places.

According to above consideration, NCPN is de"ned as a seven-tupleNCPN"(P, H, Pre, Post, C, p

T, MC) where

(1) P"Mp1, p

2, 2, p

nN, n'0, a coloured "nite set of places,

(2) H"Mh1, h

2,2, h

mN, m'0, a coloured "nite set of transitions with

PXHO0, PWH"0,(3) Pre(p, h/c) : P]HPR, R'0, an input function that de"nes the set of directed

arcs from coloured P to coloured H, where R is a rational number,(4) Post(h/c, p) : P]HPR, R'0, an output function that de"nes the set of directed

arcs from coloured H to coloured P, where R is a rational number,(5) C"Mc

1, c

2,2, c

kN, k'0, a colour set of places or transitions. C(p

i) is a colour set

associated with place pi3P; C(h

j) is a colour set associated with transition h

j3H,

where

C(pi)"Ma

i1, a

i2,2, a

iuiN, u

i"DC(p

i)D, i"1, 2,2, r,

C(hj)"Mb

j1, b

j2,2, b

jvjN, v

j"DC(h

j)D, j"1, 2,2, l, (1)

where uiis all kinds of tokens in place p

i, i.e. the size of colour set corresponding

to pi; v

jis all sorts of di!erent events represented by h

j, i.e. the size of colour set

corresponding to hj,

(6) pT

: ¹Pj, j'0, a stochastic variable, where j is a variable. Each hiof NCPN is

assigned a timing of pT(h

i) to signify stochastic duration of every transition

stimulating from start to end,(7) MC : PPM0, 1, 2,2 N, a coloured marking whose value of the ith component

represents the number of tokens in the ith place, where

MC(pi)"+n

ir, M(p

i)(a

ir)"n

ir. (2)

3.2. Colour and colour function

In a NCPN model, the information is delivered through the pair S place, tokencolourT and the pair Stransition, token colourT. Each colour represents informationforming the basis of a colour set. The colour set is signi"ed by three sorts of elementsincluding object, resource and activity:

f object: "re number, "re object, occurrence time, occurrence position, environmentalcircumstance, weather condition, wind strength, "re alarm grade, information fromtraveling period of "re trucks, "rst time information from "re "eld, successiveinformation from "re "eld, extinguish information of "re;

f resource: "re brigade, "re trucks, position of "re brigade;f activity: start time, end time, stochastic duration.


Table 1Basic colour function

Colour Function De"nition Annotation

Arbitrary I$

I$(Sc

IT)"Sc

IT Identity

colour Dis Dis(ScIT)"SzT Dissipate colour

Simple Succ Succ(ScIT)"Sc

I`1T Succeed (increase value)

colour Pred Pred(ScIT)"Sc

I~1T Pre"x (decrease value)

Compound colourSucc

1Succ

1(Sc

I, c

jT)"Sc

I`1, c

jT Increase value of a component

Succ2

Succ2(Sc

I, c

jT)"Sc

I, c

j`1T

Pred1

Pred1(Sc

I, c

jT)"Sc

I~1, c

jT Decrease value of a component

Pred2

Pred2(Sc

I, c

jT)"Sc

I, c

j~1T

Proj1

Proj1(Sc

I, c

jT)"Sc

jT Dissipate colour of one (several)

componentProj

2Proj

2(Sc

I, c

jT)"Sc

IT

The linear transformation of colour associated with transition is realized by thecolour function. As for most PN models, there are some basic functioning codes thatcan be applied either in their simple forms or in a combination form of simplefunctions. The basic colour functions are shown in Table 1.

3.3. Enabling and stimulation rules of transition

In a NCPN, the enabling and stimulation rules are:

(1) A transition hj3H with colour c

kis enabled if, and only if,

M(pi)*Pre(p

i, h

j/c

k) for all p

i3P'p

i30h

j. (3)

(2) An enabled transition hj

with ck

stimulates at a marking M, yielding the newmarking M@,

M@(pi)"M(p

i)#Post(h

j/c

k, p

i)!Pre(p

i, h

j/c

k), for i"1, 2,2, n. (4)

(3) Transition hlis enabled by c

l1and written as h

l/c

l1. After stochastic duration of

dl1, the marking M

1evolves as M

2and is written as M

1[h

l(d

l1)/c

l1'M

2. The

enabled series of transitions permits the marking changes from M1

to Mk`1

, ex-pressed as follows:

Mk`1

(pi)"M

1(p

i)#+[Post(h

j(d

lj)/c

lj, p

i)!Pre(p

i, h

j(d

lj)/c

lj)]. (5)

As shown in Fig. 2, there are three places connected with transition h1

and theircolour sets are demonstrated in Table 2.

For h1, there are two input functions and two output functions:

Input functions: Pre(p1, h

1/c

I), Pre(p

2, h

1/c

I)

Output functions: Post(h1/c

I, p

2), Post(h

1/c

I, p

3).


Fig. 2. Establishment of colour function for transition h1.

Table 2Colour element connected with transition h

1

Node of net Element of node Element of colour

P1

There is a "re call C(P1)"S"re number, "re object, occurring moment, occurring

position, environmental situation, weather condition, windscaleT"C

I3SObjectT

P2

119CC is on duty C(P2)"S"re numberT"C

II3SObjectT

P3

119CC preliminarilyreceive information of"re call

C(P3)"S"re number, "re object, occurring moment, occurring

position, environmental situation, weather condition, windscaleT"C

I3SObjectT

h1

Dealing with "re call C(h1)"[S"re number, "re object, occurring moment, occurring

position, environmental situation, weather condition, windscaleT#Sstart moment of receiving "re call, end moment ofreceiving "re call, stochastic duration of receiving "recallT"(C

I#C

III)3[SObjectT#SActivityT]

Since the elements of a node are labeled by òbject, resource and activitya, thecolour set can be divided into sub nets, such as C

I, C

II, C

III, etc. Hence

Pre(p1, h

1/C

I)"C(p

1)"C

I(i.e. I

$(C

I)"C

I, belong to identity function),

Pre(p2, h

1/C

I)"C(p

2)"C

II(i.e. Pro

j1(C

I)"C

II, belong to dissipate function),

Post(h1/C

I, p

2)"C

IIPost(h

1/C

I, p

3)"C

I.

On the basis of the above stimulation rules of transition, NCPN can be applied notonly to the basic structure of a discrete event dynamic system but also to describe theevolution process of the system states.

4. Modelling for dispatching process of urban 5re-5ghting

In setting up the systematic model for the dispatching process of urban "re-"ghting,emphasis should be put on: (1) performance analysis of multi-rule; (2) real-time as well


as optimum requirement. On the other hand, the purpose of the study is to providedecision support for commanders within the actual "re-"ghting process and ordinar-ily, readiness training. Hence, from the viewpoint of dispatch modelling, the process of"re-"ghting should be divided into a series of basic activities and events in accordancewith logical relations among these activities and events. Analysis of the quantitativerelationships among various parameters as well as the behaviour of the whole systema!ected by the dispatching rules will illuminate the complete "re-"ghting dispatchingprocess. It is anticipated that such a decision scheme for the dispatching process couldbe used to realize optimal control of the urban "re disaster "eld.

4.1. Procedure of modelling for dispatching process of urban xre-xghting

Based on these initiatives, the procedure of modelling the dispatching process ofurban "re-"ghting comprises:

(1) The method of hierarchical decomposition to process dispatching into a series ofsub-processes, such as receiving a "re call, judging the grade of "re alarm,dispatching "re control forces, etc.

(2) Structuring the net models of each sub-process in line with NCPN.f de"ning each component of P and H;f for each component of place, determine its dimension of colour, the implication

of the colour dimension and the corresponding colour set;f determine other parameters concerning P and H, such as the stochastic variable

distribution for the stimulation duration of all transitions.(3) Establish the corresponding colour functions in respect of coloured places and

transitions. Introduce and execute the various dispatching rules through thecomputation of colour functions.

(4) Combine the sub-processes and construct the entire NCPN model for the dis-patching process.

(5) Start the simulation according to the principle of discrete event simulation; drivethe simulation clock on the basis of "xed increment time ("xed step duration) andoperate the NCPN model. When the proportion of simulation step and practicaltime is 1 : 1, the simulating process is synchronized with the practical operatingprocess and the dispatch simulation can be applied directly in actual control.

(6) Select corresponding optimal decision strategies in accordance with a compre-hensive analysis of system performance indices taken from simulation results.

4.2. Systematic model for dispatching process of urban xre-xghting

In accordance with the NCPN method and from the background of the Shanghai119 Command Center, a systematic model for urban "re-"ghting process has beenset up, as illustrated in Fig. 3, in which each place and transition is expressed asfollows:

(1) Place: P. p1: There is a "re call; p

2: 119 Command Center (119CC) is on duty; p

3:

119CC preliminarily receive information of "re call; p4: There is no need for


Fig. 3. Non-autonomous coloured Petri net model for the dispatching process of urban "re-"ghting.

"re-"ghting; p5: Fire alarm grade has been ascertained; p

6: Fire brigades are on

duty; p7: Responsible "re brigades have been sent out; p

8: Responsible "re

brigades have arrived "re "eld; p9: Information during travelling of "re trucks has

been acquired; p10

: Fire-"ghting has begun; p11

: First time information has beenreported to 119CC from "re "eld; p

12: Successive information has been reported

to 119CC from "re "eld; p13

: Reinforcing "re trucks have arrived "re "eld; p14

:Fire "eld has been controlled; p

15: Information concerning "re "eld has been

reported to 119CC; p16

: Fire-"ghting has been ended; p17

: Information of "reextinguish has been reported to 119CC from "re "eld; p

18: Reinforcing "re

brigades are on duty.(2) Transition: H. h

1: dealing with "re call; h

2: judging "re alarm grade; h

3: dispatch-

ing responsible "re brigades to "ght "re; h4: going to "re "eld; h

5: deploying

"re-"ghting and reconnoitering "re "eld; h6: "ghting "re; h

7: reporting informa-

tion of "re "eld to 119CC; h8:dispatching reinforcing "re brigades; h

9: summing

up "ght; h10

: rejoining.

As for the dispatching process of urban "re-"ghting, the state variation of thesystem is characterized by the production or dissipation of those elements in placesand transitions. Moreover, the transmission of information within a non-autonomousPN model is expressed as the evolution of marking throughout the model. Thesecorrespond to states of the "re "eld as well as the dispatching scheme for "re controlforces in the practical system. Due to the complexity of the dispatching process,relevant markings turn into multi-information carriers and need to be represented bya colour set.

The colour set of elements for place set and transition set is signi"ed by the threeaspects òbject, resource and activitya. The marking structures are represented bySplace, object, resource, activityT and Stransition, object, resource, activityT.


Table 3Colour element in place

Place Colour element

P1

Fire number, "re object, occurring moment, occurring position, environmental situation,weather condition, wind scale

P2

Fire numberP3

Fire number, "re object, occurring moment, occurring position, environmental situation,weather condition, wind scale

P4

Fire numberP5

Fire number, grade of "re alarmP6

Fire brigade, "re trucks, position of "re brigadeP7

Fire brigade, "re trucks, position of "re brigadeP8

Fire number, "re brigade, "re trucksP9

Fire number, information from traveling process of "re trucksP10


Fire number, "rst time information from "re "eldP12

Fire number, successive information from "re "eldP13



Fire number, information from traveling process of "re trucks, "rst time information from "re"eld, successive information from "re "eld, extinguish information of "re

P16


Fire number, extinguish information of "reP18

Fire brigade, "re trucks, position of "re brigade

From the perspective of a certain place or transition, the information contained ina marking is usually less than that de"ned by the colour set. Hence, some colourelements are redundant for the token entering the place or transition at a certainmoment. The colour elements for the place set and the transition set are respectivelyillustrated in Tables 3 and 4.

While the colour set of elements for both the place set and the transition set hasbeen de"ned, the corresponding function is decided by the input and output functions.These two are related to the transition and can be de"ned separately.

As shown in Fig. 2, transition h1

is taken as an example to illustrate the establishingprocess of those input functions and output functions corresponding to transition.Other input functions and output functions in connection with transitions h

2to

h10

can be given out in the same way.

4.3. Simulation of dispatching process based on NCPN model

The purport of system simulation is to approach the behaviour of a complex systemin the real world by studying the behaviour of an arti"cial simple system. Simulationstudy of general discrete event systems is based on logical relations among variousentities as well as a common time origin for the activity of each entity. Simulationstrategies, such as event scheduling, activity scanning or process interaction can beused for actuating a simulation clock. During a proper time period, the simulation


Table 4Colour element in transition

Transition Colour element

h1

Fire number, "re object, occurring moment, occurring position, environmental situation,weather condition, wind scale, start moment of receiving "re call, end moment of receiving"re call, stochastic duration of receiving "re call

h2

Fire number, "re object, occurring moment, occurring position, environmental situation,weather condition, wind scale, start moment of judging "re alarm grade, end moment ofjudging "re alarm grade, stochastic duration of judging "re alarm grade

h3

Fire number, "re alarm grade, "re brigade, "re trucks, position of "re brigade, start momentof dispatching responsible brigade, end moment of dispatching responsible brigade, stochas-tic duration of dispatching responsible brigade

h4

Fire number, "re brigade, "re trucks, position of "re brigade, outgoing moment of "re truck,arriving moment of "re truck, stochastic duration of "re truck traveling

h5

Fire number, "re brigade, "re trucks, start moment of deploying "ght and reconnoitering "re"eld, end moment of deploying "ght and reconnoitering "re "eld, stochastic duration ofdeploying "ght and reconnoitering "re "eld

h6

Fire number, "re brigade, "re trucks, start moment of "re-"ghting, end moment of "re-"ghting, stochastic duration from start of "re-"ghting to controlling "re "eld, stochasticduration from controlling "re "eld to putting out "re, stochastic duration from putting out"re to summing up of "re-"ghting

h7

Fire number, information from traveling process of "re trucks, "rst time information from"re "eld, successive information from "re "eld, extinguish information of "re, start moment ofreporting information from "re "eld, end moment of reporting information from "re "eld,stochastic duration of reporting information from "re "eld

h8

Fire number, "re brigade, "re trucks, position of "re brigade, information from travelingprocess of "re trucks, "rst time information from "re "eld, successive information from "re"eld, start moment of dispatching reinforcing "re trucks, end moment of dispatchingreinforcing "re trucks, stochastic duration of dispatching reinforcing "re trucks

h9

Fire number, "re brigade, "re trucks, position of "re brigade, start moment of summing up of"re "ghting, end moment of summing up of "re "ghting, stochastic duration of summing upof "re "ghting

h10

Fire number, "re brigade, "re trucks, start moment of rejoining of "re trucks, end moment ofrejoining of "re trucks, stochastic duration of rejoining of "re trucks

model is attempting to reproduce the occurrence and development of events in thesystem. Meanwhile, performance parameters of the system will be statistically ana-lysed and a function evaluation of the system will be revealed. Thereafter, the technicalbasis for designing and improving the system can be provided.

During the simulation experiment on the dispatching process of urban "re-"ghting,it is necessary to generate various kinds of simulation behaviour, e.g. as the systemstate variables change with time. Using such data, the simulation results can beobtained through the comprehensive analysis of model behaviour.

4.3.1. Probability model for xre occurrenceGiven that occurrence of urban "re in the Shanghai Municipality can be regarded

as a set of stable, independent and non-overlapping discrete events, the Poissonprocess is adopted to describe the "re occurrence.


Fig. 4. Time distribution of branch process: from "re truck outgo to "re truck arrive "re "eld (Histogram).

Hence at a certain point in time, the probability of k "res within a unit time period isexpressed as

p(k)"jke~j

k!, (6)

where j is the average occurrence ratio for di!erent kinds of "res.This facilitates the construction of the "re occurrence function model in the

simulation system.

4.3.2. Probability model of time distribution for branch process of xre-xghtingThe probability model of time distribution for branch process of "re-"ghting is

constructed as follows:

(1) Deal properly with the statistical data. For example, a histogram is given out onthe basis of data involving the time distribution of the branch process "re truck traveltime, as shown in Fig. 4.

(2) Assume the corresponding probability distribution, be it continuous or discrete.For example, the histogram (Fig. 4) is assumed to have a Gamma distribution asshown in Fig. 5.

(3) Estimate parameters of the suggested distribution, such as skewness and kurto-sis, etc.

(4) Test the hypothesis in accordance with statistical inference method.

4.4. Composition of simulation system for dispatching process of urban xre-xghting

On the basis of the above theory, the structure of a simulation system based ona data base, a model base and a rule base has been set up as shown in Figs. 6}8.


Fig. 5. Time distribution of branch process: from "re truck outgo to "re truck arrive "re "eld (GammaDistribution).

Fig. 6. Composition of simulation system for the dispatching process of urban "re-"ghting.

5. Case study

Within the Shanghai Municipality area, a "re brigade named Zhenru Fire Stationand its corresponding area of responsibility is taken as the research sample frame. Thesimulation experiment is based on the developed simulation system and on residential"res.

5.1. Zhenru xre station and its area of responsibility

Zhenru "re station is located in the west part of the Shanghai Municipality and has"ve pieces of "re apparatus including one pumper, one water tanker, one foam truck,


Fig. 7. Composition of the pickup data base.

one lighting truck and one aerial ladder. Its responsibility covers 98 streets and about670 hydrants. The important protected units include a university, a store and a cottonmill.

5.2. Probabilistic distribution for branch process of xre-xghting

Using the statistical method as described in Section 4.3 of this paper, the "re-"ghting process from three aspects òbject, resource and activitya among 13563 "recases from the Shanghai Municipality are studied in detail. The probability densityfunction for the time distribution of branch process of "re-"ghting resulted ina Gamma distribution and the characteristics of each distribution are stated asfollows.

f branch process: from "re truck outgo to "re truck arrive "re "eld (Fig. 5),

f1(x)"

[email protected]

C(4.256845)x'0; (7)

f branch process: from "re truck arrive "re "eld to start "re-"ghting,

f2(x)"

[email protected]

C(2.624738)x'0; (8)

f branch process: from "re truck arrive "re "eld to general director arrive "re "eld,

f3(x)"

[email protected]

C(2.757645)x'0; (9)


Fig. 8. Main #ow of the simulation program.

f branch process: from "re truck arrive "re "eld to "rst reinforcement arrive "re "eld,

f4(x)"

[email protected]

C(4.346375)x'0; (10)

f branch process: from "re brigade start "re-"ghting to "re brigade control "re,

f5(x)"

[email protected]

C(1.974737)x'0; (11)

f branch process: from "re brigade control "re to "re brigade basically put out "re"eld,

f6(x)"

[email protected]

C(1.676094)x'0; (12)


Fig. 11. Fire occurrence sort.

Fig. 10. Fire occurrence position.

Fig. 9. Fire occurrence time in simulation cases.

f branch process: from "re brigade basically put out "re to put out residual "re,

f7(x)"

[email protected]

C(2.975327)x'0. (13)

5.3. Simulation case

Among various kinds of "re cases, the residential "re occurs most frequently.During the simulation experiment described in this paper, 200 residential "res wererandomly simulated and the result is compared with 235 actual residential "res thatwere attended by the Zhenru Fire Station from 1997 to 1998. The result of the analysisis abbreviated in Figs. 9}14 and Tables 5}10.


Fig. 12. Time distribution of branch process: from "re occurrence to receive "re call.

Fig. 13. Time distribution of branch process: from receive "re call to "re truck arrive "re "eld.

Fig. 14. Time distribution of branch process: from "re brigade start "re-"ghting to "re brigade put out "re.

5.4. Discussion

5.4.1. Analysis based on xre objectIn the simulation study, the objects of the randomly generated "res include several

items such as (1) "re occurrence time, (2) "re occurrence position, (3) weathercondition, (4) category of building being a!ected, (5) "re alarm grade, (6) "re situationduring "re calling, (7) condition of surrounded buildings, (8) concentrating conditionof #ammable materials, (9) phone call numbers during "re calling, etc.

The "re occurrence position was mainly located in area II (41%, Fig. 10), involvinghousing in the Caoyang District, the Baiyu District, and the Changfeng District. Most


Table 5Phone call number during "re call in simulation cases of residential "re

Phone call number Single SeveralNumber of cases 188 12Percentage (%) 94 6

Table 6Fire situation during "re call in simulation cases of residential "re

Fire situation during "re call Initial stage Developing stageNumber of cases 177 23Percentage (%) 88.5 11.5

Table 7Situation of surrounding buildings in simulation cases of residential "re

Situation of surrounding buildings Sparse DenseNumber of cases 166 34Percentage (%) 83 17

Table 8Situation of surrounding #ammable material in simulation cases of residential "re

Situation of surrounding #ammable material Sparse DenseNumber of cases 176 24Percentage (%) 88 12

Table 9Fire alarm grade in simulation cases of residential "re

Fire alarm grade One Two Three FourNumber of cases 83 89 27 1Percentage (%) 41.5 44.5 13.5 0.5

simulating "re cases were caused by solid materials (sort A, 64%, Fig. 11), the otherswere liquid materials (sort B, 18%) and gas materials (sort C, 18%). The "re situationduring "re calling belonged mostly to the initial developing stage (88.5%, Table 5) andthe phone call frequency number was single (94%, Table 6). The condition ofsurrounding buildings and concentrated #ammable materials was chie#y sparse (83%,Table 7; 88%, Table 8, respectively).


Table 10Number of dispatched "re trucks in simulation cases of residential "re

Number of dispatched "re trucks 1 2 3 6 7 8 10Number of cases 32 81 72 7 5 2 1Percentage (%) 16 40.5 36 3.5 2.5 1 0.5

Compared with the actual "res, the simulated "re object approximately re#ectedthe basic features of residential "res occurring in that area.

5.4.2. Analysis based on time distribution of xre-xghting processThe branch process of "re-"ghting simulated in residential "res consists of several

stages, such as from "re occurrence to receive "re call, from receive "re call to "retrucks arrive "re "eld, from start "re-"ghting to put out "re, etc.

The simulated results indicated that: (1) the duration from "re occurrence to receive"re call was about 2}4 min (75%, Fig. 12), (2) the duration from receive "re call to "retrucks arrive "re "eld focused on 5}10 min (60%, Fig. 13), (3) the duration from start"re-"ghting to put out "re was mainly 5}10 min (55%, Fig. 14), (4) the total durationfrom "re occurrence to put out "re was approximately 15}20 min (35%).

On the whole, the simulation of time distribution of the "re-"ghting process was inaccordance with the "re-"ghting action attended by the Zhenru Fire Station.

5.4.3. Analysis based on dispatching processDuring the simulation experiment, the "re alarm grade was judged primarily as

Grade Two (44.5%, Table 9) and Grade One (41.5%) and the number of dispatched"re trucks was less than three trucks (92.5%, Table 10). This was basically inaccordance with the dispatching rules applied by the Zhenru Fire Station.

In general, the comparative analysis of the simulation study from the perspectives of"re object and time distribution of the "re-"ghting process re#ected primary featuresof residential "res attended by the Zhenru Fire Station. On the other hand, analysis ofthe corresponding dispatching rules indicated that certain revisions are necessary tothat aspect of the modelling process.

6. Conclusion

1. A new non-autonomous coloured Petri net (NCPN) method is developed in thepaper. The model is able to carry out simulation research on the dispatchingprocess of urban "re-"ghting.

2. Compared with classical Petri net theory, the factors of time and colour areintroduced into the NCPN model. Therefore, a systematic algorithm can beformulated.

3. In accordance with the NCPN method and given the backdrop of the Shanghai119 Command Center, a simulation system for the dispatching process of urban"re-"ghting is established.


4. Taking the Zhenru Fire Station and its corresponding area of responsibility asa research object, the simulation experiment is carried out on the basis of thedeveloped simulation system. The model behaviour and the time distribution of the"re-"ghting process have been analysed and compared with actual "res.

Acknowledgements

We gratefully acknowledge the Shanghai Fire Bureau, the Shanghai 119 CommandCenter as well as the Shanghai Fire Protection Association for their fruitful coopera-tion. We also like to express a special thank to the support of the National ScienceFund for Distinguished Young Scholar of China.

The authors are grateful to one of the referees for his comments and guidance in thepreparation of this paper.

Appendix A. Petri net

A.1. Basic notions

A Petri net (PN)47 is a directed bipartite graph with two disjoint sets of nodes:places and transitions. In a graphical representation of a Petri net, places are represent-ed by circles, and transitions are represented by bars (certain authors representtransitions by boxes). In a Petri net, there are a "nite number of places and transitions.Nodes are connected by directed edges. A place is an input to a transition if there is anedge from the place to the transition. That edge is an input arc. A place is an output ofa transition if there is an edge from the transition to the place. That edge is an outputarc. An integral multiplicity can be associated with each input and output arc (defaultis 1).

A typical Petri net is shown in Fig. 15.

A.1.1. Stimulating a transitionA Petri net is marked if tokens are associated with the places. The dynamic

behaviour of the system is determined by the movement of tokens. The tokens movebased upon the stimulation of transitions. A transition is enabled to stimulate if thenumber of tokens in each of its input places is at least equal to the multiplicity of thecorresponding input arc from that place. When a transition stimulates, tokens areremoved from each of its input places and deposited in each of its output places. Thenumber of tokens removed from each of the input places of a stimulation transition isequal to the multiplicity of the corresponding input arc; the number of tokensdeposited in its output places is equal to the multiplicity of the corresponding outputarc. At any instant of time, more than one transition can be enabled but only onetransition is allowed to stimulate. In a graphical representation of a Petri net, tokensare denoted by small dots or integers within a place. Multiplicity of arcs is denoted byputting a backslash on the arc and placing a positive integer with it. If multiplicity is


Fig. 15. A typical Petri net.

Fig. 16. Stimulation of transition in a Petri net.

not indicated, then default multiplicity of 1 is assumed. The transitions in Figs. 16 ((a),(b) and (c), before stimulation) are enabled because in each case places p

1and

p2

contain at least one token. This is not the case for the example shown in Fig. 16(d)where in transition h

1is not enabled, since p

1does not contain any tokens. Stimula-

tion of a transition hjconsists in withdrawing a token from each of the input places of

transition hjand in adding a token to each of the output places of transition h

j. This is

illustrated in Fig. 16 as well. In Fig. 16(b) we note that there are two tokens in placep3

after stimulation because there was already one beforehand. In Fig. 16(c) weobserve that a token remains in place p

1after stimulation has taken place.


A.1.2. MarkingA marking of a Petri net is the distribution of tokens in the set of places of the Petri

net. Thus stimulation of a transition results in a new marking. Each marking de"nesa state of the system. If the number of tokens in the net is bounded, then there area "nite number of markings. A marking is reachable from an original marking if thereis a sequence of transition stimulations starting from the original marking that resultsin that marking. The reachability set (graph) of a Petri net is the set of all markings thatare reachable from the initial marking. The number of tokens contained in a placepiwill be called either M(p

i) or m

i. For example, in Fig. 16(a) before stimulation, we

have m1"1, m

2"1, m

3"m

4"0. The net marking, M, is de"ned by the vector of

these markings, i.e. M"(m1, m

2, 2, m

n). The marking at a certain time de"nes the

state of the PN, or more precisely the state of the system described by the PN. Theevolution of the state thus corresponds to an evolution of the marking, an evolutionthat is caused by stimulation of transitions, as we have seen. In practice, the markedPetri nets are always considered and they are called quite simply Petri nets. On theother hand, unmarked PNs may be speci"ed when necessary.

When a PN is used to describe the evolution of a system in an autonomous way, inwhich the time of stimulation is unknown or not indicated, it is de"ned as anautonomous PN. When a PN describes the operation of a system which is subjectedto the external events (such as the disturbance or control from personnel) and/or limitof time, it is named as a non-autonomous PN.

De5nition A.1. A basic PN is formally de"ned as a "ve-tuple PN"(P, H,Pre, Post, M) where

(1) P"Mp1, p

2, 2, p

nN, n'0, a "nite set of places;

(2) H"Mh1, h

2,2, h

mN, m'0, a "nite set of transitions with PXHO0, PWH"0;

(3) Pre(p, h) : P]HPM0, 1N, an input function that de"nes the set of directed arcsfrom P to H;

(4) Post(h, p) : H]PPM0, 1N, an output function that de"nes the set of directed arcsfrom H to P;

(5) M : PPM0, 1, 2,2N, a marking whose the ith component represents the numberof tokens in the ith place.

De5nition A.2. Given that PN"(P, H, Pre, Post, M):

(1) K is a capacity function of PN, if K is the mapping from P to N`XMuN,K : PPN`XMuN, where N`"M1, 2, 3,2N, K(P)"u represents the "nite capacity ofP is in"nite.

(2) Assume that K is a capacity function of PN, M : PPN0

is a marking of PN ifand only if p3P : M(p))K(p), where N

0"M0NXN`.

De5nition A.3. x3X is an element of PN"(P, H, Pre, Post, M), 0x is the preset (alsocalled input set) of x if 0x"MyD (y, x)3FN, x0 is the postset (also called output set) ofx if x0"MyD(x, y)3FN, F is the #ow relation representing the movement of tokens.


Fig. 17. A P-timed Petri net.

In a basic PN, the enabling and stimulation rules are:

(1) A transition h3H is enabled if, and only if, for all p3P, p30hPM(p)*Pre(p, h)'p3h0PM(p)#Post(h, p))K(p), it is written as M[h';

(2) An enabled transition h stimulates at a marking M, yielding the new marking M@as follows:

M@(p)"GM(p)!Pre(p, h), p30h!h0,

M(p)#Post(h, p), p3h0!0h,

M(p)!Pre(p, h)#Post(h, p), p30hWh0,

M(p), pN 0hWh0.

(A.1)

A.2. Timed Petri net

A timed Petri net enables a system to be described whose functioning is timedependent. For example, a certain time may elapse between the start and the end of anoperation. If a mark in a certain place indicates that this operation is in progress,a timed PN enables this time to be taken into account. Timed PNs are useful forevaluating the performances of a system. There are two main methods for modellingtiming: either the timings are associated with the places (the PN is said to be P-timed),or the timings are associated with the transitions (the PN is said to be H-timed).

A.2.1. P-timed Petri netA timing d

i, possibly of zero value, is associated with each place p

i. For this

discussion, di

is considered as a constant value, but in a general case di

could bea variable.

When a token is deposited in place Pi, this token must remain in this place at least

for a time di. This token is said to be unavailable for this time. When the time d

ihas

elapsed, the token then becomes available. Only available tokens are considered forenabling conditions. In most applications, functioning at maximal speed is considered.This means that a transition is stimulated as soon as it is enabled. This is illustrated inFig. 17.

A.2.2. H-timed Petri netA timing d

j, possibly of zero value, is associated with each transition h

j. A token can

have two states: it can be reserved for the stimulation of a transition hj

or it can be


Fig. 18. A H-timed Petri net.

non-reserved. Only non-reserved tokens are considered for enabling conditions, asshown in Fig. 18.

Depending on the system to be modelled, one of the models (P-timed or H-timed)may be easier to use than the other one. However, it is always possible to pass froma P-timed PN to a H-timed PN, and vice versa.

A.3. Coloured Petri net

The coloured PNs comprise tokens to which colours are attributed. They forma category of nets whose intuitive perception is less clear than for the basic PNs. Theyare of great value for the modelling of certain complex systems.

The set up of a basic PN is based on the physical structure of a real system. Its mainweakness is that the size of PN grows swiftly with any expansion of a real system, andthereby militates against further analysis of the model. In order to enrich the informa-tion obtained from places of PN, the tokens in the same place should be identi"ed.Therefore, each token is associated with a kind of an identi"er or colour and theinformation is represented by the vector Splace, token colourT. In a general case, therelationship between a stimulated colour and a coloured token is de"ned by arcfunction. A colour may be a n-tuple, conveying complex information. The stimulationof a transition is able to clear away a particular colour and produce a new one.

De5nition A.4. A coloured PN is formally de"ned as a six-tuple CPN"

(P,H, Pre, Post, C, M0) where P is a place set, H is a transition set, C"Mc

1, c

2,2N is

a colour set, Pre and Post are functions associated with stimulation colours, M0

is aninitial marking.

(1) Place: A place contains coloured tokens, which may be associated with samecolours. There are three tokens of SaT, two tokens of SbT and one token of SeT inplace p

1, as shown in Fig. 19.

(2) Transition: A stimulation colour set is associated with each transition, in whicheach kind of colour indicates a di!erent sort of stimulation possibility. In Fig. 19,transition h

1may be stimulated by color SaT, SbT and SeT.

(3) Input and output functions: An input function or output function establishes thecorresponding relationship between each particular colour of transition andcolours in places. Compared with a basic PN, there is an independent variableincluded in the functions Pre and Post. This variable is a stimulation colour c

kof


Fig. 19. A coloured Petri net.

transition hj. The colour set C

k"Sc

k1, c

k2,2, c

knT is ascertained by a n-tuple.

Thereby, Pre(pi, h

j/c

k) and Post(h

j/c

k, p

i) generally correspond to linear combina-

tion of token colours in pi, as shown in Fig. 19:

Pre(p1, h

1/SbT)"f (SbT)"SaT#SbT. (A.2)

In the stimulation process of transition, the transformation of colour may takeplace. As for h

1stimulated by colour SbT in p

1, there is a SbT coloured token removed

and an SaT coloured token added.A coloured PN can be applied not only to the static structure of a system, but also

to characterize the dynamic behaviour of the system.

References

[1] Chow WK. An approach for evaluating "re zone models. J Fire Sci 1998;16(1):25}31.[2] Peacock RD, Reneke PA, Forney CL, Kostreva MM. Issues in evaluation of complex "res models.

Fire Safety J 1998;30(2):103}36.[3] Quintiere JG. Fire growth: an overview. Fire Technol 1997;33(1):7}31.[4] Friedman. Survey of Computer Models for Fire and Smoke. J Fire Prot Eng 1992;4:81}92.[5] Collier PCR. Fire in a residential building: comparisons between experimental data and a "re zone

model. Fire Technol 1996;32(3):195}218.[6] Staggs JEJ. A discussion of modeling idealised ablative materials with particular reference to "re

testing. Fire Safety J 1997;28(1):47}66.[7] Ingason H. Modelling of a two-dimensional rack storage "re. Fire Safety J 1998;30(1):47}70.[8] Cooper LY. VENTCF2: an algorithm and associated FORTRAN 77 subroutine for calculating #ow

through a horizontal ceiling/#oor vent in a zone-type compartment "re model. Fire SafetyJ 1997;28(3):253}88.

[9] Hasofer AM, Beck VR. A stochastic model for compartment "res. Fire Safety J 1997;28(3):207}26.


[10] Vorobov OYu. Random set models of "re spread. Fire Technol 1996;32(2):137}73.[11] He Y, Beck V. Smoke spread experiment in a multi-story building and computer modeling. Fire Safety

J 1997;28(2):139}64.[12] Luo M, He Y, Beck V. Application of "eld model and two-zone model to #ashover "res in a full-scale

multi-room single level building. Fire Safety J 1998;29(1):1}26.[13] Harmathy TZ. Simpli"ed model of smoke dispersion in buildings by stack e!ect. Fire Technol

1998;34(1):6}17.[14] Nam S. Development of a computational model simulating the interaction between a "re plume and

a sprinkler spray. Fire Safety J 1996;26(1):1}34.[15] Woodburn PJ, Britter RE. CFD simulations of a tunnel "re-part I. II. Fire Safety J 1996;26(1):35}63.[16] Tsui Hon Wing T, Kwok WC. Zone modelling of tunnel "re development. Fire Eng

J 1998;58(194):11}3.[17] Magnusson SE, Frantzich H, Harada K. Fire safety design based on calculations: uncertainty analysis

and safety veri"cation. Fire Safety J 1996;27(4):265}88.[18] Johnson P. The process of "re safety design. Fire Technol 1996;32(4):297}307.[19] Beard AN. Fire models and design. "re Safety J 1997;28(2):117}38.[20] Ramachandran G. Probability-based building design for "re safety. Fire Technol 1995;31(4):355}68.[21] Klein RA. Risk assessment in "re service practice: model or speci"c assessment of risk. Fire Eng

J 1998;58(194):2}5.[22] Harding J. Risk assessment for "re safety. Fire Eng J 1998;58(194):6}8.[23] Dennett MF. Dynamic statistical analysis-the research tool ignored by the "re service. Fire Eng

J 1998;58(193):32}6.[24] Jones WW. The evolution of HAZARD: the "re hazard assessment methodology. Fire Technol

1997;33(1):167}82.[25] Yoshida Y. Evaluating building "re safety through egress prediction: a standard application in japan.

Fire Technol 1995;31(2):158}74.[26] Watts JM. Fire risk evaluation model. Fire Technol 1995;31(4):368}71.[27] Miles SD, Cox G. Prediction of "re hazards associated with chemical warehouses. Fire Safety

J 1996;27(4):265}88.[28] P. Johnson, Hazard I. A "re safety analysis methodology. Fire Aust Summer 1991/92;16}8.[29] Chandrasekaran V, Grubits SJ, Hildebrandt, M. Mathematical modeling and neural network simula-

tion in "re safety engineering research. Winter Fire Aust 1993;18}25.[30] Radke J. Spatial decision support system for urban/wildland interface "re hazards. Proceedings of

ESRI User, URL, 1995.[31] Hill M. Fire service management * The need for change. Fire Aust 1997;2:4}7.[32] Lai P-C, Lam K-C. Use of the geographic information systems approach in optimising "re manage-

ment. Fire Eng J 1998;58(192):27}32.[33] Klein RA. Information technology (IT) in strategic and tactical planning by the "re service. Fire Eng

J 1998;58(192):33}41.[34] Large C. Using CAD and GIS in "re-"ghting incident command and control. Fire Eng

J 1997;57(188):33}5.[35] Bruschlinsky N, Wagner S. Aktuelle Probleme des Brandschutzes. Deutsche Feuerwehr-Zeitung

1996;4:36}42.[36] Tamaki H, Araki M. Simulation-based scheduling package using generalized petri net models. IEEE

Trans Software Eng 1993;3:451}6.[37] Lin JT, Lee C-C. A three-phase discrete event simulation with EPNSim graphs. Simulation

1993;60(6):382}92.[38] De Bosschere K, Almhana J. Performance evaluation of a blackboard using stochastic Petri nets.

Simulation 1995;65(4):269}78.[39] Gourgand J-M, Norre S. Petri net based methodology for task scheduling on multiprocessor

architectures. Simulation 1993;61(3):185}92.[40] Tsai JP, Yang SJ, Chang YH. Timing constraint Petri nets and their application to schedulability

analysis of real-time system speci"cations. IEEE Trans Software Eng 1995;21(1):32}49.


[41] John. On the existence of supervisory policies that enforce liveness in discrete-event dynamic systemmodeled by controlled Petri nets. Automat Control 1997;42(7):36}42.

[42] Koh I, DiCesare F. Modular transformation methods for generalized Petri nets and their applicationto automated manufacturing systems. IEEE Trans Systems Man Cybernet 1991;21(6):1512}22.

[43] Lee KH, Jung MY. Petri net application in #exible process planning. Comput Ind Eng1994;27(4):505}8.

[44] Chabot J-L, Ducamp F, Signoret J-P, Joulain P, Hutinet T. Hybrid Monte-Carlo simulation usingPetri nets and "re code for analyzing "re scenarios in nuclear power plants. Proceedings of PSAM'4,New York, 1998.

[45] Xin H. Simulation theory study on urban "re "ghting and dispatching process. PhD thesis, TongjiUniversity, Shanghai, People's Republic of China, 1998.

[46] Han X, Li J, Shen ZY, Chen HG. Decision support system for dispatching and commanding of urban"re-"ghting based on model. Proceedings of '97 Shanghai Fire Protection Association AnnualMeeting, 1997, p. 1}5.

[47] David R, Alla H. Petri nets for modeling of dynamic systems * A survey. Automatica1994;30(2):175}202.


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Non-autonomous coloured Petri net-based methodology for the dispatching process of urban fire-fighting