System Dynamics '95 — Volume IT
SYSTEM DYNAMICS SIMULATION SOFTWARE
———DYNAMOX
Jiugiang Han, Guoji Sun
System Engineering Institute,
Xi’an Jiaotong University , Xi’an, PRC
ABSTRACT
The purpose of this paper is to present the characteristic, functions and program structure
of system dynamics simulation software ——DYNAMOxX that can be used on XENIX oper-
ation system. This software is mainly composed of six parts. (1) dispatch management
module, ( 2) parameter modify module, (3) model compiler module, (4) model run module
» (5) database access module, ( 6) model library access module. In order to illustrate our
software ,we give a simple example about the organisms relationship model between deers,
beasts and grass in Kaibab plateau .
INTRUDUCTION
System dynamics method and simulation technique is a very good study way that si used to
plan and decision the complex systems for society economics , management . biology .
population and enviroment etc.. In system donamics method, the main tool used to study
those problems is a system dynamics simulation software, This kind of simulation software
was earliest developed by MIT . Late on ,it is popularized to all over the world. The sys-
tem donamics software called Micro ——Dynamo was introduced into china in the 1980s,
because its model size is too small, it can’t become a support enviroment used to scientific
study ,so it is replaced by another system dynamics simulation language DYNAMOC devel-
oped by authors. DYNAMOC has played important role in pushing the research and applica-
tion of system dynamics method forward in china. It has been extensively used to the study
on society, economics, population and environment system etc. . But, the application filed
of system dynamics simulation technique is becoming more and more wide , the problem to
be researched more and more complex, and the eqaution size to be solved more and more
huge. Particularly ,it can not meet the needs of simulating many large scale economic deci-
sion support system modles. In addition, there also exist some disadvantages, such as, lim-
ited model size, single user, data no leaving from modle and lack of data common enjoy (
S62
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share) capability etc... Hence ,in order to overcome all those shortcomings , we have devel-
oped a new system dynamics simulation software — ——DYNAMOxX that can be run on
XENIX operation system. DY NAMOX software has successfully been used in "the decision
support system about science, technology , economic and society harmonize development in
SHAAN XI province ”.
THE CHARACTISTICS OF THE SOFTWARE
Many U ser
Data common enjoy (share): DYNAMOX can be used by many users on XENIX support
enviroment, and provides the function to operate database. When many users use DY-
NAMOkxX, the data in database can be shared by each user. Data leaving from modle; In tra-
ditionary system dynamics simulation software, data can ‘t leave from modle so that simula-
tion result data of different modles can not be used each other. DYNAMOX can storage us-
er modle to modle library and simulation data to database respectively. Model Size: In DY-
NAMOX, system dynamics simulation model size is only limited by memory space in com-
puter because of using dynamic memory allocation technology. DYNAMOX< can simulate
system dynamics model with 10000 equations on personal computer.
Algorithm and Interactive
Many integration methods: DYNAMOX provides three kinds of integration rules included
Euler, fourth order Runge
Kutta and changable step. These integration methods can
entirely meet the needs of different simulation accuracy and speed. Many kind of equations
and functions; DYNAMOX can solve all kinds of equations and functions stipulated in s
tandard DYANMO langauge. In addition the independent variable of table function may be
both equal and unequal interval, and provides relative table functions too. Parameter opti-
mization; DYNAMOX< can optimize five model parameters each time. After user enters the
parameters to be optimized and objective function according to the syntax of DYNAMOX,
the parameters can be optimized immediately. Interactive: Because of using menu technique
full screen and providing large scale assistance operation informations, when user only en-
ters a few commands, simulation process may be completed. During simulation run, user
can pause the run at any time, and modify parameter and display data etc.. After simula-
tion end, user can also modify parameter and rerun, but it is unnecessary to recompile mod-
le.
THE STRUCTURE OF THE.SOFTWARE
System Dynamics '95 — Volume II
The structure of system dynamics simulation software program is mainly composed of ten
parts ,i.e. man—machine interface part, dispatch management, parameter modify ,data ac-
cess model access , model compiler model run , database and model library. The software
structuer is shown in Figure. 1.
parameter data data
modify access . base
i
man— i
; dispatch model model
machine iam .
. management compiler run
interface
error model model
diagnosis access library
Fig. 1. DYNAMOX Overall structure
Dispatch Management and Man—Machine Interface
Man-Machine interface module recieves user ‘s choice to DY NAMOX menu on full
screen, and sends these commands to dispatch management module. According to the
choice to system function, the dispatch management module harmonizes the operation of ev-
ery module in overall structure. And controls system run . The module can not only com-
bine the data from database wiht the model from model library into a run model ,but the
data and the model in the run model can be separated from each other ,and sends them to
database and model library respectively.
Model Compiler
The model compiler module is a nucleus in DYNAMOX, its performence affect directly the
speed of compiling and runing for model. In order to enable DYNAMOX’‘s compiler module
program to be independent of a special computer, we use a medium langauge that is a exe-
cutable code generated by compiling source program. Because DYNAMO language stipi-
lates that a undifined variable can be first used, after medium code generate, it is necessary
to check all being used ariables. Later on the medium codes are changed into object code a-
gain,and do arrangement sequence, last, executable code is got. This is the design thought
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of the model compiler module program. The model compiler module program consists of
phrase analysis .syntax analysis , psedo— machine code generate, object code generate,
variable check and automatic arrangement sequence module. The model compiler module is
shown in Fig 2.
phrase syntax pseudo. object
analysis analysis code code
source executa~ arrange variable
program ble code sequence check
Figre . 2. compiler module flow chart
In fig. 2. , Source program means system dynamics simulation program written by user
according to the syntax stipulated by DY NAMOX . For instancey (R RATE. KL =A.K
* B.K-+C.K_ ) is a system dynamics simulation source program, sometimes, it is also
called a system dynamics equation. Phrase analysis program reads in source program in one
by one letter and one by one statement, and registers the type of every equation ,analyzes
the equation phrase, checks whether the subscript of equation name acording with phrase
regulation or not. When a equation name and its type are accoding with phrase regulation,
dynamic memory allocation program will build a equation tree (i. e. the memory structure
table )for the equation on the basis of the the equation name. Syntax analysis is an expres-
sion treatment program that analyses and treats the expression at right side in an equation.
The syntax analysis program checks whether source program is according with syntax regu-
lation or not. Because the expression at right side in an equation includes either arithmetic
operation or logic operation, or both, the analysis algrithm for expression uses a operation
sign priority rule of the expression — oriented. During expression treatment, contant,
variable and function can be treated by a semantics analysis program. First, the semantics
analysis program takes out a operation sign and a operand from the expression in order,
through analysis and treatment »yields a operation instruction that is called medium (pseudo
—Machine) code,at the same time,also builds a same medium code tree with the equation
tree structure so that variable check and the generation of optimization objectve code can be
done later on. Next, the operands that can not temporrarily become medium code are tem-
porarily pushed in a operand stack, After the whole equation is treated, compiler stipatch
program will treat next a equation continually. In this way,until meeting RUN equation or
the source program end, syntax analysis of the source progra: for a model will be complet-
System Dynamics '95 — Volume II
ed and all pseudo—machine codes are generated too.
For instance, in treatment equation (R RATE. KL =A.K * B.K-+C.K_ ) process,
the semantics analysis program first generates two instructions stored variable A. K and B.
K, and pushes the two address pointers stored the two temporary instructions into operation
stack. later on,it generate a multiplication operation, the two address pointers kept variable
A.K and B. K in operation stack are poped from the stack again, and, is changed into a
medium code instruction for A. K * B. K. But the medium code instruction is only as tempo-
rary operation instruction in generation addition instruction, and its address pointer will be
pushed into the stack, then generates another instruction stored variable C. K. Last, it
generates a addition instruction, its two operands are the address pointer stored A. K * B. K
in stack and the instruction stored variable C.K respectively. At this moment, the address
pointer of the addition instruction is only pushed into the stack , and it is as the tree root of
the medium code tree built by expression A. K * B. K +C.K .
After the medium code trees for all equations are correctly generated , variable verifica-
tion starts. As mentioned above, because DYNAMOX’s syntax stipulate that undefined
variable can be first used, it is nesessary to verify whether all variables at right side of a e-
quation appear at left side of the equation or not, and whether their subscripts accord with
syntax regulation or not. In variable check process, variable check program first searches
those medium code instructions stored variables. Next, by looking for the equation trees ac-
cording to the variable name found already, seeks the equation of the same name to the
variables. Then, obtains the permitable subscript of the variable by looking for variable
table according to the equation and variable type found already, and compares the per-
mitable subscript with actual subscript, if both subscripts are same, the variable has been
defined , else will search continuosly . In this way, until all variables are checked and accord
with stipulate.
The generation mode to objective code instruction is same with that of pseudo— ma-
chine code instruction. Before the interpreter program written in C language executes objec-
tive code instruction, the medium code instruction passed variable verification should first be
transformed into objective code instruction. In transformation process ,operands may be both
immediate number, register and address pointer. Because of using the generation algorithm
of optimization objective code tree and generating objective code chain by producing the ob-
jective code of medium code tree, the operation for a * b only generates a multiplication in-
struction , but it does not generate transmission data instruction, and the equation can be
calculated as long as objective code chain is executed in order. In this way, it is both shorten
the length of objective code chain and enhance the speed of treating equation largely. Ar-
rangement sequence program provides automatic arrangement sequence function, user does
not need to consider the programming sequence for source program. there are four kinds of
equations that need.to arrange sequence. They are R equation,A equation, N equation and
S equation.
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Arrangement sequence is made by scanning objective code equation tree. After all equa-
tion tree are scanned once, if the equation to be arranged order can be found in the equations
trees of unarrangement sequence, this arrangement order is successful, else , the arrange-
ment sequence is failure. In arrangement order ,the arrangement sequence program arranges
same kind of equations at continuous place in arrangement sequence table, and every type of
equation has its start address and value. After all equations are only arranged sequence suc-
cessfuly, the simulation for the model can be done.
Model Run
The model run module is composed of three parts, i.e. run initiating program , algebra e-
quation calculation and differential equation calculation program. Run initiaing program is
used to set the initial value of zero for every equation except C (contant), B(train), SPEC
and T( table) equation, and keeps the initial values of train variable and SPEC variable so
that is used when rerun. Similar, it can also be used to set the initial value of unzero for ev-
ery equation . Run initiaing includes both to initial the all system variables and functions,
and it is mainly uesd to searche the address of the system variable and its value by scaning
system variable table. The system variables includes simulation total time, integration step »
integration mothod etc.
N equation,R equation and A equation calculation program mainly consists of the pro-
gram of searching equation address, the program of researching equation chain code and the
equation calculation program . First, the program of searching equation address seeks the
address storaged the equation in stack by scanning equation tree, then, seeks the equation
chain code according to the equation address found already, last, the value of the equation is
calculated by equation calculation program . The calculation program for every kind of equa-
tion above mentioned is almost similar.
L equation calculation program: Because N, R, A equation is a kind of algebra equa-
tion, its calculation belong to algebra calculation. However ,L equation is a kind of differen-
tial equation, its calculation is an integration calculation . In L equation calculation process,
in order to calculate the vlue of L equation, it is necesary to dispatch relative integration
rules, i. e. Euler, forth—order Runge—Kutta and Changeable step rules. Other calcula-
tion process is same with N,R,A equation calculation process.
Parameter Mod ification
During run ,parameter modification module not only can modify any parameter in model
and all system variables, such as constant, run time and output variable, but also change
the output mode of each output variable, but not change integration rule. If the output mode
for some variable has been changed , and the variables must be outputed in new output
mode, it is necessary to rerun. However, because parameter modifying only changes objec-
tive code, rerun does not need to recompile source program. In this way, it enhances the
System Dynamics '95 — Volume II
speed of the whole system run largely.
Model and Data Access
Model access module is a model library ranagement program. It has two functions. First
function is to storage user ‘s simulation model to model library. Another function is to take
out the relative simulation model from the model library and send it to the dispatch manage-
ment module. Data access module is a database management program ,it can storage the data
produced by running simulation model into database . In order to output simulation result ,
it is necessary to take out the data from database. sometimes ,when the initial condition of a
model equation needs the simulation result of another model, in the data format stipulated
by DYNAMOX and ALRACL database management mode ,the data access module access-
es the database.
EXAMPLE
We simulated many system dynamics models, such as world model (world dynamics i. e.
W5 and W2) and the planning model for some area (over 3200 equations) and so on. In
addition, in order to illustrate our DY NAMOX model size, we simulated a pure mathemat-
ics model with 10000 difference equations that have not practice sense. Here ,we give a ex-
ample about the organisms relationship model between deers, beasts and grass in Kaibab
plateau . Its system dynamics flow chart is, and the simulation result in figre. 4 , and in-
clude DYNAMOxX< source program .
CONCLUSION
DYNAMOX is a system dynamics simulation software suitable for microcomputer on
XENIX enviroment, and it has been successfully used in practical system. particlarly, has
been used in "the decision support system about harmonizing science,technology, economic
and society development in SHAAN XI ‘province’. Many users think that DY NAMOX’s
sperformence is superior to earlire system dynamics simulation language in many aspects. Its
popularization will certainly promote the study and application of system dynamics simula-
tion technique in many fields, Paticularly ,in the decision support system about harmonizing
science ,technology,economic and society development planning.
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Parallel Program
NOTE DEER
dp. k=dp. j+ (dt) (dngr. jk —dpr. jk)
dp: i
dpi=4000
dngr. kl=dp. k * dgrf. k
dgrf. k=tabhi(tdgrf,fr. k,0. 25,2,. 25)
tdgr! + 75/—. 5/—. 25/0/. 12/. 2/. 23/. 24
fr. k=fpd. k * nfpd
nfpd=1 area
fpd. k=£. k/dp. k
dpr. ki==dkr. k * pp. k
aa. k==dp. k/area
area=800000
dkr. k=tabhi(tdkr dd. k,0,.1,. 01)
tdkr=0/. 2/1. 2/3. 2/5. 4/7. 6/8. 6/9. 3
7/9. 8/10/10
NOTE BEAST
L_ PP.K=PP.J+(DT)(PNGR. JK —PBR. JK)
~APF APF Rr POF H RP ROZAe
N PP=PPI
C PPI=8000
R_ PNGR.KL=PP. K * PGRF.K
A PGRF. K=TABHL(TPGRF ,DKR. K,0,. 6,. 1)
T TPGRF: 04/0/. 02/. 035/. 045/. 05/. 05
R
Cc
Cc
PBR. KL=PP. K * STEP(RF RST)
RF=. 2
RST=1905
F.K=F. J+(DT)(GR. IK—FC. JK)
F=FI
FI=350000 DP 1.04e005
L
N
c
R_ GR.KL=(FCAP—F.K)/FRT.K
C FCAP=350000
A ERT.K=TABHL(TFRT ,F.K/FCAP,0,1,. 25)
T TFRT=20/8/3/2/1
R FC.KL=DP.K * FCPD.K
A FCPD.K=TABHL (TFCPD,FR. K ,0,1.5,. 25)
T TFCPD=0/. 25/.5/.75/1/1. 12/1. 2
NOTE CONTROL 5e
SPEC DT=.1 r
SPEC LENGTH=1950
SPEC PRTPER=1
SPEC TIME=1900
GRAP DP/PP/F
RUN
+
ges
dear pure } 2 speed each dear grass amount
wy cnt
t
des ! each dear grass
consumption
™ Nyt Dee
/ density art — speed
oe
[ \
catch coefficient grass tata
! ta)
jt =
| catch dear speed grass rise speed
i *
C a (t)
beast total *" grass rise time
w
yt
beast pure rise speed grass yield ability
Figre . 3. System Dynamics flow chart
‘Sadie cd
1388, Bia) 1958
Figre . !. Simulation Result
can
System Dynamics '95 — Volume II
REFFERENCE
Wang, H.B. 1989. System dynamics guide ,Energy publishing house.
Aho,A. V. 1976. Optimal Code Generation for Expression Trees. Journal of the Associa-
tion for Computing Machinery vol. 23. NO.3 pp 488 —507.
Addisson Weslay Publishing Company Inc. 1983. User Guide and Refference Manual for
Micro——DYNAMO System Dynamics Modelling language IBM—PC Version,
Uhran J. J. 1984. The Structure of NDTRAN—— a system simulation language, IEEE
TRANSACTION ON SYSTEM VOL SMC—14 NO.
Phillips. J. B. 1978. Threaded Code for Laboratory Computers, SOFTWARE —PRAC-
TICE AND EXPERIENCE, VOL. 8, PP257—263.
aa
