This document discusses various modeling techniques for complex system dynamics models, including rates of change, delays, tables, and test functions. It provides examples of using different types of rate equations, as well as examples of modeling delays using DELAY and SMOOTH commands. Tables can be used with the TABLE command to describe variables that are not simple equations. RAMP, NOISE, PULSE and STEP commands are discussed as ways to test models using continuous, random, pulse and step functions.

1. Modeling Complex SD
DELAYS AND TABLES
Dennis T. Beng Hui, De La Salle
University-Manila

2. Types of Rate Equations
(Var.kl = …)
Constant*Level.k
Level.k/life
(goal.k-level.k)/adjustment
aux.k*level.k
level.k/aux.k
norm.k+effect.k
norm.k*effect.k
Dennis T. Beng Hui, De La Salle
University-Manila

3. The Spreading Virus Problem
Virus starts with a few people who are
susceptible to the virus. These
susceptible people will become infected
and in turn become sick. Once people
get sick, they start taking medicine, as
time progresses, these people will
slowly get cured and on their way to
recovery.
Dennis T. Beng Hui, De La Salle
University-Manila

4. The Spreading Virus Problem
Susceptible People
Recovered People
Infected People
Sick People
Dennis T. Beng Hui, De La Salle
University-Manila

5. Examples of Delays: Delay1
R SYMP.KL=DELAY1 (INF.KL, TSS)
Where TSS = time to show symptoms
INF = infection rate
SYMP = symptom rate
Healthy Incubate Sick Recovered
INF SYM REC
Delay1(INF.KL,TIME)
Dennis T. Beng Hui, De La Salle
University-Manila

6. Examples of Delays: Delay3
SYMP.KL=DELAY3 (INF.KL, TSS)
Where TSS = time to show symptoms
INF = infection rate
SYMP = symptom rate
Susceptible Incubate1 Incubate2 Incubate3 Sic
INFC INC1 INC2 INC3
Delay3(INFC.KL,TSS)
Dennis T. Beng Hui, De La Salle
University-Manila

7. Effect of Delays
What happens to the diagram if there is
an incubation period?
What do you think is the behavior of
the levels and the rates in this system?
SMOOTH – delay command for
information. Ex. smooth1, smooth3
Dennis T. Beng Hui, De La Salle
University-Manila

8. Effect of Delays
Dennis T. Beng Hui, De La Salle
University-Manila

9. The TABLE COMMAND
TABLE – use to describe a variable that
is not a simple algebraic equation
SYNTAX:
A VAR.K = TABLE (table_name, input_to_table, min-x, max-x, x-inc)
T table_name = y0/y1/y2/ … /yn
NOTE: n is equal to the number of x points available between min-x up to max-x.
Dennis T. Beng Hui, De La Salle
University-Manila

10. TABLE Example
A SALESMEN.K = TABLE (TSE, DDRM.K, 0, 10, 1)
T TSE = 400/388/348/292/212/152/100/60/32/12/8
R ORDERS.KL = SALESMEN.K*SALES/PERSON.K
Where
TSE = table for SALEMEN
DDRM.K = delivery delay (level or auxiliary variable, or even a rate
variable)
X 0 1 2 3 4 5 6 7 8 9 10
Y 400 388 348 292 212 152 100 60 32 12 8
Dennis T. Beng Hui, De La Salle
University-Manila

11. TEST Commands
RAMP - continuous growing or declining linear function of TIME.
Var = RAMP(A,B)
Where A = represents the slope of the linear function
B = represents the starting time of the ramp
NOISE - The noise function allows us to vary the value of a
variable by –0.5 to 0.5. This command allows us to exhibit a
little bit of randomness, but still maintaining the pattern of
behavior. NOISE exhibits a uniform distribution.
Var = A*NOISE()+B
Where A and B are constants and that the value of Var is
centered between A and B.
Dennis T. Beng Hui, De La Salle
University-Manila

12. TEST Commands
PULSE – creates a sudden increase in the behavior and
drops back to its original state.
PULSE(HEIGHT,WIDTH,FIRST,INTVL) – from VENSIM
-A pulse of height , starting at time FIRST and every INTVL
lasting WIDTH time units.
STEP – creates a step change in the behavior and does
not return to its original state.
STEP(H,T) – from VENSIM
- Returns 0 till time T and then H.
Note: DYNAMO commands for PULSE and STEP will have a slightly
different syntax.
Dennis T. Beng Hui, De La Salle
University-Manila