1. Levels and Rates
The Bath tub Example
Dennis T. Beng Hui, De La Salle
University-Manila

2. Stock Flow Diagram (Flow
Diagrams)
Stock and flow diagrams are ways of
representing the structure of a system
with more information than a simple
causal loop diagram.
Stocks (levels) are fundamental to
generating behavior in a system.
Dennis T. Beng Hui, De La Salle University-
Manila

3. Stock Flow Diagram (Flow
Diagrams)
Flows (rates) causes stocks to change.
Stock and flow diagram is a common
step toward building a simulation
model because they help define the
types of variables that are important in
causing behavior.
Dennis T. Beng Hui, De La Salle University-
Manila

4. Stock Flow Diagram
Stocks or levels
Flows or Rates
Auxiliary
Table Function
Constant
Exogenous Variable
Variable not defined in diagram
Information Link
Material Link
Source or Sink of material
Dennis T. Beng Hui, De La Salle University-
Manila

5. Population Stock Flow
Diagram
Population
Birth Death
% Birth Women % of Population
Giving Birth dying
Dennis T. Beng Hui, De La Salle University-
Manila

6. Aids Stock Flow Model
HIV AIDS
Infection Rate Incubation Rate Death Rate
Dennis T. Beng Hui, De La Salle University-
Manila

7. Stock Flow of Ordering
system
Amount of
Delivery Invty
Orders
Amount to
Demand Rate
replenish
Dennis T. Beng Hui, De La Salle University-
Manila

8. Stock Flow of Ordering
system (Alternative)
Order Demand
Amount of
Inventory
Net of Orders and
Delivery
Deliver
Dennis T. Beng Hui, De La Salle University-
Manila

9. Coffee Temperature Stock
Flow Diagram
Coffee Temperature
Change in Temp
Heat Loss
Room Temp
Dennis T. Beng Hui, De La Salle University-
Manila

10. Stock Flow of Household
Expenditure
Available
Income Money Allowance
Utilities
Amount of
Overtime
Dennis T. Beng Hui, De La Salle University-
Manila

11. Problem and Addiction Stock
Flow diagram
Addicition
Change in level Level
Amount of
New Problems Problem
Solved Problems
Dennis T. Beng Hui, De La Salle University-
Manila

12. Classes of Equations
Level equations
Rate equations
Auxiliary equations
Supplementary equations
Initial-value equations
Dennis T. Beng Hui, De La Salle University-
Manila

13. Level equations
Level equations have varying contents
of reservoirs of the system. They
would exist even if the system is in rest
and no flows existed.
Examples are stocks, inventories and
others.
New values of levels are calculated at
each of the closely spaced solution
intervals.
Dennis T. Beng Hui, De La Salle University-
Manila

14. Level equations
Levels are assumed to change at a
constant rate between solution times,
but no values are calculated between
those times.
Levels determine rates
Example:
L INVTY.K=INVTY.J+DT(MAKES.JK- SALES.JK)
Dennis T. Beng Hui, De La Salle University-
Manila

15. Rate equations
Rate equations are decision functions.
Defines the rates of flow between the
levels of the system.
A rate equation is evaluated from
presently existing values of levels in
the system, very often, including the
level from which the rate comes and
the one into which it goes.
Dennis T. Beng Hui, De La Salle University-
Manila

16. Rate equations
The rate in turn cause the changes in
the levels.
Rates determine levels.
Example:
R BIRTH.KL = POPN.K*0.20
Dennis T. Beng Hui, De La Salle University-
Manila

17. Auxiliary equations
Auxiliary Equations are components of
a rate equation. These are equations
that assist but are incidental.
Helps in keeping the model in close
correspondence to the actual system.
Dennis T. Beng Hui, De La Salle University-
Manila

18. Auxiliary equations
These equations can be substituted
forward into one another and hence
into rate equations.
Unlike rate equations, auxiliary
equations must be evaluated in proper
order.
Dennis T. Beng Hui, De La Salle University-
Manila

19. Auxiliary equations
Example:
A DRUGS.K = POPN.K * 0.1
R USERS.KL = DRUGS.K * 0.2
L AIDS.K = AIDS.J + DT(BIRTH.JK + USERS.JK)
Dennis T. Beng Hui, De La Salle University-
Manila

20. Supplementary equations
Supplementary Equations are used to
define variables which are not actually
part of the model structure but arise in
printing and plotting values of interest
about the model.
These equations are denoted y “S”.
Dennis T. Beng Hui, De La Salle University-
Manila

21. Initial-value equations
Initial-Value Equations are used to define
initial values of all levels and some rates
that must be given before the first cycle of
model equation computation can begin.
These also be values of some constants
from other constants.
Example:
N INVTY = 100
Dennis T. Beng Hui, De La Salle University-
Manila

22. Computational Interval
(Solution Interval)
DT represents “Delta Time”
It is the model time elapsing between
computations in the simulation model.
Dennis T. Beng Hui, De La Salle University-
Manila

23. Computational Interval
(Solution Interval)
The solution interval must be short enough
so that its value does not seriously affect the
computed results.
It should also be long enough as
permissible to avoid unnecessary digital-
computer time
DT should be between one-half to one-tenth
of the smallest time constant in the
model.Common values are 0.50, 0.25, and
0.125)
Dennis T. Beng Hui, De La Salle University-
Manila

24. Coffee Cooling Model using
Dynamo
*Coffee Cooling Temperature
NOTE COFTEMP.K = Coffee Temperature in Celsius
L COFTEMP.K=COFTEMP.J+DT*(COOL.JK)
N COFTEMP=100
NOTE COOL.KL = Cooling Rate of Coffee
R COOL.KL=K(ROOM-COFTEMP.K)
C ROOM=25
NOTE K is a constant
C K=.01
SPEC DT=.25/SAVPER=.25/LENGTH=5
NOTE Time is in minutes
SAVE COFTEMP,COOL,ROOM
Dennis T. Beng Hui, De La Salle University-
Manila