System variables and flow diagram -- and the translation of flow diagram to DYNAMO language
Modeling of Agricultural Systems [AGS721]
LAB 4
System variables and flow diagram -- and the
translation of flow diagram to DYNAMO language
System variables
In simulation modeling concerns, typically there are five types of system variable i.e. level, rate, auxiliary, constant, and exogenous variable. Each variable type represents different forms of equation in the simulation model. Among these variables, the level and rate variable are the system key variables in which they characterize the dynamic of the system. Other variables, however could influence the level or rate variables which consequently affect behavior of the system. The following sections describe characteristic and role of each type of system variable in the model.
Level and Rate Variable
Level variable is the variable that accumulates its quantity over time. That is the quantity of level variable can increase or decrease through time. Hence, the unit of level variable generally is unit of amount or number e.g. amount of money in the bank account, number of population, number of eggs, and volume of water.
Rate variable is the activity, movement or flow of material per unit of time into or out of the level variable. Therefore unit of rate variable is the amount or quantity flow (into or out of level variable) per unit of time e.g. number of birth/year, amount of interest paid ($)/year, and number of chicks hatched/week. In order to make the clear picture about the relationship between the level variable and rate variable, we may compare level of water in the tank as level variable and the inflow and outflow of water per unit of time as the rate variables (see Jongkaewwattana, 1995 page 55).
There are notations which was suggested by Forrester (1968) to represent each type of system variables which are very helpful to be used for the construction of simulation model (see Jongkaewwattana, 1995 page 56). When these notations are put together according their relationships, it is called the flow diagram. Generally, the construction of flow diagram is a step ahead after causal-loop diagram is determined. But, it is a step prior to model formulation. Hence, modelers have to convert the causal-loop diagram into the flow diagram, and consequently convert the flow diagram into the computer model. According to Forrester's notations, the level variable is represented by the rectangular symbol and rate variable is represented by valve-like symbol as shown in figure below. The cloud-like symbol represents source of material that flows into the level variable or it can also represents sink which accepts the outflow of material from level variable. The arrow symbol represents material flow in or out of level variable. Figure in Jongkaewwattana (1995) page 57 compares the flow diagram using Forrester's symbols and the dynamic of water level in the tank.
Exercise:
1. Convert the following causal-loop diagrams into flow diagram using Forrester's notations.
(a) Population growth model
(b) Insecpopulation dynamic model
(c) Tree population dynamic
2.Construct model (in DYNAMO language) in (a) and (b) using given information.
(a) Birth rate= Population*Fractional birth rate
Fractional birth rate = 0.3 person/person year
Death rate=(Population)/(Average life span)
Average life span=70 years
Initial population size=10,000
(b) Hatching rate=(Number of eggs)/(Eggs duration)
Eggs duration=15 days
Pupation rate=(Number of larvae)/(Larval period)
Larval period=150 days
Maturation rate=(Number of Pupae)/(Pupa period)
Pupa period= 240 days
Initial number of eggs=1,000 eggs
Initial number of larvae=0
Initial number of pupae=0
Initial number of adults=0
References:
Forrester, J.W. (1968). Industrial Dynamics.
Cambridge, Mass: MIT Press.
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