The Best of Creative Computing Volume 1 (published 1976)
Dynamic Modeling Using Fortran IV (construction of formal models of systems whose behavior is followed by computer simulation, System Dynamics, Jay W. Forrester)
Dynamic Modelling Using FORTRAN IV
Jay Martin Anderson
Bryn Mawr College
Introduction
"Dynamic modelling," as used in this paper, means the construction of formal
models of systems whose behavior
in time is followed by computer simulation. Specifically,the paper will refer to
the techniques of System Dynamics,as pioneered and developed by M. I. T.
Professor Jay W.Forrester.System Dynamics is a general theory of system
structure which rests on four essential elements:
(1) The cause-and-effect links between elements of a system and the position of
these elements within
feedback loops are identified.
(2) The model is expressed in a formal, mathematical language in which the
qualitative interactions identified
in (1) are made quantitative.
(3) The behavior of the model is examined by computer simulation.
(4) The consequences of changing system structure are evaluated by iterating on
steps (1)-(3) until a viable
policy or set of policies for the system under study has evolved.
The integrity, if not the beauty, of System Dynamics has often been commented
upon by Forrester and his
students and colleagues. Our purpose here is not to debate the merits of System
Dynamics as a technique or theory,nor to expound its practice, but rather to
focus on step (3) of the preceding four-step program: the computer simulation of
System Dynamics models.
In recent years a number of System Dynamics models have reached the public eye,
including Forrester's and
Meadows World models, and the several environmental models described in Toward
Global Equilibrium.These
models are cast in the computer language DYNAMO,developed expressly for the
purpose of serving the System
Dynamics community. DYNAMO affords a one-to-one relationship between computer
equations and System Dynamics concepts, assumes for itself the labor of
arranging the equations in a computable order and providing printed
or plotted output. DYNAMO is a compile-and -go processor which provides its own
careful diagnostics, and is available for use in a limited number of
computational environments from Pugh-Roberts Associates, 65 Rogers Street,
Cambridge, Mass. 02142.
In spite of its simplicity and beauty, DYNAMO falls short in classroom
situations for at least two reasons. First,it is not widely available, and, in
all but the versions for IBM OS/360 and IBM CP/CMS on the 360/67, it is an
expensive proprietary product. Second, because it is a compile-and-go processor,
there is no opportunity to form load modules for repetitive classroom use; the
cost of recompiling the source program must be borne at every use.
It is to these shortcomings that the present paper is addressed. A recipie is
provided for translating System
Dynamics models or existing DYNAMO programs into FORTRAN. In following this
recipie, the FORTRAN programmer takes upon himself much of the effort that the
DYNAMO processor does for the DYNAMO programmer.
Nonetheless, the result is a program which is considerably more "transportable,"
and which can reside as a load module for frequent classroom execution.
It will be assumed that the reader is familiar with the elements of System
Dynamics as contained in Principles of Systems. The particular recipie presented
here is cast in IBM FORTRAN IV(G1) but can easily be modified for
other dialects. The recipie treats only a subset of DYNAMO, but a subset wide
enough to accomodate, for example, the WORLD models.
The emphasis is on recipie: a method for formulating System Dynamics models in
FORTRAN, but not a program
nor a compiler nor a processor for so doing. The recipie admits some latitude,
both in the use of particular
ingredients and in the embellishments possible in a well equipped kitchen.
One example of the recipie is presented here: Forrester's World Model. Two other
examples along with the
technical appendices are available from the author. They are a model for "The
Tragedy of the Commons" and a
predator-prey model illustrating one of the concepts in The Silent Spring. These
two have both been used in the undergraduate classroom.
The Recipie
The purpose of the dynamic modelling program is to describe the behavior in time
of generalized systems.
Mathematically, this behavior is the result of integration of coupled
differential equations. It is presumed that rates of change are sufficiently
slow that integration may be accomplished by a simple coarse-grid approximation
to the area under a curve comprised of straight line segments.Rates, auxiliary
variables, and levels may be calculated; up to ten such quantities may be
tabulated in printed form and up to five may be plotted, although the FORTRAN
programmer may easily circumvent these arbitrary limits.
The main program includes seven sections. These are Specifications, Functions,
Inputs, Initialization, Auxiliaries and Rates, Outputs, and Levels. This
seven-part structure corresponds to DYNAMO's ability to order modelling
equations. Within each part, the order of the equations must be carefully
planned by the FORTRAN programmer.
Specifications and Functions.These sections may be thought of as essentially
instructions to the FORTRAN
compiler; the remaining five sections form the logical flow of the modelling
program, as shown in Figure 1.
Input. This section reads control information for the simulation, as well as
values of constants, table-functions,and initial values. Information for the
plotter subroutine is also read at this point. Parameters of the model may be
printed to help clarify and annotate the subsequent output.
Initialization. This section provides for starting the simulation clock, some
housekeeping, and setting initial values of all levels.
Auxiliaries and Rates. In this section the computation of auxiliaries and rates
from existing levels, and from
previously calculated auxiliaries or rates, is carried out.
Output. Results of the simulation can be printed line by line as the simulation
proceeds, but information for
plotting is best saved until an entire page of graphical output has been
accumulated. The arbitrary limits of ten printed and five plotted variables were
chosen for simplicity in constructing a page-wide line of tabular information
and for clarity in reading simultaneous plots. A print-plot subroutine which
forms plots on a line-printer much like those formed by DYNAMO, is described in
the Appendix.Clearly the FORTRAN programmer with more sophisticated graphical
devices will wish to call upon these in writing output.
Levels. The integration is completed, and the clock and levels are updated. The
details of the seven-step "recipie" are given in the appendix.
