Lecture
At the third stage of modelling — the stage of obtaining and interpreting
the modelling results — the computer is used to carry out working calculations using the program that has been written and debugged. The results of these calculations make it possible to analyse and formulate conclusions about the characteristics of the operating process of the modelled system S.
Features of obtaining the modelling results. When implementing
the modelling algorithms on a computer, information is generated about the states
of the operating process of the systems under study
zt Z . This information is the source material for determining approximate estimates of the required
characteristics obtained as a result of the computer experiment, i.e. the evaluation criteria. By an evaluation criterion we shall mean any quantitative indicator by which the results of modelling the system can be judged. The evaluation criteria may be indicators obtained on the basis of processes
that actually occur in the system, or obtained on the basis of specially
constructed functions of these processes.
In the course of the computer experiment, the behaviour of the model M under study of the operating process of system S is examined over a given time interval
0, T
. Therefore, in the general case, the evaluation criterion is a vector random
function defined on this same interval
qt q t q t q t n
, ,...,
1 2
.
Simpler evaluation criteria are often used, for example, the probability of a particular state of the system at a given moment in time
t*0, T,
the absence of failures and faults in the system over the interval
0, T
and so on. When interpreting the modelling results, various statistical characteristics of the distribution law of the evaluation criterion are calculated.
Let us consider the general scheme for recording and processing the results of modelling a system. We shall consider a hypothetical model M intended for studying the behaviour of system S over a time interval
0, T
. In the general case, the criterion for interpreting the modelling results is a non-stationary random n-dimensional process
qt, 0 t T . For definiteness, we assume that the state of the modelled system S is checked every
t
time units, i.e. the «principle
t
» is used. In this case, the values are calculated
qjt, j 0, k , of the criterion
qt
. Thus, the properties of the random
process
qt
are judged from the properties of the random sequence
qjt, j 0, k ,
or, in other words, from the properties of an m-dimensional vector of the form
qt q0, qt,..., qk 1t, qT, m nk 1, T kt .
The operating process of system S over the interval
0, T
is modelled
N-fold, obtaining independent realisations
qi
, j 1, N , of the vector
q . Operation
of the model over the interval
0, T
is called a model run.
In the general case, the algorithms for recording and statistically processing the modelling data contain three loops.
The inner loop makes it possible to obtain the sequence
q t qj t j
,
j 0, k
at the time instants
t 0, t, 2t, ..., kt T .
The intermediate loop, in which N-fold repetition of
the model run is organised, makes it possible, after the corresponding statistical processing of the results, to judge the estimates of the characteristics of the modelled variant of the
system. The completion of the modelling of a variant of system S may be determined not
only by a specified number of realisations, but also by a specified accuracy of the modelling results.
The outer loop encompasses both preceding loops and additionally
includes blocks that control the sequence of modelling the variants
system S. Here a search is organised for the optimal structures, algorithms and parameters of system S.
The scheme considered makes it possible to carry out statistical processing of the modelling results in the most general case, with a non-stationary criterion
qt. In particular cases, one can limit oneself to simpler schemes. If
the properties of the modelled system S are determined by the value of the criterion
qt
at a certain given moment in time, for example, at the end of the model's operating period
t kt T , then the processing reduces to estimating the distribution of the n-dimensional vector
qt
from independent realisations
q t i
, i 1,N , obtained as a result of N model runs.
If, in the modelled system S, after a certain time has elapsed since
the start of operation
t k t
0 0
a stationary regime is established, then it can be judged from a single, sufficiently long realisation
q t 1
of the criterion
qt
, stationary and ergodic on the interval
t , T 0
.
Another feature of the statistical methods used in practice for
processing the modelling results is related to the study of the process
of the operation of systems using models of block construction. In this
case, it is often necessary to apply separate modelling of individual blocks of the model, when the simulation of input actions for one block is carried out
on the basis of criteria estimates obtained previously at another block of the model. In separate modelling, there may be either a direct recording of criterion realisations in the queue (buffer), or their approximation, obtained on the basis of statistical processing of the modelling results, with the subsequent use of random number generators to simulate these
actions.
Sub-stages of the third stage of modelling.
3.1. Planning the computer experiment with the model of the system.
Before carrying out the working calculations on the computer, a plan must be drawn up
for conducting the experiment, indicating the combinations of variables and parameters,
for which the modelling of system S is to be carried out. The planning of
the computer experiment is intended to ultimately provide the maximum amount of the required
information about the object of modelling with minimal expenditure of computer resources. In this connection, a distinction is made between strategic and tactical planning of the computer experiment. In strategic planning of the experiment, the task is to construct an optimal experiment plan for achieving the goal set for the modelling. Tactical planning of the computer experiment pursues the specific goals of the optimal implementation of each particular experiment from the set of experiments required and specified
during strategic planning (for example, solving the problem of choosing the optimal stopping rules in the statistical modelling of system S on
a computer).
3.2. Determining the requirements for computing resources. It is necessary to formulate requirements regarding the time for using computing resources, i.e. to draw up a schedule of work on one or several computers, and
also to indicate the peripheral devices of the computer that will be required for the modelling. It is also reasonable, based on the resources required, to assess
the possibility of using a personal
computer or a local computer network for implementing the specific model.
3.3. Carrying out the working calculations. After the model's program and the plan for conducting the computer experiment with the model of system S have been drawn up, one can
proceed to the working calculations on the computer, which usually include: a)
preparing sets of source data for input into the computer; b) checking the source
data prepared for input; c) carrying out the calculations on the computer; d) obtaining the output data, i.e. the modelling results.
It is reasonable to carry out the computer modelling in two
stages: check calculations, followed by working calculations. Moreover, the check calculations
are carried out to verify the computer model and to determine the sensitivity
of the results to changes in the source data.
3.4. Analysis of the system modelling results. In order to effectively
analyse the output data obtained as a result of the calculations on
the computer, it is necessary to know what to do with the results of the working calculations and how to
interpret them. These tasks can be solved on the basis of the preliminary analysis carried out at the first two stages of modelling system S. The planning of
the computer experiment with the model makes it possible to derive the required amount of output data and to determine the method of analysing it. In doing so, it is necessary
that only those results needed for further analysis be printed out. It is also necessary to make fuller use of the capabilities of the computer from
the point of view of processing the modelling results and presenting these results in the most illustrative form. Calculating the statistical characteristics before the results are output from the computer increases the efficiency of using
the machine and reduces to a minimum the processing of the output information after it has been output from the computer.
3.5. Presentation of the modelling results. As already noted,
at the third stage of modelling attention must be paid to the form of presentation of the final modelling results in the form of tables, graphs,
diagrams, charts and so on. In each specific case, it is advisable to choose
the most suitable form, since this significantly affects the efficiency of their subsequent use by the customer. In most cases
tables are considered the simplest form, although graphs more clearly
illustrate the results of modelling system S. In interactive (dialogue) modes
of modelling, the most rational means for the real-time display of the modelling results are multimedia technology tools.
3.6. Interpretation of the modelling results. Having obtained and analysed the modelling results, they must be interpreted in relation to the object being modelled, i.e. system S. The main content of this
sub-stage is the transition from the information obtained as a result of the computer experiment with the model to information relating to the object of modelling,
on the basis of which conclusions will be drawn regarding the characteristics of
the operating process of the system S under study.
3.7. Summarising the modelling results and issuing recommendations.
The performance of this sub-stage is closely related to the preceding second stage. In
summarising the modelling results, the main features obtained in accordance with the experiment plan for the model must be noted, the hypotheses and assumptions must be checked, and conclusions must be drawn on the basis of these results. All of this makes it possible to formulate recommendations for
the practical use of the modelling results, for example, at the stage of
designing system S.
3.8. Preparing the technical documentation for the third stage. This
documentation must include: a) the plan for conducting the computer experiment; b) the sets of source data for the modelling; c) the results of modelling the system; d) the analysis and evaluation of the modelling results; e) conclusions
based on the results obtained from the modelling; and an indication of ways to further improve the computer model and the possible areas of its application.
The complete set of documentation on modelling a specific system S on a computer must contain technical documentation for each of
the three stages considered.
Thus, the process of modelling system S comes down to carrying out the listed stages of modelling. At the stage of constructing the conceptual model, the object being modelled is studied, and
the necessary approximations are determined and a generalised scheme of the model is constructed, which
is converted into a computer model at the second stage of modelling by sequentially constructing the logical scheme of the model and the program scheme. At
the final stage of modelling, working calculations are carried out on the computer, and
the results of modelling system S are obtained and interpreted.
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