Teaching complex systems using EXTEND

Abstract

Simulation tools are important in engineering courses for students. EXTEND is an example of this kind of powerful tools and of general purpose. This work describes the experience at University of Lleida (UdL), located in Spain, about the use of EXTEND in an optional course of simulation to be learnt by engineering students. The aim of the course is to introduce students to the process of modelling and simulation of complex systems. Thus, capabilities of students are better exploited and analyses of complex systems become easier. All of this result in a more friendly and attractive way for students to learn.

Keywords

Simulation tools, EXTEND, learning, Engineering, software matemático-estadístico, docencia de ingenierías, estudio de casos, Cataluña.

Introduction

The use of simulation tools offers an excellent way to introduce engineering students in the modelling, simulation and analysis of complex systems. This type of tools deploys principally a visual, intuitive environment that facilitates the system modelling combined with the computational power for calculations. This helps users to obtain simulated results and to perform later analyses. In addition, a characteristic of these tools is the possibility of programming blocks or modules fitting specific needs of the users, beyond the own ones included in the bookshops of the same application.

This work especially is intended to describe the utility of EXTEND in the study, development and analysis of more or less complex systems for students of Engineering; without neglecting the consolidation of concepts as static - dynamic system or random-determinist as well as brief keys of EXTEND's operation (see [1] and [2] for further details).

History of the Course

The course described here is entitled: "Optimization by means of Simulation" [3] and it is an optional subject for postgraduates from diverse Engineering degrees (Industrial, Computer Engineering and Agronomics) at University of Lleida. The course recalls the usefulness of the classical methodologies of mathematical programming and remarks their limitation in the resolution of real complex problems. Initially the traditional methodologies of optimization with restrictions of equality and with restrictions of inequality applied to concrete problems of engineering are studied. Later on, real problems where the ideal exact solution is impossible are introduced and therefore numerical approximations by means of the real system simulation are obtained. For deploying simulation models there are different software tools, one of them is EXTEND that has different libraries containing blocks with different functionalities, which can be connected visually, and to be used in the construction of the models.

The use of the simulation, and more especially the analysis of the results, serves to review concepts of statistics that the students must have acquired: probability, distributions, descriptive statistics, esteeming, tests or contrasts of hypothesis.

On the other hand, the need of modelling complex systems can lead to the use of models ad-hoc where self programming becomes present. Though programming is possible with EXTEND, only the basic elements are taught in this course. For instance, connections between blocks, creation of new libraries, modification of new blocks from existing ones and basic functionality of main blocks are introduced. In no case there is intended that students have to program blocks by them themselves.

The course was given by the first time four years ago and during this period the content in mathematical programming has been losing weight in favour of the modelling and analysis of system results and that besides stimulate more the learning of the student. The modelling with EXTEND facilitates the structure and visual presentation of the problem, as well as their modular development of constructed form, going from the general thing to the particular thing (development TOP-DOWN). This methodology facilitates the achievement of good habits of modelling since they are related to object orientated programming methodology.

Basic aspects of the course

The teaching of this course has been planned attending to four principles: the use of examples, an increment of the complexity, the design of intuitive models and the discussion of the methodology. The set of examples used during the course are of different types. Some of them consist of the calculation of the average consumption of a vehicle, or the work in progress in a production line by using a kanban system, or the study of hazard games. Nevertheless in general, always the students are invited to take an active part in the classroom and propose their own problems to be discussed.

The learning process is complex and requires clear and simple concepts accompanied of examples with a progressive difficulty. This progression can be observed along the course in which initially the students just analyze the simulated models but at the end of course they must be able of developing the model from the problem formulation.

It’s important to emphasize the methodology used in every developed example. To discuss advantages and disadvantages of alternative approaches, or even to explore other valid solutions. An illustrative example would be the election of a representation in constant time or by means of discreet events. The comprehension of the proposed models and their visualization is the key for their learning. The intuition of the models is obtained by the visual environment of EXTEND's development and a schematic presentation little recharged with the examples.

Simulation with the use of extended

In this section some examples used in class are presented to illustrate the concepts, the skills and the educational methodology.

Throwing coins

This example is simple and polyvalent, very versatile in the aims that can be obtained by it. Initially it will be used the generating block of random numbers. This block can generate random values 0-1 with a proportion 0.5 respectively.

It is possible to realize the count of faces after 100 throwings, after 1000, 10000 or more. A block " Plotter I/O " will allow us to represent graphically the result of the frequencies obtained in every test (to see Fig. 1). The block " Mean&Variance " provides to us the estimation of the percentage of faces obtained in every test and besides, optionally a confidence interval for the sample variance associated with the estimation. Expected values from the sample (i.e. mean and variance) can be compared with the theoretical ones.

This represents the first example of confrontation between simulated and theoretical values, so it serves to put the student on the real problem: the analysis of simulated results. Unfortunately, theoretical results not always are known and from this is derived the importance of the sample variance as a way to measure the error in the estimation process.

Fig. 1. Example of the throwing coins. Model and results of 10 repetitions for 100 throws.

Queue in a bank establishment

The problem of queue turns out to be an example familiar to the student and as simple as that of tossing a coin. We consider a simple case with a bank office consisting of an ATM (automatic teller machine) to illustrate this kind of typical models related with discrete events. In this case clients arriving to the office must be served in a first-in-first-out order. The activity consisting of the transactions and queries to the machine consume time. After a client is served, he exists the office and the ATM is ready to serve another one as the Fig 2 represents.

Fig. 2. Example of a queue in a bank establishment.

Ideally the client wants to find the machine free or idle to be served as soon as possible. If more than one client coincides at the same time, then a queue appears. In this type of systems some variables interesting for being studied are the average size of the queue, the average waiting time, the number of clients served by unit of time, the maximum queue length, etc.

Also, in cases when the queue obeys to a serving process involving many activities, it can be interesting the study of how to organize these activities in order to improve the efficiency of the system. Simple models can be solved analytically but realistic queue models become complex many often and almost impossible to be solved without the assistance of simulation.

Kanban

The introduction in the organization of production lines is not simple. With EXTEND it is possible to illustrate easily the concept and shape of simple and intuitive way a Kanban system. On the other hand, it is interesting the comparison of different organisation systems and the flexibility of EXTEND allows the modeller to modify the design of the model. Then, the construction of a Kanban system or a migration to a CONWIP systems can be done with relative ease as the Fig shows. 3. Hence, comparisons of both systems performances are directly obtained, analysed and dicussed by students.

Fig. 3. Example of Kanban.

Ecosystems: relation predator - prey.

Another used example is the relationship between predators and preys within an ecosystem [4]. These relationships affect the growth of both populations and becomes interesting the finding of some kind of equilibrium representing the sustainability of the ecosystem. Predator and prey can be represented graphically as well as the available feed in their own habitat in connection with the “enemy” population. Interesting solutions are of periodic oscillations for every population (Fig. 4). Although analytical solution is possible, when the model includes more complicated relationships it turns out to be prohibitive to deal with resulting differential equations known as Lotka-Volterra's equations described in the simplest version in the Appendix.

Fig. 4. Example Ecosystems: relation predator - prey.

Discusion

The graduation as engineer is not an easy task. The quantity of concepts and the difficulty of the teacher in transmitting the knowledge with traditional didactic resources is complicated. The use of EXTEND in the classroom facilitates the development of simple examples that students can understand, many times intuitively. Hence, increasing the complexity of the examples and showing the process of modelling and analysis of results qualifies to the student to repeat this process after a short training period with similar instances including much more complexities.

EXTEND also allows to perceive the difference between theoretical and real results. For example, when tossing a fair coin, only punctually the number of faces will equal to that of crossings, though their relative frequency will converge to a limit that we will be call a probability of obtaining face, and that for balanced coins is of 0.5.

Scarcely the students of any engineering are able of retaining all the algorithms and procedures of resolution of optimization problems. In the real life, few occasions they will need them and even less they will be able to apply them. On the other hand, to handle methodological alternatives to solve real problems, like simulation, turns out to be extremely useful as this work reveals [5].

The pending work for the next course is to compile a collection of examples deployed and classified under two criteria: difficulty and thematic field.

Conclusions

EXTEND is a powerful tool simulation, useful in the modelling problem of engineering. It facilitates the introduction to the students in the process of shaped and system simulation. These tools stimulate the learning of the students and facilitate the analysis of complex systems in the classrooms, allowing to practise a more intuitive and attractive teaching way for students.

Appendix

The Lotka-Volterra model is one of the easiest models dealing with the interactions between predator - prey. The model was developed by Lotka (1925) and Volterra (1926).

Where:

P = Preys density.
D = Predator density.
r = Rate of growth of the prey population.
a = Depredation coefficient.
b = Rate of growth of the predator population by eaten prey.
m = Rate of mortality of predators.

References

[1] Krahl, D. 2003. Extend: an interactive simulation tool. In Proceedings of the 2003 Winter Simulation Conference, ed. S. Chick, P. J. Sánchez, D. Ferrin, and D. J. Morrice, 198-196. IEEE, Piscataway, NJ.
[2] http://www.imaginethatinc.com 2005. (Accedido el 28/08/2005)
[3] http://www.udl.es/usuaris/MatFDiE/OptiSim.html 2005. (Accedido el 28/08/2005)
[4] Derrick, W. 1984 Ecuaciones diferenciales con aplicaciones. Fondo Educativo Interamericano, México, 1984, p.p. 297-299.
[5] Plà, L.M. 2005. A stochastic model for planning swine facilities. Accepted in Winter Simulation Conference. Orlando. USA