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Systems Models

Basic Models for System Thinking

Prof. Derek Hitchins

Contents

  • Fundamentals
  • First System Model
  • System Definition and Ideas
  • The First System Principle and Corollary
  • Nature of Systems Models
  • Second System Model
  • Self-similarity, Nesting, Recursion and Hiding
  • Generic Reference Model
    • Generic Reference (Function) Model
    • Generic Reference (Form) Model
    • Generic Reference (Behaviour) Model
  • The GRM in Action

Fundamentals

The concept "System" is one of organization, structure, relationship, order, method

Systems may be:-

  • tangible
  • perceptions
  • transcendentals

One system may exhibit more or less order than another:-

  • "degrees of system"
  • greater entropy - less system


First System Model

This a nesting model, of systems within systems within systems...

  • To understand, identify the System of Interest (SOI).
    • It contains intra-connected sub-systems, which are systems in their own right, existing within their own environment.
  • The SOI is interconnected to other, sibling, systems within their mutual environment, all within a Containing System.
  • The Containing System is similarly connected to its sibling systems (not shown) all existing within their environment. and so on.
  • Some siblings may be interconnected through the Containing System boundary to systems within other Containing Systems.


This simple model provides surprising strength and clarity of perception once applied to real situations, to identify real system relationships. for instance:-

  • in electronics, parts exist within modules, exist within subassemblies, exist within assemblies, exist within units, exist within systems, exist within platforms...and so on ad infinitum
  • in management, people exist within sections, exist within departments, exist within divisions, exist within companies, exist within groups, exist within industries...


These ideas of containment and hierarchy couple with the concept of emergence. The Containing System above contains several interconnected siblings, including the SOI. Because the SOI and its siblings mutually interact, their combined effect is not the same as though they were virtually separate, like snooker balls in a bag.

Instead, the Containing system will exhibit some properties, capabilities and behaviours which emerge from these interactions. As a result, even simple systems, with few siblings, may exhibit quite unexpected behaviour, varying from oscillations to deterministic chaos.

Don't let the simplicity of the model blind you to the potential complexity of the behaviour. That would be to think in static terms. System thinking is dynamics.

System Definition and Ideas

System:-

"An open set of complementary, interacting parts with:-

  • properties,
  • capabilities and
  • behaviours


emerging both from…

  • the parts and from
  • their interactions"


The definition presents ideas of:-

  • Emergence, defining Hierarchy, resulting from...
  • ...Interaction
  • Containment, nesting, Babushka Russian Dolls
  • Completeness, yet...
  • ...Openness
  • Complementation, hence variety, cohesion, synergy and...
  • ...Dynamic stability
  • Entropy, internal energy...hence efficiency, effectiveness, net contribution and quality

Russian Dolls - Russian-style

                                            The First System Principle and Corollary

First Principal of Systems:-

The properties, capabilities and behaviour of a system derive from its parts, from interactions between those parts, and from interactions with other systems.

Corollary to the First Principle

Altering the properties, capabilities or behaviour of any of the parts, or any of their interactions, affects other parts, the whole system, and interacting systems.

Nature of System Models

  • Scale independent
  • Type independent
  • Extensive
  • Synthetic, (c.f. Cartesian)
  • Address:-
    • Emergence
      • non-linear dynamics
      • intra-acting synergies
    • Behaviour
      • stimulus-response
      • fractal / self-similar
  • Deductive/refutable

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Second System Model

The model shows the same general idea as the first model above, but now the emphasis is on the openness of the system to inflows and outflows. As you can see, inflow might comprise energy, resources and / or information. Outflow might comprise residue, waste and / or product according to your viewpoint about any particular system. and the system itself has properties, shown in the box.

As for the first model, the second model is to be viewed dynamically.

  • What happens if the inflow exceeds the outflow?
  • Is the Containing System stable, does it oscillate over time, is it dynamically stable?
  • How is information stored&endash;in the structure?


Self-similarity, Nesting, Recursion and Hiding

Another way to look at nesting systems is shown below. Three open systems are shown interconnected. Reading the interconnection legends, you will see that:-

  • one systems Dissipation is another systems Energy
  • one systems Residues is another's Resources
  • information is not conserved - it can be passed on without losing it.


The interactions create complementary network. If all three systems are now "hidden" within the System container, you can see that the inflows and outflows from the container are also Energy/Dissipation, Resources/Residues and Information.

This is self-similarity up and down the hierarchy of containment.


The combination of systems and interconnections may such that each systems requisite inflows are provided by other systems outflows, and vice versa. This situation creates a Complementary Set of systems. These are common in Nature and appear as ecologies. Economies can operate similarly, both at micro and macro levels.

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Generic Reference Model (GRM)

Systems methods are very powerful, and can address the solving of complex problems in a way unparalleled by reductionsit methods. However, systems methods - which are at the heart of systems thinking, systems, design, systems engineering and the systems methodology - are often misunderstood, since they often rely on representations of systems in the abstract: which can create some confusion amongst hard-nosed, pragmatic engineers, for example! The idea is explained in the Systems Methods, Systems Metaphors, System Abstractions which it may prove advantageous to read before "diving into" the GRM...

The GRM presents an "internal" view of any system. As the map below shows, it is possible to think of any system under three headings:-

  1. Being, the state of existence
  2. Doing, the state of activity
  3. Thinking, the state of sentience

Many system simply exist, without directed activity or sentience. e.g. the solar system. Some systems are able to do things, exhibit purpose and pursue goals, e.g. animals, assembly plants. Yet again, some systems can think, and can adapt their behaviour according to circumstance, e.g. higher animals, companies.

The GRM is developed using several formal approaches, to provide some rigour. As with all good system models, it is type independent and scale independent. It is expanded out in successive levels of decomposition, starting at the top level, the GRM Map

Generic Reference (Function) Model

This model describes the "doing" features of any system that has such features. It comprises three parts:-

  • Mission Management
  • Resource Management
  • Viability Management


Together, these three form the "Management Set," so called, because they describe the management of their respective features.

Mission Management

All that any system can do in terms of pursuing a Mission is to collect information, set or reset objectives using that information (in part) strategize and plan the pursuit of Mission, Execute the plan and, if necessary, cooperate with others in the environment.

Closure of the circle corresponds with closure, i.e. completeness of the set of the set of continual actions.

 

Resource Management

Similarly, all that any system can do in managing resources is: acquire them, store them, distribute them, convert and utilize them, and discard any waste or product.

Closure of the circle corresponds with closure, i.e. completeness of the set of the set of continual actions.

Viability Management

Viability is altogether more complex:-

  • For any system to remain viable, it has to maintain its existence within an environment even as that environment may change.
  • That environment may engender threats to the system, which may also experience internal defects and deficiencies.
  • Through all of this, the internal parts of any system must complement interact with each other so as to provide both a mutually supportive internal environment and to achieve any desired external effects.


From the above, the following generic features have been carefully extracted to identify the basis of system viability.

Note the mutual interdependence of each feature:-

  • Homeostasis provides a stable environment within which internal systems may continue to operate efficiently and effectively
  • Evolution, on the other hand, seeks to adapt to change, and so acts over much longer time spans than homeostasis
  • Survival, usually comprised of Avoidance of Detection, Self-defence and Damage Tolerance, is clearly essential in the short term, but also to enable progressive evolution
  • Maintenance, usually comprised of detection, location, replacement and disposal of defective parts, is also clearly essential for continued viability
  • All of the above provide a basis for synergistic interactions between the parts, but it is also true that synergy between the parts enables Maintenance, Homeostasis and hence all the others too.


Mission Elements Together

The three figures above may be combined as shown, to show their mutual interdependence:-

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Generic Reference (Form) Model

Form is shown as comprised of three parts:-

  • Structure
  • Influence
  • Potential


  • Structure and Potential are straightforward as shown.
  • Influence bases its subdivisions on the concept of system stability, static or dynamic.
    • If a system is stable, the argument goes, then those influences which seek to disperse its parts and those that seek to make them stick together must be in balance.
    • The effect of these influences must vary according to the environment that mediates them - hence the model.


In applying the model to a real-world system, one would have to identify these various influences, of course. Not always easy, but knowing that they must exist is a good start point.

Generic Reference (Behaviour) Model

Behaviour Model proposes how Behaviour might be selected generically:-

  • does not identify which behaviour results from a given stimulus


Of three first-level Models, Behaviour is the most complex and subtle:

  • based on a variety of psychological models
  • proposes way in which both instinctive and sentient entities respond to stimulus
  • appropriate for individuals and groups
  • recognizes essential nature-nurture conflict
  • establishes Belief as central to behaviour

GRM as an Integrated Whole

  • Possible to view Being, Doing and Thinking elements of GRM as independent
  • Useful as a check-list to see if a system description has missing elements, but...
  • ...falls well short of full potential
  • Different parts of Model identify different facets of same system,
    • e.g. Thinking affects the manner of Doing;
    • Doing depends on Being;
    • Being enables Thinking (cogito ergo sum!)



GRM in Action

Instead, the GRM can be used in a powerful methodolgy for understanding emergence and for measuring effectiveness. Consider the following sequence of figures: -

The first figure shows two systems, Blue and Red, interacting in an operating environment. Only in such a dynamic, interactive situation is it possible to sensibly observe, say, Blue's emergent properties, capabilities and behaviours (PCBs). As Blue acts on Red through the environment, Red is affected and changes. This change is a measure of Blue effectiveness. But, Red also acts on Blue, so Blue is changed. Thus, once Red and Blue start to interact, each changes and is changed by, the other. This results in a dynamic, in which the emergent PCBs and effectiveness of both Blue and Red unfold over time. Thus, effectiveness is not some fixed, arbitrary figure, and is not really capable of being specified a priori. Instead it is an emergent property of the interaction of a system of interest (e.g. Blue) when it interacts with other systems in some operating environment.

This is not really news. The top speed of a sports car is only some 35 miles per hour when going through the centre of London, say. It may have potential for 135 mph, but that is not what it can achieve when interacting with other vehicles in a transport environment. News or not, people still insist on trying to specify effectivness as an independent variable, without regard to other systems or the environment. Wrong.

The second repeats the top level model of the GRM

The third figure shows a Blue GRM interacting with a Red GRM in some Green environemnt

The fourth figure in the series shows how an engaged system such as blue may be related to its logistics, procurement and supplier systems, in this case for a defence system such as a ship, a plane or a tank. Red might have a similar support.

In this way, as shown by the figures, it is possible to employ the GRM as a reference model in active situations. Such situations might include co-operation between two or more systems, competition between systems in some market, or conflict between two opposing groups. The model is still generic.

Finally in this set, the following diagram elaborates the previous Blue GRM to show the level of detail to which you can go - and still remain generic

The Function Model has been divided into its three constituents. Resource Management and Viability Management have been set to apply to all three layers, and Mission Management. This, then, could be used as a C3I model - see Command and Control on this web site - where C3I is Command, Control, Communications and Intelligence.

This layered model is only half of the model represented in the previous figures, where two interacting systems were seen to be necessary. A useful way forward, then, is to instatiate and replicate the layered model and connect up the two representations so that they may co-operate, compete, or engage eath other as appropriate. Instantiations of logistics supply can be added and connected up, as shown in the previous figure. One GRM can be held constant while the other is evolved using genetic or hill climbing algorithms, to achieve maximum effectiveness. The evolved GRM can then be held constant while the first is now evolved. And so on. I call this systolic evolution.

The method and approach are universal, as befits a systems generic reference method.

Well, there we are - that's a beginning. System models are many and various. Bak and Chen produced a useful model of sand trickling on to a pile, reaching a particular cone size, and thereafter maintaining that size as more sand was poured on, resulting in avalanches. They called this phenomenon Self-Organized Criticality. They were investigating tectonic plate movement, but the same phenomenon appears to apply to:-

  • stock exchange prices
  • distance between cars on the motorway or freeway
  • deaths in war
  • scarce skills in a factory
  • etc.


So, systems models are many and various - and they can address so many complex things, in ways that conventional approaches simply cannot touch.

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Derek Hitchins

http://www.hitchins.net


© D K Hitchins 2016