Simulation involves designing a model of a system and carrying
out experiments on it as it progresses through time. Models enable
you to see how a real-world activity will perform under different
conditions and test various hypotheses at a fraction of the cost
of performing the actual activity.
One of the principal benefits of a model is that you can begin
with a simple approximation of a process and gradually refine
the model as your understanding of the process improves. This “step-
wise refinement” enables you to achieve good approximations
of very complex problems surprisingly quickly. As you add refinements,
the model more closely imitates the real-life process.
All professions use models of one form or another. But the word
"model" does not always have the same meaning to business
professionals, managers, scientists, and engineers.
Systems
The real world can be viewed as being composed of systems. A
system is a set of related components or entities that interact
with each other based on the rules or operating policies of the
system:
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Entities are the internal components of the system. Entities
are involved in processes—activities in which they
interact with each other. |
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Operating policies—the types of controls and availability
of resources—are the external inputs to the system.
They govern how the system operates and thus how the entities
interact. |
Over time, the activities and interactions of entities cause
changes to the state of the system; this is called system behavior
or dynamics. Systems can be mathematically straightforward, such
as a flower growing in the soil and turning towards the sun to
maximize photosynthesis. Or they can be more complex, such as
supply chain operations composed of planning, selling, distribution,
production, and sourcing subsystems.
Models
A model is an abstracted and simplified representation of a
system at one point in time. Models are an abstraction because
they attempt to capture the realism of the system. They are a
simplification because, for efficiency, reliability, and ease
of analysis, a model should capture only the most important aspects
of the real system. Most models can be classified into four basic
types:
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A scaled representation of a physical object, such as a
1:18 diecast model of a Ferrari, a clay model of a proposed
packaging bottle, or a scale model of the solar system. |
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A graphical or symbolic visualization, such as a flow chart
of office procedures, the board game Monopoly (which represents
the hotels and facilities of Atlantic City), or an architect’s
plans for a building. |
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An analytical or mathematical formula that yields a static,
quantitative solution. For instance, an analytic model might
consist of several independent sample observations that have
been transformed according to the rules of the model. Common
examples of analytic models are spreadsheet models or linear
programming models. |
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A mathematical description that incorporates data and assumptions
to logically describe the behavior of a system. This type
of model is typically dynamic—it has a time component
and shows how the system evolves over time. ExtendSim products
are tools for building mathematically-based, dynamic models
of systems. |
Dynamic modeling is the foundation for computer modeling. Thus,
the word “model” will be used to mean a description
of the dynamic behavior of a system or process.
ExtendSim models typically have a time component and can show
cause and effect and the flow of entities throughout a system
(you can also create ExtendSim animations that show spatial relationships.)
Simulation
The Merriam-Webster OnLine Dictionary defines simulation as “the
imitative representation of the functioning of one system or
process by the functioning of another”. This means that
to determine how an actual system functions, you would build
a model of the system and see how the model functions.
Simulations run in simulation time, an abstraction of real time.
As the simulation clock advances, the model determines if there
have been changes, recalculates its values, and outputs the results.
If the model is valid, the outputs of the simulation will be
reflective of the performance or behavior of the real system.
Simulation with ExtendSim means that instead of interacting
with a real system you create a logical model that corresponds
to the real system in certain aspects. You simulate the operations
or dynamics of the system, then analyze one or more areas of
interest. You do this in order to reduce risk and uncertainty
so that you can make informed, timely decisions.
The formalism you use to specify a system is termed a modeling
methodology. The three main modeling methodologies are:
In addition to these main modeling methodologies, other modeling
approaches are useful and usually based on one of the three main
methods:
As you might expect, you can use different methods to model
different aspects of real-world systems. For example, at a chemical
plant you could model the chemical reactions as a continuous
process, the control logic of the chemical process using discrete
event modeling, and the tanks, valves, and flow of the production
process with discrete rate.
It is good to note, however, that there is no such thing as
the model
of a system: a system can be modeled in any number of different
ways, depending on what it is you want to accomplish. In general,
how you model the system depends on the purpose of the model:
what type, level, and fidelity of information you want to gather
and the amount of detail, or level of abstraction or granularity,
of the model. Once that has been determined, you can intelligently
choose which type of
model to build.
Comparison of main modeling methodologies
The three main modeling methodologies are continuous, discrete
event, and discrete rate. Continuous modeling (sometimes known
as process modeling) is used to describe a flow of values. Discrete
event models track unique entities. Discrete rate models share
some aspects of both continuous and discrete event modeling.
In all three types of simulations, what is of concern is the
granularity of what is being modeled and what causes the state
of the model to change.
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Continuous |
The time step is fixed at the beginning of the simulation,
time advances in equal increments, and values change based
directly on changes in time. In this type of model, values
reflect the state of the modeled system at any particular
time, and simulated time advances evenly from one time step
to the next. For example, an airplane flying on autopilot
represents a continuous system since its state (such as position
or velocity) changes continuously with respect to time. Continuous
simulations are analogous to a constant stream of fluid passing
through a pipe. The volume may increase or decrease at each
time step, but the flow is continuous. |
|
Discrete
event |
The system changes state as events occur and only when
those events occur; the mere passing of time has no direct
effect on the model. Unlike a continuous model, simulated
time advances from one event to the next and it is unlikely
that the time between events will be equal. A factory that
assembles parts is a good example of a discrete event system.
The individual entities (parts) are assembled based on events
(receipt or anticipation of orders). Using the pipe analogy
for discrete event simulations, the pipe could be empty or
have any number of separate buckets of water traveling through
it. Rather than a continuous flow, buckets of water would
come out of the pipe at random intervals. |
|
Discrete
rate |
Discrete rate simulations are a hybrid type, combining
aspects of continuous and discrete event modeling. Like continuous
models they simulate the flow of stuff rather than items;
like discrete event models they recalculate rates and values
whenever events occur. Using the pipe analogy for a discrete
rate simulation, there is a constant stream of fluid passing
through the pipe. But the rates of flow and the routing can
change when an event occurs. |
These 3 main modeling types are compared
and contrasted in the tables below.
In some branches of engineering, the
term discrete is used to describe a system with periodic or constant
time steps. Discrete, when it refers to time steps, indicates
a continuous model; it does not have the same meaning as discrete
event or discrete rate. Continuous models in ExtendSim are stepped
using constant time intervals; discrete event and discrete rate
models are not.
Other modeling approaches
Although there are several other approaches to modeling, they
usually fit within one of the three major categories. For example,
System Dynamics and Bond graphs are subsets of continuous modeling,
and queuing theory models are
subsets of discrete event modeling.
Because of their specialized use, three specific modeling approaches
(Monte Carlo, State/Action, and Agent Based) are described below.
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Monte Carlo |
Widely used to solve certain problems in statistics,
Monte Carlo simulations provide a range of results rather
than a single value. This approach can be applied to any
ExtendSim model and used wherever uncertainty is a factor.
Monte Carlo modeling uses random numbers to vary input
parameters for a series of calculations. These calculations
are performed many times and the results from each individual
calculation are recorded as an observation. The individual
observations are statistically summarized, giving an indication
of the likely result and the range of possible results.
This not only tells what could happen in a given situation,
but how likely it is that it will happen.
You build a Monte Carlo simulation in ExtendSim by incorporating
random elements in a model and obtaining multiple observations.
There are two ways to do this:
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The classical Monte Carlo method is to take a single
mathematical equation or set of equations, then cause
the equation to be calculated many times. In this type
of simulation, time is not a factor. The entire model
is run to completion and evaluated at each step; each
subsequent step performs a new calculation. |
|
An alternative Monte Carlo approach, typically applied
in a discrete event model, is to either divide a single
simulation run into multiple sections (batch means)
or run the simulation many times (multirun analysis).
Monte Carlo is incorporated by adding randomness to
the model, running it many times, and analyzing the
results. This method can be applied to any continuous,
discrete event, or discrete rate model. |
|
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Agent-based |
With agent-based modeling you usually do not know model
dynamics in advance; instead, you obtain that information
from the interaction of the agents in the model.
Agent-based models share the following characteristics:
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The identification of individual entities within
the model. |
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A set of rules that govern individual behavior. |
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The premise that local entities affect each other’s
behavior.
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Agent-based modeling is concerned with individual entities
(called “agents”) that interact with other
agents within their specified locality. All the agents
have a set of rules to follow but they also have a degree
of autonomy such that model dynamics cannot be predefined.
This is because agents can have intelligence, memory, social
interaction, contextual and spatial awareness, and the
ability to learn.
|
|
State/Action |
With state/action modeling a system is modeled as a
collection of discrete states. Sometimes known as a state
chart, a state/action model represents a system that responds
to an event by transitioning to another state. The model
is composed of a series of states where each state depends
on a previous state. A state has an associated action and
an event that will cause that state to change to another.
The transition from one state to the next is not sequential;
each state can lead to any other state.
There are rules that govern the communication and transition
between the states:
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All states accept events. |
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One or more states may create an event as a result
of a transition by another state or group of states. |
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A group of states can be set to transition conditionally,
for instance to only change if another state or group
of states achieve a specific stage. These are known
as guard conditions. |
State/action models are independent of any of the three
modeling methodologies (continuous, discrete event, or
discrete rate.) They are useful for specification and
verification in many areas, from computer programs to
business processes.
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Comparison Table
Modeling Method |
|
|
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| ExtendSim library |
Value library
Electronics library |
Item library |
Rate library |
| What is modeled |
Processes |
Individual items |
Flows of stuff |
| Examples |
Processes: chemical, biological, economic,
electronic, geological. |
Things: traffic, equipment, work product,
people.
Information: data, messages, and network protocols at the
packet level. |
Rate-based flows of stuff:
homogeneous products (powders, fluids, oil, and gas), high-speed
or high-volume production and packaging, data feeds and streams,
mining. |
Table of continuous, discrete event, and discrete
rate differences
Use this table as a guide to help determine which style to use
when modeling a system.
Factor |
Continuous |
Discrete event |
Discrete rate |
What is modeled |
Values that flow through the model. |
Distinct entities ("items" or "things"). |
Bulk flows of homogeneous stuff. Or flows
of otherwise distinct entities where sorting or separating
is not necessary. |
What causes a change
in state |
A time change |
An event |
An event |
Time steps |
Interval between time steps is constant.
Model recalculations are sequential and time dependent. |
Interval between events is dependent on
when events occur. Model only recalculates when events
occur. |
Interval between events is dependent on when
events occur. Model only recalculates when events occur. |
Characteristics of what is modeled |
Track characteristics in a database or assume
the flow is homogeneous. |
Using attributes, items are assigned unique
characteristics and can then be tracked throughout the model. |
Track characteristics in a database or assume
the flow is homogeneous. |
Ordering |
FIFO |
Items can move in FIFO, LIFO, Priority,
time-delayed, or customized order. |
FIFO |
Routing |
Values need to be explicitly routed by
being turned off at one branch and turned on at the other
(values can go to multiple places at the same time). |
By default, items are automatically routed
to the first available branch (items can only be in one
place at a time). |
Flow is routed based on constraint rates and
rules that are defined in the model (flow can be divided
into multiple branches). |
Statistical detail |
General statistics about the system: amount,
efficiency, etc. |
In addition to general statistics, each
item can be individually tracked: count, utilization, cycle
time. |
In addition to general statistics, effective
rates, cumulative amount. |
Typical uses |
Scientific (biology, chemistry, physics),
engineering (electronics, control systems), finance and
economics, System Dynamics. |
Manufacturing, service industries, business
operations, networks, systems engineering. |
Manufacturing of powders, fluids, and high
speed, high volume processes. Chemical processes, ATM transactions.
Supply chains. |
Recommended package |
ExtendSim CP |
ExtendSim OR, ExtendSim
AT, or ExtendSim Suite |
ExtendSim AT or ExtendSim
Suite |
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