Page 181 - DCAP601_SIMULATION_AND_MODELING

Unit 10: Simulation of a PERT Network (II)

harder is knowing what the accuracy (compared to measurement resolution and precision) of Notes
the values is. Often it is expressed as “error bars”, a minimum and maximum deviation from the
value seen within which the true value (is expected to) lie. Because digital computer mathematics
is not perfect, rounding and truncation errors will multiply this error up, and it is therefore
useful to perform an “error analysis” to check that values output by the simulation are still
usefully accurate.
Even small errors in the original data can accumulate into considerable error later in the simulation.
While all computer analysis is subject to the “GIGO” (garbage in, garbage out) restriction, this
is especially true of digital simulation. Indeed, it was the observation of this inherent, cumulative
error, for digital systems that is the origin of chaos theory.

Types

Computer models can be classified according to several independent pairs of attributes, including:
1. Stochastic or deterministic (and as a special case of deterministic, chaotic) - see External
links below for examples of stochastic vs. deterministic simulations

2. Steady-state or dynamic
3. Continuous or discrete (and as an important special case of discrete, discrete event or DE
models)

4. Local or distributed.
Equations define the relationships between elements of the modeled system and attempt to find
a state in which the system is in equilibrium. Such models are often used in simulating physical
systems, as a simpler modeling case before dynamic simulation is attempted.
1. Dynamic simulations model changes in a system in response to (usually changing) input
signals.
2. Stochastic models use random number generators to model chance or random events;
3. A discrete event simulation (DES) manages events in time. Most computer, logic-test and
fault-tree simulations are of this type. In this type of simulation, the simulator maintains
a queue of events sorted by the simulated time they should occur. The simulator reads the
queue and triggers new events as each event is processed. It is not important to execute the
simulation in real time. It’s often more important to be able to access the data produced by
the simulation, to discover logic defects in the design, or the sequence of events.
4. A continuous dynamic simulation performs numerical solution of differential-algebraic
equations or differential equations (either partial or ordinary). Periodically, the simulation
program solves all the equations, and uses the numbers to change the state and output of
the simulation. Applications include flight simulators, construction and management
simulation games, chemical process modeling, and simulations of electrical circuits.
Originally, these kinds of simulations were actually implemented on analog computers,
where the differential equations could be represented directly by various electrical
components such as op-amps. By the late 1980s, however, most “analog” simulations were
run on conventional digital computers that emulate the behavior of an analog computer.
5. A special type of discrete simulation which does not rely on a model with an underlying
equation, but can nonetheless be represented formally, is agent-based simulation. In agent-
based simulation, the individual entities (such as molecules, cells, trees or consumers) in
the model are represented directly (rather than by their density or concentration) and
possess an internal state and set of behaviors or rules which determine how the agent’s
state is updated from one time-step to the next.

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