Lecture Notes for Simulation

Outline

Overall, a simulation has four phases:
1. Understand the problem to extract a system.
2. Abstract the system as a model.
3. Run the experiments on the model.
4. Analyze the experiment results.
Each phase has sub-phases.
- Among them will be validation and verification.
Simulation development is roughly linear.
- There may be feedback loops between phases.
- Feedback may happen when validation or verification fail.

Start with a real system.
End with a model of the system.
The model is an abstraction of the real system.
The problem directs the abstraction.
- Important system parts appear in the model.
- Irrelevant system parts are left out of the model.
- Good modelers know the difference between importance and irrelevance.
  - Understanding the problem helps.

There are three broad types of models:
1. Physical models (wind tunnels).
2. Mathematical models (Markov chains).
3. Programming models (ns programs).
The model type determines the appropriate simulation technique.
- Or the simulation technique can determine the model type.
  - But, if you have a hammer...

An entity receives an event and performs an activity in response.
- One activity is to ignore the event.
An event's activity may
- Change the entity's state by altering attributes.
- Send events to other entities
If this isn't an accurate or helpful representation of a system's dynamics, then maybe discrete-event simulation isn't appropriate.
- Biological systems are complex and highly parallel.

A model too is a set of entities, activities, events and attributes.
- These are based on the associated system.
- Verification is concerned with the relation between a system and its model.

Model dynamics are similar to system dynamics.
- Entities react to events.
But, the modeler is responsible for everything.
The two main components of model dynamics are:
1. The world view (What initiates state change?)
2. Time management.

Which comes first: entities, events, or activities?
- That is, which of entities, events, or activities drives the simulation?
A model's world view answers this question.
There are three main world views:
1. Event oriented
2. Activity oriented, called activity scheduling
3. Entity oriented, called process oriented
We will be interested mainly in the event-oriented world view.

Events are the driver; change occurs because of events.
The modeler identifiers the significant events and their effects on the model.
- The activities performed in response to the event.
- The scheduling required by the event.
The simulation manages events.

Activities are the main cause of change in the simulation.
Activities are treated as functions of time.
- Entities still exist, but events are less useful.
The activity-scheduling world view is appropriate when there are too many entities or events to keep track of.
- Continuous-change simulations such as fluid flow, for example.

Entities are the main cause of change in the simulation.
- Also called the transaction-oriented world view.
Entities respond to explicit time events, as well as other events.
The process-oriented world view is useful for autonomous systems.
- Also workflow and business-process models.

Simulated time is the time period represented by a simulation.
- Simulated time's duration is T_end - T_start.
Simulation run-time is the amount of time needed to run the simulation.
The relation between simulated time and simulation run-time is not tight.
- Longer simulated time means longer run-times.
  - Practically, the relation is linear or small polynomial.
- Units need not be related at all.
  - Nanosecond durations can take hours of run-time.
  - Centuries-long durations can take days of run-time.

Simulations are as functions of time.
- Dynamic simulations are, anyway.
Dynamic simulation models should include some notion of time passing.
Time management implements simulated time.
There are two common approaches to time management:
1. Periodic scan.
2. Event scan.

Periodic-scan time management regularly advances simulated time by a fixed increment.
- Also known as fixed-time increment, Interval-oriented, time-sliced, or unit-advance scan).
The fixed interval is the time unit.
- Times smaller than the time unit don't exist.
- The choice of the time unit is up to the modeler.
Before (or after) advancing the clock, the simulation handles the events that occurred during the time unit.
- These events cannot be distinguished within the simulation.
- Activities completely within a time unit are lost.
  - State changes are observable between intervals, not within them.

Event-scan time management advances simulated time relative to pending events.
- Also known as event advance or variable-time increment scan.
The clock advances to the pending event nearest in the future.
- The advance intervals are not fixed, but are determined by pending events.
- The advance intervals are irregular, based on inter-event gaps.

Fixed interval uses simple bookkeeping (interval buckets).
Event scan needs an ordered queue.
Fixed intervals can waste time on empty intervals.
Event scan is efficient; every tick does work.
The correct interval size is important (precision vs. run-time).
Event scan is self-regulating.
Fixed intervals can be imprecise and inaccurate.
Event scan captures every event with full detail.
Fixed interval can handle large numbers of events.
Event scan can get bogged down with large event populations.

A model is an abstraction of a system.
- The problem determines the abstraction.
A model comprises events, entities, attributes, and actions.
A model's dynamics are determined by its world view and how it manages time.

This page last modified on 10 February 2005.