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With these notes, all the chapters that were named during the lesson series are walked by. This course is taught in the 2nd year in the second semester.
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Aantekeningen Analyse moduleSPS
Lesson 1 – Chapter 1 + 2
Simulation = an imitation of a system
Primary simulation approaches:
1. Monte Carlo Simulation
- Aim: to model risk in an environment where the outcome is subject tot chance
- Random sampling, not always dynamic
- Mostly used in financial applications for portfolio management
Figuur 1 Input: sources of chance, then Simulation, Outcome: distribution of risk
2. Discrete-event simulation (=DES)
- World represented as queues and activities
3. System dynamics (continuous simulation)
- World represented by Stocks (f.i. population) and Flows (f.i. birth rate)
- Need to model time continuously Population
- Constant (small) time step (Δt) to
approximate continuous time
- Typical used in business strategy/policy and Birth rate Death rate
Fertility Average lifetime
more general continuous simulation in science
and engineering
Nine steps approach
1. Define the problem
2. Set the goals
3. Describe the system
4. Collect data and information
5. Built a model
6. Verify and validate
7. Experiment
8. Analyze the results
9. Documentation and presentation
Alternatives to simulation
1
, Why simulation:
DES = time is modelled in discrete
steps of variable length
The simulation updates whenever
there is a change of state in the system.
The system is modelled as series of events
DES is used for modelling queuing systems
Why use DES:
o Systems are subject to variability, are interconnected and complex
1. Variability
- Predictable variability e.g. shift changeovers, preventative maintenance
- Unpredictable variability e.g. customer arrivals, breakdown
2. Interconnectedness
- Variability does not occur in isolation but is connected to other sources of
variability.
3. Complexity
- Combinatorial complexity = the number of
combinations of system components that are possible.
- Dynamic complexity = related to the interaction of
components in a system over time.
Characteristic of a system:
- Status: set of variables to describe a system at a certain moment
o Discrete event = change of status
- The timing of events is dependent on uncertainty
o Uncertainty can be generated by random numbers
- Using DES we can build dynamic models for experimentation purposes.
Three-phase method:
- In this method events are classified into two types:
o B (bound or booked) events
These are state changes that are scheduled to occur at a point in time.
In general B-events relate to arrivals or the completion of an activity
o C (conditional) events
These are state changes that are dependent on the conditions in the
model. In general C-events relate to the start of some activity
2
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