Week 6 Flashcards
what is a system?
A system is a collection of entities that act and interact
toward the accomplishment of some logical end.
* e.g., banks, climate
what is the state of a system?
The state of a system is the collection of variables necessary to describe the status of the system at any
given time
* State variables in a bank: number of busy tellers, number of customers in the bank, time of arrival of each customer
why do we study systems?
- To gain insight into the relationships among various components
- To predict performance under some new conditions being considered
- Experiment with the actual system vs. a model of the system
- Physical, mathematical models
- Analytical solutions
what is the discrete model type of system?
State variables change instantaneously at separated points in time (e.g., no. of customers waiting in a line in a bank)
what is the continuous model type of system?
State variables change continuously with respect to time (e.g., global CO2 levels, position and velocity of an airplane)
what are deterministic vs stochastic system?
Unlike deterministic models that produce the same exact results for a particular set of inputs, stochastic models are the opposite; the model presents data and predicts outcomes that account for certain levels of unpredictability or randomness.
what is a simulation?
-Imitates the way a real-life system changes overtime.
- Consider effects of changes without actually changing the system.
- Best when changing the system is too disruptive, costly or dangerous, or would take a ridiculous length of time.
- Allows the use of stochastic input
- its used in decision-making situations where it may not be possible to search for an optimum solution
what are the business situations where simulations are used?
- new product development: an organisation deciding whether to develop a new product may simulate the probability that the new product of service will be profitable
- reservation systems: a simulation model allows airlines to try out the different overbooking strategies to assess the likely consequences
- inventory systems: simulations allows the decision maker to assess the effects of changing elements of the existing inventory system on costs and service levels
- queuing systems: simulation modelling allows features such as arrival frequency, service times, and queue capacity, queueing theory enables the careful analysis and optimization of waiting lines
how do you build a discrete event simulation model?
- Describe system (e.g., a queuing model)
- Number of servers
- Attributes of entities (distribution of inter-arrival times, distribution of service times, etc.) - Define possible events (e.g., arrivals and departures as in the queueing model)
- Define performance indicators
- Average number of customers in queue, average time customer spends in system, fraction of time a server is busy - Generate random entities for a given period of time and collect sample data
what is monte carlo simulation?
the process of generating random values for uncertain inputs in a model, computing the output variables of interest, and repeating this process for many trials to understand the distribution of the output results
how do we perform simulations for basic and complex systems?
- For basic models, use spreadsheets
= We will perform simulations using Excel - For complex systems, off-the-shelf software
= Simul8, OptQuest, Risk Solver, Coding (C, C++, Java)
how do you do data modelling and distribution fitting?
- Identify the underlying probability distribution as opposed to collecting sample data
- Begin by using a histogram to look for distinctive shapes
- Summary statistics (mean, median, standard deviation) provide useful information
what is the outline of a simulation study?
Outline of a simulation study
1. Formulate the problem
Define the problem, objectives, measures of performance
2. Collect data and form the simulation model raw data to be fit into probability distributions
3. Select software and implement
4. Validate the simulation model
against collected data from the real system
5. Plan simulation experiments
number of runs, length of each run, warm-up period
6. Conduct experiments and analyse results
derive statistical estimates, point estimates, confidence
intervals
what are the capabilities of simulation study?
Capabilities
* Time compression and expansion
* Understand “why”
* Explore possibilities “what if?”
* Diagnose problems and identify constraints
* Fewer assumptions
* Handles randomness and uncertainty
* Dynamic behaviour
* Flexible, easy to modify
* Credible and results are easier to explain (visual)
what are the limitations of simulation study?
Limitations
* “Run” rather than “solved”
* Cannot identify optimal solutions on their own
* Requires specialised training and machinery
* Costly (machinery and time).
