A full set of operations research knowledge points
table of Contents
Chapter 11 Basic Concepts of Simulation
1. The concept of simulation
- Simulation is also called simulation. Its basic idea is to construct an experimental model, which is very similar to the main performance of the system we are studying.
- Simulation is a quantitative process. He first designs a model for the process and then organizes a series of trial and error to predict what will happen throughout the process.
- Analytical solution: If the relationship that constitutes the model is quite simple, it is possible to use various mathematical methods to obtain accurate data on the problem we are interested in
- The Monte Carlo method is a method of applying random simulation experiments. It needs to conduct random observation and sampling on the researched system, and obtain the parameter values of the system through observation and statistics of the sample.
- The Monte Carlo method is a simulation technique. It uses a series of random numbers to create a distribution function. The method proposes a cumulative distribution as a method to generate "occurrence" events and "service" event distributions. Monte Carlo method often uses a table format. And graphical representation to analyze and solve practical application problems.
2. Reasons for using simulation
- Since it is difficult to observe the actual environment, simulation may be the only method available
- It is impossible to find a numerical solution
- Actually observing a system may be too expensive
- It is impossible to have enough time to operate the system extensively
- The actual application and observation of a system can be too destructive
3. System simulation process
The system simulation process is the process of establishing a model and verifying and correcting the model through magical operation, so that the model is constantly improving.
There are the following steps:
(1) Determine the problem to be simulated and the system
(2) Model the model to be used Formula
(3) Test model: compare its situation with the surrounding situation of the real problem
(4) Identify and collect the required data to test the model
(5) Execute the model
(6) Analyze the model results
(7) Re-execute the model Item model has been tested with new answers
(8) to make the simulation effective
Fourth, the shortcomings of simulation
- Simulation is inaccurate
- A good simulation model can be very expensive
- Not all methods can be simulated, but the answer itself cannot be derived
- Simulation can produce a method of estimating the answer, but not the answer itself.
Probability distribution and its application in simulation (simple application)
Model Carlo Method is a simulation technique that uses a series of random numbers to create a distribution function
Five, probability distribution
We divide the probability distribution into two types:
discrete and continuous. Discrete probability distribution allows variables to take only a limited number of values.
Continuous probability distribution allows variables to take any value within a certain range.
Six, random variables, random numbers, random number distribution
- Variables change randomly within a certain range, called the cumulative frequency of random variables, called random numbers
- Single channel random queuing: It is formed by a service desk, random arrival and random service time
- A random variable is a variable with a variety of different values. These different values appear as one of the results in another random experiment. The random variable may be discrete or continuous. If a random variable is allowed to have a finite number of values in a given range, it is a discrete random variable. On the other hand, if a random variable is allowed to have any number of values in a given range, it is a continuous random variable.
- Uniform random number is the sampling sequence number of uniformly distributed random variables, and it is the most basic kind of random number.