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# 数学代写|运筹学代写Operations Research代考|KMA255 Introduction to Simulation

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## 数学代写|运筹学代写Operations Research代考|Introduction to Simulation

The main reason for a researcher to resort to simulation is twofold. First of all, simulation is probably the most flexible tool imaginable. Take queuing as an example. While it is very difficult to incorporate reneging, jumping queues, and other types of customer behavior in the usual analytical models (see, e.g., Chap. 15 of this volume), this presents no problem for simulation. Similarly, recall that the queuing formulas that have been derived refer to steady-state solutions. A system may have to run for a very long time to reach a steady state, assuming that one exists. As a result, a modeler may be more interested in transient states, which are easily available in a simulation.

The second reason is that simulation is very cheap. Building a model that simulates the opening of a new restaurant will most certainly be a lot less expensive than trying it out. Even if costs are no subject, the time frame can be compressed in a simulation. For instance, if we were to observe the demand structure of a product, a long time would be required, so that results would probably be available when the product has become technologically obsolete anyway.
The main steps of a discrete-event simulation include

1. Building the model
2. Assigning numbers to uncertain events according to their likelihoods
3. Generating uncertain events
4. Applying predetermined policies
5. Evaluating the results including verifying the model.

## 数学代写|运筹学代写Operations Research代考|Random Numbers and Their Generation

Random numbers have been around for a long time. Among the earlier systematic efforts to generate random numbers is the work by statistician L.H.C. Tippet, who produced the first random number tables that were based on census numbers. In the mid-1950s, the Rand Corporation published a tome A Million Random Numbers. Today, we distinguish between true random numbers and pseudo-random numbers.

Roughly speaking, true random numbers are generated by way of a random process, while pseudo-random numbers are machine generated by means of a deterministic process. An obvious way to generate true random numbers is to roll dice. Assuming that we have a usual six-sided die which is not loaded or skewed, each side has a chance of $1 / 6$ of coming up; i.e., the probability of each number is $16 \frac{2}{3} \%$. It is not difficult to devise differently shaped dice that have ten sides, once for each possible digit. Note that for the time being we only deal with uniformly distributed random numbers, i.e., those in which all possible numbers have the same chance of appearing. If two-digit random numbers are sought, use multiple dice, roll them all, and add their numbers. Note, however, that care must be taken: taking, for instance, two standard six-sided dice, rolling them and adding up their numbers, will not result in uniformly distributed results. As an example, the outcome of ” 2 ” is only possible, if both dice show a ” 1 ,” which has a probability of $1 / 36$. On the other hand, an outcome of “8” has a probability of $5 / 36$, as it can be realized from 2 and 6,3 and 5,4 and 4,5 and 3 , and 6 and 2 .

However, changing the numbers on the faces enables us to use the same process to generate random numbers that have an equal probability of appearing. If the first die has the numbers $0,1,2,3,4$, and 5 on its side, the second has $0,6,12,18,24,30$, and 36 on its sides, the third has $0,36,72,108,144$, and 180 , and the fourth die has numbers $0,216,432,648,864$, and 1080 , then the number that results from adding the face values of the four dice is a uniformly distributed random number between 0 and 1295 .

## 数学代写|运筹学代写Operations Research代考|Introduction to Simulation

1. 构建模型
2. 根据可能性为不确定事件分配数字
3. 产生不确定事件
4. 应用预定策略
5. 评估结果，包括验证模型。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。