数学代写|排队论代写Queueing Theory代考|COE755

statistics-lab™ 为您的留学生涯保驾护航 在代写排队论Queueing Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写排队论Queueing Theory方面经验极为丰富，各种代写排队论Queueing Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

数学代写|排队论代写Queueing Theory代考|Defining a Queue System

A number of elements must be prescribed in order to define a queue system, including

1. The type of probability distribution used for the arrival process, with one or more parameters.
2. The type of probability distribution used for the service process, with one or more parameters.
3. The number of servers in the service station (for example, the number of check-out stations in service at a grocery store).
4. The maximum number of customers that can be in the system, if limited.
5. The size of the population of potential customers, if limited.
Some of this information is presented in compact form as an identifier of the form A/S $/ s / K / N$ , where
6. A designates the type of distribution used for arrival times,
7. S designates the type of distribution used for service times,
8. $s$ designates the number of servers,
9. $K$ is the maximum number of customers that can be in the system at any one time, and
10. $N$ is the size of the population of potential customers.
Typical designators for the distributions are
11. M for the exponential distribution (Markovian),
12. $\mathrm{E}_k$ for an Erlang distribution (which we will use later), and
13. D for the deterministic distribution (constant times),
14. G for a general distribution (unspecified except for mean and standard deviation).
The size of the calling population is important because customers that enter a queue system should be removed from the list of potential customers. This decreases the mean arrival rate, but usually the decrease is too small to worry about. Unless the calling population is small enough for the decrease to matter, it is best to consider it to be infinite. In this case, the fifth designator $N$ is often omitted. Similarly, the number of customers that can be in the system at any one time is usually limited, but most of the time the capacity is large enough that it is never actually reached. In this case, it is best to consider the maximum system size to be infinite. As with infinite calling population size, it is common to omit the fourth designator $K$ when the queue size is unlimited.
15. The most commonly used systems are of the form $\mathrm{M} / \mathrm{M} / \mathrm{s}$, meaning that the arrival and service processes are exponentially distributed and the system size and calling population are unlimited. We will study these systems in Section 4.

数学代写|排队论代写Queueing Theory代考|Properties of Queue Systems

The number of customers in a queue system changes over time. When the system first begins to operate, there are generally no customers. Those customers who arrive before the servers are all occupied get to begin service immediately, while customers who arrive later only get to begin service when they get to the front of the queue. Thus the probability that there are 4 customers in the system is initially 0 , but it rises as the system remains open.

Suppose a queue system has the property that the mean arrival rate does not change as the system size changes. This requires that both the maximum system size $K$ and the calling population $N$ are infinite and that there are no unusual features that can lower the arrival rate as the system size increases. Given a mean rate of service completions of $\mu$ for each of $s$ servers, the total service capacity is a mean rate of $s \mu$. The ratio of mean arrival rate to mean total service completion rate, given by
$$\rho=\frac{\lambda}{s \mu}$$ then represents the fraction of the service capacity that is used. For this reason, it is called the utilization factor for the queue system. The quantity is often used even in cases where $\lambda$ is not fixed, but the interpretation as utilization factor no longer holds.
For both modeling and computation, it is also helpful to define the arrival-service ratio
$$\gamma=\frac{\lambda}{\mu}$$
This parameter represents the expected number of arrivals during the average amount of time for a service completion, which we might call the “load” of the system. In modeling, the most frequent scenario is one in which the rates $\lambda$ and $\mu$ are fixed and the problem is to choose the optimal number of servers. The parameter $\gamma$ is much more useful than $\rho$ in this context because it is strictly a property of the scenario while $\rho$ combines elements of the scenario data $(\lambda$ and $\mu$ ) with the independent variable of the optimization problem $(S)$. Computationally, we’ll find $\gamma$ more useful that $\rho$ in cases where the arrival rate depends on the system state.

排队论代写

数学代写|排队论代写Queueing Theory代考|Defining a Queue System

1. 用于到达过程的概率分布类型，具有一个或多个参数。
2. 用于服务过程的概率分布类型，带有一个或多个参数。
3. 服务站中服务器的数量（例如，杂货店服务中的结账站数量）。
4. 系统中可以容纳的最大客户数（如果有限制）。
5. 潜在客户的人口规模（如果有限）。
其中一些信息以紧凑形式作为 A/S 形式的标识符呈现/秒/钾/否， 在哪里
6. A 指定用于到达时间的分布类型，
7. S 指定用于服务时间的分布类型，
8. 秒指定服务器的数量，
9. 钾是任一时刻系统中可以存在的最大客户数，并且
10. 否是潜在客户的人口规模。
分布的典型指示符是
11. M 为指数分布（马尔可夫），
12. 和k对于 Erlang 发行版（我们稍后会用到），以及
13. D 为确定性分布（恒定时间），
14. G 表示一般分布（除均值和标准差外未指定）。
呼叫人口的规模很重要，因为进入队列系统的客户应该从潜在客户列表中删除。这会降低平均到达率，但通常降幅很小，无需担心。除非呼叫人口足够小以至于减少很重要，否则最好将其视为无限大。在这种情况下，第五个指示符否经常被省略。同样，在任何时候系统中可以容纳的客户数量通常是有限的，但大多数时候容量足够大，实际上永远不会达到。在这种情况下，最好将最大系统规模视为无限大。与无限呼叫人口规模一样，通常会省略第四个指示符钾当队列大小不受限制时。
15. 最常用的系统具有以下形式米/米/秒，这意味着到达和服务过程呈指数分布，系统规模和呼叫人口是无限的。我们将在第 4 节中研究这些系统。

数学代写|排队论代写Queueing Theory代考|Properties of Queue Systems

$$\rho=\frac{\lambda}{s \mu}$$

$$\gamma=\frac{\lambda}{\mu}$$

广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。