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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写随机分析stochastic analysisl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。我们的专家在代写随机分析stochastic analysisl代写方面经验极为丰富，各种代写随机分析stochastic analysisl相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 统计代写|随机分析作业代写stochastic analysis代写|Queues with deadlines: optimality of EDF

We now assume that the customers have deadlines to enter in service. We denote $E_{n}$ the deadline of customer $C_{n}$ and $D_{n}=E_{n}-T_{n}$, the initial remaining time before the deadline (termed lead time) of $C_{n}$. We assume that the sequence $\left(D_{n}, n \in \mathbf{Z}\right)$ is stationary and we work on the canonical space $(\Omega, \mathcal{F}, \mathbf{P}, \theta)$ of arrivals, services and lead times. We denote then $D$ the projection of $\left(D_{n}, n \in \mathbf{Z}\right)$ on its first coordinate, interpreted as the lead time of customer $C_{0}$.

We assume that $\left(\sigma_{n}, n \in \mathbf{Z}\right)$ is an i.i.d. sequence, independent of the arrival process (and therefore of $\left(\xi_{n}, n \in \mathbf{Z}\right)$ and of $\left(D_{n}, n \in \mathbf{Z}\right)$ ), and that the random variables $\xi$, $\sigma$, and $D$ are integrable. The deadlines of the customers are smooth, as opposed to the case of hard deadlines (or impatience times) discussed in section 4.6. Indeed, a customer who did not enter service before his deadline does not leave the system, but continues to wait for his turn. The deadlines must then be seen here as indicators of the timing requirement of the customers.

We study hereafter the capacity of the system to minimize the lateness of the customers with respect to this requirement, by comparing the different service disciplines. Let us assume that the stability condition [4.3] holds. We denote again $\mathrm{TA}{n}$ the waiting time of $C{n}$ before reaching the server, and $B_{n}=$ $T_{n}+\mathrm{TA}{n}$, the moment where $C{n}$ enters service.

## 统计代写|随机分析作业代写stochastic analysis代写|Processor sharing queue

We now introduce a system of a particular type, which has the capacity to serve all the customers simultaneously (thus there is no waiting room). The price for such a mechanism (which models many physical systems) is that the instantaneous processing speed for each customer is divided by the number of customers in the system. That is, if there are $p$ customers in the system at a given time, their respective residual service time decrease by $1 / p$ per unit of time.

We make the same probabilistic hypotheses, and keep the same notation as before. Since the server is working, whatever happens, at speed unit when the system is not empty, it is easy to be convinced that the workload sequence $\left(W_{n}, n \in \mathbf{N}\right)$ satisfies Lindley’s equation [4.1]. So there exists a stationary workload to the condition [4.3].
To characterize more accurately the equilibrium state, we aim to construct the stationary versions of remarkable characteristics, such as congestion of the system, waiting time or sojourn time. However, the service profile at equilibrium, from which we will deduce these quantities, has a different form for this system as for a classical $\mathrm{G} / \mathrm{G} / 1$ queue. We show here how to construct the latter, using the renovating events.
Once again, we recall the notation and definitions introduced in Appendix A.3. We define for every $n, S_{n}^{\mathrm{PS}}$ the service profile at $T_{n}^{-}$, starting from an arbitrary profile $S_{0}^{\mathrm{PS}} \in \mathcal{S}$, by ordering by convention, the non-zero terms of $S_{n}^{\mathrm{PS}}$ in decreasing order. Clearly, $S_{n}^{\mathrm{PS}} \in \mathcal{S}$ for any $n \in \mathbf{N}$. We have the following result.

## 统计代写|随机分析作业代写stochastic analysis代写|Queues with deadlines: optimality of EDF

䖸们假设 $\left(\sigma_{n}, n \in \mathbf{Z}\right)$ 是一个独立同分布序列，独立于到达过程 (因此 $\left(\xi_{n}, n \in \mathbf{Z}\right)$ 和 $\left(D_{n}, n \in \mathbf{Z}\right)$ )，并且随机变量 $\xi, \sigma$ ，和 $D$ 是可积的。与第 $4.6$ 节中讨论的䃅性 截止日期 (或不㟨烦的时间) 不同，客户的截止日期很顺利。事实上，在截止日期之前没有进入服务的客户不会离开系统，而是继续等待轮到他。在这里，最后 期限必须被视为客户时间要求的指标。

## 统计代写|随机分析作业代写stochastic analysis代写|Processor sharing queue

䖸们做出相同的概率假设，并保持与以前相同的符号。由于服务器正在工作，无论发生什么，在系统不为空时以速度单位工作，很容易确信工作负载顺序 $\left(W_{n}, n \in \mathbf{N}\right)$ 满足 Lindley 方程 [4.1]。因此，条件 [4.3] 存在固定的工作量。

## 有限元方法代写

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## 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。

assignmentutor™您的专属作业导师
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