Optimality gap of asymptotically derived prescriptions in queueing systems
Optimality gap of asymptotically derived prescriptions in queueing systems
复制标题
排队系统中渐进处方的最优差距
DOI：
10.1007/s11134-016-9476-z
复制
发表时间：
2016
期刊：
影响因子：
1.2
通讯作者：
R. Randhawa
中科院分区：
文献类型：
--
作者：
R. Randhawa
在复杂的系统中，在优化系统性能时，诉诸近似是很常见的。这些近似值通常涉及选择特定的系统参数，然后随着该参数增长而无限制，然后研究系统的性能。在这样的渐近方案中，我们证明，如果对目标函数的近似值准确至O（1）\ documentClass [12pt] {minimal} \ usepackage {amsmath} \ useyySym} amssymb} \ use-package {amsbsy} \ usepackage {Mathrsfs} \ usepackage {upgreek} \ setLength {\ oddSidemargin} { - 69pt} \ 69pt} \ begen一些规律性条件，从此近似值为O（1）最佳选择，即它们的最佳差距渐近为零。此结果的结果是，著名的Square-Root人员配备规则，用于M / m / s和m / m / s+m / s+m \ documentClass [12pt] {minimal} \ usepackage {amsmath} \ usepackage { } \ usepackage {amsfonts} \ usepackage {amssymb} \ use-package {amsbsy} \ usepackage {Mathrsfs} \ usepackage {upgreek} \ setLength {\ oddSidemargin} { - 69pt} \ 69pt} \ begin {document}线性预期稳态客户等待成本和线性容量的总和成本是O（1）最佳的。我们还讨论了这些系统中非线性客户等待成本的情况的扩展。
In complex systems, it is quite common to resort to approximations when optimizing system performance. These approximations typically involve selecting a particular system parameter and then studying the performance of the system as this parameter grows without bound. In such an asymptotic regime, we prove that if the approximation to the objective function is accurate up to O(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(1)$$\end{document}, then under some regularity conditions, the prescriptions that are derived from this approximation are o(1)-optimal, i.e., their optimality gap is asymptotically zero. A consequence of this result is that the well-known square-root staffing rules for capacity sizing in M / M / s and M/M/s+M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M/M/s+M$$\end{document} queues to minimize the sum of linear expected steady-state customer waiting costs and linear capacity costs are o(1)-optimal. We also discuss extensions of this result for the case of nonlinear customer waiting costs in these systems.