Queueing Models and Performance Analysis -- Telecommunication Systems and Other Applications

排队模型和性能分析——电信系统和其他应用

• 批准号: RGPIN-2018-04572
• 负责人: Tavakoli, Javad
• 金额: $ 1.89万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=681639
• 关键词: Queueing; Models; Performance; Analysis; Telecommunication

The objective of this proposed research program is to reveal patterns, structures and properties, search for new approaches, develop and extend advanced methods, and propose efficient approximations and computational procedures. We expect that new discoveries can be employed in both modelling and analysis, for various multi-dimensional stochastic systems, including multiple waiting lines queues, tandem queues, and other queueing models which are incorporated with mechanisms such as bulk queues, coupled servers, adaptive services, and priorities. These stochastic systems offer new challenges, as outlined above, and through our development of proposed advanced methods in dealing with these challenges, we aim at providing solutions to engineering and computer problems and other queueing applications.***When explicit properties are expected, explicit solutions for probability distributions are not, in general, available for the complex systems proposed in this research. Therefore, approximations, asymptotic properties, performance bounds, become key components in the study. The proposed research is to use, extend, and further develop the following methodology and approaches: the kernel method for asymptotics; boundary-value problems (BVP) approach and analytic (uniformization / algebraic) method for explicit solutions; the matrix analytic method (MAM) for processes with infinitely many phase states, among others.******New discoveries made and new results obtained from the proposed program, from extending the kernel method to random walks with killing or absorbing states to more general structured walks and to high-dimensional models; from generalizing the matrix-analytic method for dealing with processes with infinitely many phase states; from exploring the limit of the power of the BVPs, and uniformization and algebraic methods for explicit solutions; from studying the decay rate in quasi-stationary distributions by spectral properties, are expected to be original and significant results in advances in queueing theory, stochastic modelling and analysis, and produce profound impact on system design and performance evaluation, telecommunication systems and other applications.**

该建议的研究计划的目的是揭示模式，结构和属性，搜索新方法，开发和扩展高级方法，并提出有效的近似值和计算程序。我们希望可以在建模和分析中使用新的发现，用于各种多维随机系统，包括多个等待线的队列，串联排队以及其他排队模型，这些模型与诸如散装队列，耦合服务器，适应性服务，适应性服务等机制结合在一起。如上所述，这些随机系统提供了新的挑战，并且通过开发提出的高级方法来应对这些挑战，我们旨在为工程和计算机问题以及其他排队应用程序提供解决方案。因此，近似值，渐近特性，性能界限成为研究中的关键组成部分。拟议的研究是使用，扩展和进一步开发以下方法和方法：渐近学的内核方法；边界值问题（BVP）方法和分析方法（均匀化 /代数）方法；矩阵分析方法（MAM）用于无​​限多个相状的过程，以及其他相位。从概括矩阵分析方法来处理无限多相状态的过程；通过探索BVP的功率的极限，以及明确解决方案的均匀化和代数方法；通过研究准平台分布中的衰减速率，预计将是排队理论，随机建模和分析的进步的原始结果，并对系统设计和性能评估，电信系统和其他应用产生深远的影响。**