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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712601
• 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.

该研究计划的目标是揭示模式、结构和性质，寻找新方法，开发和扩展先进方法，并提出有效的近似和计算程序。我们期望新的发现可以用于各种多维随机系统的建模和分析，包括多排队队列、串联队列以及其他与批量队列、耦合服务器、自适应服务等机制相结合的排队模型和优先事项。如上所述，这些随机系统提出了新的挑战，通过我们开发处理这些挑战的先进方法，我们的目标是为工程和计算机问题以及其他排队应用提供解决方案。 当期望显式属性时，概率分布的显式解通常不适用于本研究中提出的复杂系统。因此，近似、渐近性质、性能界限成为研究的关键组成部分。拟议的研究是使用、扩展和进一步发展以下方法论和途径：渐近的核方法；边值问题（BVP）方法和显式解的解析（均匀化/代数）方法；用于具有无限多个相状态的过程的矩阵分析方法（MAM）等。 从所提出的程序中取得的新发现和获得的新结果，从将核方法扩展到具有杀伤或吸收状态的随机游走，到更一般的结构化游走和高维模型；推广用于处理具有无限多个相态的过程的矩阵分析方法；探索 BVP 能力的极限以及显式解的统一化和代数方法；通过光谱特性研究准平稳分布的衰减率，预计将在排队论、随机建模和分析方面取得原创性和重大成果，并对系统设计和性能评估、电信系统和其他应用产生深远影响。