Mathematical Sciences: Singular Perturbation Techniques in Queueing Theory

数学科学：排队论中的奇异扰动技术

• 批准号: 9300136
• 负责人: Charles Tier
• 金额: $ 9.72万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-05-15 至 1997-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9300136&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singular; Perturbation; Techniques

The investigators plan to develop new techniques for obtaining approximations to the performance measures of queueing systems. The new asymptotic and singular perturbation techniques will be applied to a wide variety of equations, such as difference, integral and differential-difference equations, that arise in these models. The methods are based on the WKB method, boundary layer analysis and matched asymptotic expansions. New nontrivial extensions of theses methods have previously been developed and have been shown to yield remarkably accurate results. The new approximations developed by the investigators will be directly applicable to models of large computer and communications systems. In such systems, customers (computer jobs, voice messages, data packets, or video images) contend for limited system resources. The behavior of these systems is measured by performance measures such as throughput and response time. To design new systems, it important that analytic models be analyzed to assess system operating characteristics.

研究人员计划开发新技术， 获得与评估的性能指标的近似值， 系统. 新的渐近和奇异摄动方法 将应用于各种各样的方程，例如 差分、积分和微分-差分方程， 在这些模型中出现。 该方法基于WKB方法， 边界层分析和匹配的渐近展开。 新 这些方法的非平凡扩展以前已经被 已经被证明可以产生非常精确的 结果 研究人员开发的新近似值将 直接适用于大型计算机机型， 通信系统。 在这样的系统中，客户（计算机 作业、语音消息、数据分组或视频图像）竞争 有限的系统资源。 这些系统的行为是 通过性能指标（如吞吐量和响应）来衡量 时间 为了设计新系统，分析模型 分析以评估系统运行特性。