Stochastic Comparison Approach to Parallel Server Queues

该奖项的目标是开发用于排队模型性能分析的随机比较技术。 考虑的模型将包括具有许多服务器、废弃、重尾处理和到达间隔时间的系统。 该研究将侧重于确定两个排队模型的参数条件，以确保可以比较两个模型的性能指标。将重点关注表现出某些非单调性的模型，例如带有废弃的系统，其中添加额外的工作实际上会导致系统中的数量减少。 然后，这些条件将用于在不同排队模型之间传输性能分析结果。该研究将这些条件与渐近分析和概率论工具结合起来，分析这些系统的性能如何取决于底层模型参数，重点是了解这些系统随着服务器数量增加而发生的行为，以及与异常高水平拥塞相关的某些罕见事件的概率。 这项研究还将为重尾排队系统制定和分析新颖的缩放机制。如果成功，这项研究的结果将从两个方面推进随机建模和分析的最新技术。首先，该研究将为多服务器队列的性能带来新的界限和见解，这些队列在服务系统的建模、设计和分析中出现了废弃和重尾的情况。 其次，该研究将导致新型随机比较和分析方法的发展，这些方法可能更广泛地应用于概率模型的研究。

The objective of this award is the development of stochastic comparison techniques for performance analysis of queueing models. The models considered will include systems with many servers, abandonments, and heavy-tailed processing and inter-arrival times. The research will focus on identifying conditions on the parameters of two queueing models which ensure that the performance metrics of the two models can be compared. Emphasis will be given to models which exhibit certain non-monotonicities, for example systems with abandonments, in which adding extra jobs can actually cause the number in system to decrease. These conditions will then be used to transfer performance analysis results between different queueing models. The research will combine these conditions with tools from asymptotic analysis and probability theory to analyze how the performance of these systems depends on the underlying model parameters, with an emphasis on understanding both the behavior of these systems as the number of servers grows large, and the probability of certain rare events associated with exceptionally high levels of congestion. The research will also lead to the formulation and analysis of novel scaling regimes for queueing systems with heavy tails.If successful, the results of this research will advance the state-of-the-art in stochastic modeling and analysis in two ways. First, the research will yield new bounds and insights into the performance of many-server queues with abandonments and heavy tails, which arise in the modeling, design, and analysis of service systems. Second, the research will lead to the development of novel stochastic comparison and analysis methodologies, which may be more broadly applicable in the study of probabilistic models.