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。所考虑的模型将包括具有多个服务器、丢弃以及重尾处理和到达间隔时间的系统。研究将集中于确定两个排队模型的参数的条件，以确保两个模型的性能指标可以比较。本文将重点讨论具有一定非单调性的模型，例如具有遗弃的系统，在该模型中增加额外的工作实际上会导致系统中的数量减少。这些条件将被用来在不同的排队模型之间传递性能分析结果。这项研究将把这些条件与渐近分析和概率论中的工具结合起来，分析这些系统的性能如何依赖于基本的模型参数，重点是了解这些系统在服务器数量增长时的行为，以及与异常高的拥塞水平相关的某些罕见事件的概率。如果研究成功，本研究将从两个方面促进随机建模和分析的发展。首先，这项研究将对服务系统的建模、设计和分析中出现的具有丢弃和重尾的多服务器队列的性能产生新的界限和见解。其次，这项研究将导致新的随机比较和分析方法的发展，这可能会更广泛地适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.