Stochastic Comparison Approach to Parallel Server Queues

该奖项的目的是随机比较技术的发展，性能分析的模型。 考虑的模型将包括系统与许多服务器，放弃，重尾处理和到达时间间隔。 研究将集中在确定两个模型的参数，以确保这两个模型的性能指标可以进行比较的条件。重点将给予模型，表现出一定的非单调性，例如系统与放弃，其中增加额外的工作，实际上可以导致系统中的数量减少。 然后，这些条件将用于在不同的建模模型之间传输性能分析结果。该研究将结合联合收割机这些条件与工具，从渐近分析和概率论分析这些系统的性能如何取决于基本的模型参数，重点是了解这些系统的行为作为服务器的数量增长大，和某些罕见的事件与异常高的拥塞水平的概率。 这项研究还将导致制定和分析的新的标度制度的重尾的混沌系统，如果成功的话，这项研究的结果将推进国家的最先进的随机建模和分析在两个方面。首先，该研究将产生新的边界和见解的性能的多服务器队列的放弃和重尾，这出现在建模，设计和分析的服务系统。 其次，研究将导致新的随机比较和分析方法的发展，这可能是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.