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.
