Refreshments: 10:30 AM

Seminar: 11:00 AM

Title: Multi-component matching queues with abandonment and buffers : Fluid limit and large deviations.

Abstract: In this talk, I shall talk about a regulated matching queue system in an assembly-to-order (ATO) production line. Here each product is assembled from several distinct perishable components which arrive randomly over time at the ATO station and wait in their respective class-specific queues until they are either matched or their patience expires.  A match occurs instantaneously whenever one component from each category is available, and the matched set of ingredients exits the system immediately. Due to resource constraints, each queue is subject to a buffer capacity limit. In this model, a component may leave the system for one of three reasons: successful matching, abandonment due to impatience, or rejection upon arrival due to a full buffer. For a practical example, one can consider a large hospital where surgeries require the simultaneous availability of multiple perishable medical supplies and specialist staff. We develop a properly scaled system where the arrival rates grow increasingly large without bounds. I shall talk about the fluid limit, large deviations, and variational analysis of the rate function for this scaled system. I shall also go over the peculiar analytic challenge this model poses : A muti-dimensional Skorokhod problem and its well-posedness, uniqueness and continuity properties. This is based on a upcoming joint work with Ruoyu Wu and Bowen Xie.