SNAPP Seminar || Daniela Hurtado-Lange (Northwestern University) || December 1, 2025

Speaker: Daniela Hurtado-Lange (Northwestern University) || December 1, 2025

Title: Join-the-Shortest-Queue with Markov-Modulated parameters: Poisson Equation and Transform Techniques

Abstract: In parallel-server systems with a single stream of arrivals, Join-the-Shortest-Queue (JSQ) is one of the most popular routing algorithms due to its simplicity and strong performance properties: it is well known that routing with JSQ is throughput and heavy-traffic optimal, regardless of whether the servers are homogeneous or not. Further, JSQ is optimal and does not need any information about the servers' rates. In this work, we study a JSQ system with Markov-modulated arrival and service rates. Specifically, we provide sufficient conditions on the Markov-modulated arrival and service rates to ensure state space collapse, and compute the heavy-traffic distribution of queue lengths. We establish the distribution of queue lengths using a novel hybrid methodology that combines the Transform Method for queue-lengths analysis, and Poisson Equation of the Markov-modulating chain.

Speaker's Bio: Daniela is an Assistant Professor in the Operations department at the Kellogg School of Management at Northwestern University. She received her Ph.D. in Operations Research at Georgia Tech in December 2021, and was supervised by Prof. Siva Theja Maguluri. Before joining Kellogg, she spent 1.5 years as an Assistant professor of Mathematics at William & Mary. Her research interests are performance analysis of Stochastic Processing Networks and applied probability.