Title: Free boundary problems for macroscopic queueing dynamics via Skorohod maps

    Abstract: The macroscopic description of the dynamics of a variety of queueing models can formally be posed as a free boundary problem (FBP). For example, in the (single / many server) earliest-deadline-first model, the boundary of the support of the empirical deadline distribution corresponds to the shortest deadline among currently available jobs, and this boundary plays a main role in the dynamics. For the (parallel server) join-the-shortest-workload model, it is the shortest currently available workload. The relation between the queueing models and their formal macroscopic description is important to establish rigorously. However, this task is often very hard as the FBPs may be ill posed. The talk will describe progress achieved by (1) a recently developed approach to these FBPs via Skorohod maps, (2) tools from hydrodynamic limits for interacting particle systems governed by FBPs.

    Bio: Rami Atar is with the Viterbi Faculty of Electrical Engineering of the Technion, Haifa, Israel, where he holds the Lady Davis Chair is Sciences. He is a Fellow of the IMS. His research interests are in fluid, diffusion and large deviation scale analysis of queueing models, PDE techniques in control and games, model robustness via Renyi divergence, and Skorohod maps in measure space.