Title: Ergodic risk sensitive control in Markovian parallel server networks in the Halfin-Whitt regime.
Date and time: 4 July 2025 (Friday), 10:30 – 11:30 a.m.
Venue: IEOR Seminar Room
Abstract: It is well-known that Markovian parallel server networks in the Halfin-Whitt regime approach a limiting diffusion. In this talk, we introduce the optimal scheduling problem for Markovian parallel server networks (with abandonment) in the Halfin--Whitt regime, under the long run average (ergodic) risk sensitive cost criterion where the running cost penalizes the queue length and/or the idleness of the servers. Our objective is to prove asymptotic optimality for the optimal control arising from the corresponding ergodic risk sensitive control (ERSC) problem for the limiting diffusion. In particular, we show that the optimal ERSC value associated with the diffusion-scaled queueing process converges to that of the limiting diffusion in the asymptotic regime. The challenge that the ERSC problem poses is that one cannot express the ERSC cost as an expectation over the mean empirical measure associated with the queueing process, unlike in the usual case of a long run average (ergodic) cost.
We introduce a novel approach by exploiting the variational representations of the limiting diffusion (driven by Brownian motion) and the diffusion-scaled queueing process (driven by Poisson processes), which both involve certain auxiliary controls. Using these representations, ERSC costs for both the diffusion-scaled queueing process and the limiting diffusion can be represented as the integrals of an extended running cost over a mean empirical measure associated with the corresponding extended processes using these auxiliary controls. From here, we exploit the connections of the ERSC problem for the limiting diffusion with a two-person zero-sum stochastic differential game and also make use of the mean empirical measures associated with the extended limiting diffusion and diffusion-scaled processes with the auxiliary controls.
This is a joint work with Guodong Pang.
Bio: Sumith obtained his Bachelors in Aerospace Engineering at IIT Bombay and, integrated Ph.D. in Physics from ICTS - TIFR Bengaluru. Until recently, he has been a postdoctoral fellow in the Department of Computational Applied Mathematics and Operations Research at Rice University. Prior to this, he was a postdoctoral fellow in the Department of Mathematics, IIT Bombay. His research interests lie predominantly in stochastic control, stochastic filtering and large deviations.