Research interests

Research grant support from Army Research Office (Probability and Statistics Program) W911NF-14-1-0019 (PI), W911NF-17-1-0019 (PI), NSF CMMI 1538149 (PI), NSF CMMI 1635410 (PI), NSF DMS-Applied Mathematics 1715875 (PI), and NSF DMS-Applied Mathematics 2108683/2216765 (PI) is gratefully acknowledged.

Stochastic Process Limits in Queueing and Other Probabilistic Models

One of my major interests is to develop new methods to prove scaling limits for various stochastic models. Many of the models are queueing systems and stochastic networks arising from complex service systems. Some recent work also includes shot noise processes and Hawkes process.

Optimal Control of Stochastic Networks and Stochastic Control Theory

We have worked on ergodic control problems of multiclass multi-pool networks (also called parallel-server networks) in the Halfin-Whitt regime. In order to tackle these problems, we have developed a new framework of ergodic control of (jump) diffusions.

Ergodic Properties of Queueing Models, Stochastic Networks and Other Systems

Stochastic Models in Epidemiology

We have developed probabilistic approaches to study individual based non-Markov epidemic models. In addition to the standard models, we have further developed stochastic epidemic models with varying infectivity or infection-age dependent infectivity, infection-age dependent recovery rate, varying susceptibility and waning immunity. We have also worked on spatial epidemic models, and epidemic models on large random graphs.

Generalized fractional Brownian motion

We have introduced a new generalized fractional Brownian motion (GFBM), which is a self-similar Gaussian process but with non-stationary increments. We have studied some fundamental path properties, as well as the semimartingale properties. We are exploring its applications in financial models, in particular, rough volatility and nonstationary queueing systems.

Service Operations Management

Modern service systems tend to be large and require sophisticated operational strategies, for example, customer contact centers with multi-class calls and multiple pools of agents, and hospitals with patient flows in many diagnosis and treatment centers. Large-scale service systems have the advantage of economy of scale, providing the possibility for achieving both high quality of service and high efficiency if they are well managed. The complexity of such systems also presents challenges for decision making in many perspectives, including capacity allocation, scheduling and revenue management.