My research interests focus on the area of Applied Probability, specifically Queueing Theory in Heavy Traffic and Stochastic Controls. In particular, I have been working on Matching Queue Systems in the past few years, which usually originated from practical problems in Industrial Engineering and Operation Research.
I am also interested in Math Finance problems, especially Asset pricing problems and Dynamics of the Limit Order Book (LOB). Lately, I have developed an interest in Queue Control Problems via Reinforcement Learning (RL), RL in Solving Market Making Problems in high-frequency trading, and fractional Stochastic Control Problems.
Xie, Bowen and Gao, Yijin. "Diffusion approximation of a special bandwidth sharing model via infinitesimal generators with a lifting-projection method ", Operations Research Letters, (2024), 52 (2024): 107063.
Xie, Bowen. "Multi-component matching queues in heavy traffic." Queueing Systems (2024): 1-47. (Part of a Special Issue: Product Forms, Stochastic Matching, and Redundancy).
Gao, Yijin and Xie, Bowen. "Numerical analysis for fractional Bratu type equation with explicit and implicit methods", Mathematical Methods in the Applied Sciences, 46.17 (2023): 18447-18457. (Corresponding author).
Xie, Bowen and Gao, Yijin. "On the long-run average cost minimization problem of the stochastic production-inventory model", Journal of Industrial and Management Optimization, (2024), 20(5): 1823-1844., doi: 10.3934/jimo.2023144.
Xie, Bowen and Gao, Yijin. "Population growth model with fractional operator and its numerical analysis", Journal of Mathematical Study, (2024) (accepted).
Xie, Bowen and Gao, Yijin. "Numerical analysis for fractional Riccati differential equation based on finite difference method", Journal of Nonlinear Modeling and Analysis, vol. 7, no. 1, pp. 189–208, (2025).
Xie, Bowen and Yin, Haoyu. "Admission Control for A Single Server Waiting Time Process in Heavy Traffic", arXiv preprint arXiv:2212.05674 (2025). ArXiv preprint. (submitted).
Xie, Bowen and Wu, Ruoyu. "Controlling of multi-component matching queues with buffers", (working paper).
Xie, Bowen and Gao, Yijin. "Production and process innovation model equation with external shock", (near completion).
Xie, Bowen. "An infinitesimal generator approach on weak convergence of regulated multi-class matching systems", arXiv preprint arXiv:2507.09789 (2025). ArXiv preprint. (submitted).
Xie, Bowen. "Joint stochastic control problem of monopoly's production and process innovation", (working paper).
Xie, Bowen. "Dynamics of Generally Distributed Heterogeneous Multi-Class Matching Systems", (working paper).
Xie, Bowen. "Topics of queueing theory in heavy traffic" (Ph. D. thesis), full thesis.
Xie, Bowen. "Long-run average cost minimization of a stochastic processing system" (Master article), full article.
The following are some selected topics including some accomplished work and ongoing projects.
The University of Akron
Establish a matching system through the dynamics of the LOB.
Study the long-term equilibrium along with heavy traffic regimes for incoming orders.
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Mentor: Dr. José E. Figueroa-López Washington University in St. Louis
Study the performance of reinforcement learning (RL) in solving market-making problems with inventory risk.
Attempt to train a market-making agent using RL with a real-world stock market constructed from historical Limit Order Book (LOB) data.
Attempt to conduct neural networks to approximate state-value and state-action value functions and compare their performance with tile coding as well as the theoretical solution to the optimal placement problem.
Mentor: Dr. José E. Figueroa-López Washington University in St. Louis
Study the control problem of the multi-component matching queue with limited capacities for each queue.
Attempt to conduct the generator approach to perform asymptotic analysis for Markovian models.
Simulate the matching behavior to see if one can suspect the limiting process in heavy traffic.
Advisor: Dr. Ananda Weerasinghe Iowa State University
Constructed many-component matching queue models and studied the diffusion-scaled heavy traffic limits, which is characterized by a coupled non-linear stochastic integral equation.
Established the convergence of the cost functional associated with matching queue systems.
Formulated an asymptotic relationship between the queue length processes and the virtual waiting time processes (the asymptotic Little's law) and further refined the result to $L^p$ sense on a special probability space.
Simulated the matching queue systems and the corresponding stochastic integral equations numerically.
Observe that a matching queue model without abandonment could possibly be interpreted as a basket option pricing problem.
Research also studied a single server queue control problem and its asymptotic optimality by constructing and solving a Hamilton-Jacobi-Bellman equation of the limiting process analytically and numerically.
Advisor: Dr. Ananda Weerasinghe Iowa State University
Research addressed a stochastic control problem (DCP) by constructing and solving a formal Hamilton-Jacobi-Bellman equation analytically and numerically, which in turn yields an optimal strategy.
Further applied the above result in solving a single server queue control problem (QCP) to obtain its asymptotically optimal strategy through DCP.
Advisor: Dr. Ananda Weerasinghe Iowa State University
Creative component: Long-run Average Cost Minimization of a Stochastic Processing System
Minimizing the long-run average cost related to the optimal control of a production-inventory system in stochastic control theory is addressed through its corresponding Hamilton-Jacobi-Bellman equation.
An alternative derivation of the optimal long-run average cost using the invariant distributions for positive recurrent diffusion processes is provided.