Michael C. Fu

Tong Sun, Jianshu Hao, Michael C. Fu et al.

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient interval condition that characterizes the admissible number of connections at each step, thereby guaranteeing global feasibility. Based on this result, we develop bipartite graph enumeration and sampling algorithms suitable for different problem sizes. We then extend these bipartite graph algorithms to the directed and undirected cases by incorporating additional connection constraints, as well as feasibility verification and symmetric connection steps, while preserving the same algorithmic principles. Finally, numerical experiments demonstrate the performance of the proposed algorithms, particularly their scalability to large instances where existing methods become computationally prohibitive.

Michael C. Fu

New recursive estimators for computing higher-order derivatives of mean queueing time from a single sample path of a first-come, first-served single-server queue are presented, derived using the well-known Lindley equation and applying the Leibniz integral rule of differential calculus. Illustrative examples are provided.

Xingyu Ren, Michael C. Fu, Steven I. Marcus

We review the literature on individual patient organ acceptance decision making by presenting a Markov Decision Process (MDP) model to formulate the organ acceptance decision process as a stochastic control problem. Under the umbrella of the MDP framework, we classify and summarize the major research streams and contributions. In particular, we focus on control limit-type policies, which are shown to be optimal under certain conditions and easy to implement in practice. Finally, we briefly discuss open problems and directions for future research.

Xingyu Ren, Michael C. Fu, Steven I. Marcus

We consider a stopping problem and its application to the decision-making process regarding the optimal timing of organ transplantation for individual patients. At each decision period, the patient state is inspected and a decision is made whether to transplant. If the organ is transplanted, the process terminates; otherwise, the process continues until a transplant happens or the patient dies. Under suitable conditions, we show that there exists a control limit optimal policy. We propose a smoothed perturbation analysis (SPA) estimator for the gradient of the total expected discounted reward with respect to the control limit. Moreover, we show that the SPA estimator is asymptotically unbiased.

Yijie Peng, Edwin K. P. Chong, Chun-Hung Chen et al.

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this policy is not only computationally efficient but also possesses both one-step-ahead and asymptotic optimality for independent normal sampling distributions. Moreover, the proposed allocation policy is easily generalizable in the approximate dynamic programming paradigm.