Dynamic Admission Quota Control With Controllable and Uncontrollable Demands and Random Service Time

• 成果类型: Article
• 署名作者: Dai, Jiajun; Geng, Na; Xie, Xiaolan
• 署名单位: Shanghai Jiao Tong University; Shanghai Jiao Tong University; IMT - Institut Mines-Telecom; Mines Saint-Etienne; Centre National de la Recherche Scientifique (CNRS); Universite Clermont Auvergne (UCA); Shanghai Jiao Tong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3014117
• 发表日期: 2021
• 页码: 2925-2932
• 关键词: Admission control; Hospitals; Markov processes; Mathematical model; PROCESS CONTROL; Admission quota; controllable customers; Markov decision process (MDP); random service time; uncontrollable customers

摘要

This article considers an admission quota control which determines the maximum daily admission (known as the quota) of controllable demand that shares capacity with uncontrollable demand. General arrival processes and general discrete stochastic service time are assumed. An infinite-horizon Markov decision process model is proposed to maximize the expected total discounted net reward comprising admission revenues and overcapacity costs. Through formal proofs, the optimal quota control which makes decisions before knowing demand information is found to be equivalent to the optimal classical admission control which makes decisions after knowing such information when the service time is deterministic or no more than two periods. This equivalence is shown numerically when the service time is no more than four periods. Furthermore, structural properties of the optimal quota control and bounds of the optimal quota are established. Finally, several heuristic policies are proposed and compared by numerical experiments.