多类型顾客反馈排队系统最优动态策略研究  

Dynamic optimal policy of feedback queueing systems with multi-type customers

作　　者：苏炎 李俊平 余义[1] SU Yan;LI Junping;YU Yi(School of Management,Nanjing University of Posts and Telecommunications,Nanjing 210003,China;Guangdong University of Science and Technology,Dongguan 523083,China;School of Mathematics and Statistics,Central South University,Changsha 410083,China)

机构地区：[1]南京邮电大学管理学院,南京210003 [2]广东科技学院,东莞523083 [3]中南大学数学与统计学院,长沙410083

出　　处：《系统工程理论与实践》2024年第7期2352-2361,共10页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(11771452,11971486);南京邮电大学基金(NYY222047,NYY222052);江苏省高校自然科学研究基金(23KJB110020)。

摘　　要：本文在系统缓冲区有限的情况下,研究了一类具有多顾客类型反馈排队系统的最优准入控制和动态定价策略问题.假设顾客到达系统是一个泊松流,顾客的服务时间服从指数分布,顾客类型由不同净利润值决定.在系统平均净利润最大化目标下,从策略结构角度,本文证明了准入控制最优阈值型策略的存在性、最优单调价格策略的存在性,给出了单服务员、无等待费用情形下系统有利可图的一个充要条件以及一些相关性质.此外,从计算角度,本文还基于模型的特殊结构提出了一个有效的倒向迭代算法.最后,本文利用多个数值实验验证所得结果,观察不同调控方式最优利润值的差异性,并在计算效率上与经典策略迭代算法进行比较.In this paper,we study the optimal admission control and dynamic pricing policies for feedback queueing systems with multiple customer types and finite buffers.Assume that customers arrival system is a Poisson flow,the service time of customers follows an exponential distribution,and the customer types are determined by different net profit values.Under the objective of maximizing average net profit,from the perspective of policy structure,we prove the existence of the optimal threshold policy of admission control and the existence of the optimal monotone price policy,give a sufficient and necessary condition and some related properties for the system to be profitable in the case of single server and no waiting cost.In addition,an effective backward iterative algorithm is proposed based on the special structure of the model.Finally,we use several numerical experiments to verify the results,observe the difference of the optimal profit value of different regulation methods,and compare the computational efficiency with that of the classical policy iterative algorithm.

关 键 词：反馈排队系统 多类型顾客 阈值型策略 单调价格 倒向迭代算法 

分 类 号：O226[理学—运筹学与控制论]