Optimal server control with Two Customer Classes and Classification Errors
研究两类顾客（基础与高级）和两类服务器（普通与专家）的排队系统，在顾客分类错误下，如何动态分配专家以最大化长期平均利润，并分析分类错误概率对利润的影响。
• Customer misclassification is a common phenomenon in many applications. • We provide analytical models of service systems with customer misclassification. • We identify the optimal allocation of specialists in systems with customer misclassification. • We investigate how the long-run average profit depends on the misclassification probability. • We identify under what conditions it is more profitable to serve customers with or without service continuity. We consider a Markovian queueing system with two types of customers (basic and advanced) and two types of servers (regular and specialist) in the presence of customer classification errors. We assume that there are always both types of customers waiting for service. When an advanced customer is misclassified as a basic customer, he needs to be served by a specialist after being served by a regular server. Our objective is to determine the dynamic assignment of the specialists between advanced and misclassified customers that maximizes the long-run average profit. We consider two versions of the problem that differ depending on whether the misclassified customers experience service continuity (the regular servers stay with misclassified customers while they wait for specialists, preventing the regular servers from serving other basic customers) or not (the regular servers continue serving other basic customers while misclassified customers wait for specialists). For both versions of the problem, we first characterize the optimal assignment of the specialists and then investigate how the optimal long-run average profit depends on the misclassification probability. We provide examples of systems where the optimal long-run average profit is not monotone in the misclassification probability, which is counter intuitive as one would expect misclassification to have a negative impact on system performance. We conclude our analysis by identifying under what conditions it is more profitable to serve customers with or without service continuity.