A Retrial Tandem Queue with Two Types of Customers and Reservation of Channels
A Retrial Tandem Queue with Two Types of Customers and Reservation of Channels
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两类客户重试串联队列及通道预约
DOI：
10.1007/978-3-642-35980-4_12
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
R. Savko
中科院分区：
文献类型：
--
作者：
V. Klimenok;R. Savko
我们考虑具有两个多服务器站的重试串联队列，该队列可以被视为具有两种类型客户的呼叫中心的数学模型，该客户根据等待与代理的连接的能力进行分类。顾客到达1号站时遵循平稳泊松流。如果到达的客户遇到所有服务器都忙碌，他/她会进入无限大小的轨道，并在随机时间后重试。客户的类型是在完成站1的服务时随机确定的。如果站2的所有服务器都是忙碌的，则类型1（优先级）客户永远离开系统，而类型2（非优先级）客户在有限大小的缓冲器中排队。如果缓冲区已满，则该客户离开系统。排队的顾客都不耐烦了。这意味着他们可能决定在2号站开始服务之前离开系统。假设站2的多个服务器可以被保留以仅服务于优先客户。我们计算了系统的平稳分布和主要性能指标。构造了不同预留服务器数下的服务质量评价函数。给出了数值例子。
We consider a retrial tandem queue with two multi-server stations which can be considered as a mathematical model of a call center with two types of customers classified by their ability to wait for the connection to the agent. Customers arrive at Station 1 according the stationary Poisson flow. If an arriving customer meets all servers busy he/she goes to the infinite size orbit and retries after a random time. The type of a customer is randomly determined upon completion of the service at Station 1. If all servers of Station 2 are busy type 1 (priority) customer leaves the system forever while type 2 (non-priority) customer is queued in the buffer of limited size. If the buffer is full this customer leaves the system. The customers staying in the queue are impatient. This means that they might decide to leave the system before their service at Station 2 begins. It is assumed that a number of servers of Station 2 can be reserved to serve priority customers only. We calculate the stationary distribution and the main performance measures of the system. The cost function evaluating quality of service under different number of reserved server is constructed. Illustrative numerical example is presented.