A retrial tandem queue with two types of customers and reservation of channels

Abstract

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. © 2013 Springer-Verlag.