Priority tandem queueing system with retrials and reservation of channels as a model of call center

Abstract

We study a tandem queueing system consisting of two multi-server stations and finite intermediate buffer. Customers arrive at the first station of the tandem according to a Markovian Arrival Process. The first station does not have a buffer. Customers, who do not succeed to enter the service immediately upon arrival, retry for the service after a random amount of time. After service completion at the first station, a customer leaves the system permanently or moves for the service at the second station. A part of customers entering the second station have a priority over other customers. The priority is provided by means of reservation of a part of servers for the service of priority customers only. Usually, non-priority customers are not allowed to occupy the reserved servers. However, if the queue of non-priority customers in the intermediate buffer becomes larger than some preassigned threshold while there are free servers, a non-priority customer is picked-up for the service. Customers staying in the buffer are impatient. Priority and non-priority customers have different patience time and may leave the system or return to the first station if the patience time expires. The system is analyzed in steady state. A condition for existence of the stationary regime in the system is derived, the steady state distribution and various performance measures of the system are calculated, some illustrative numerical examples are discussed. A tandem queue under consideration is suitable, e.g., for modeling call centers with Interactive Voice Response Machines. Analysis presented in this paper was implemented in borders of the applied project funded by one of the banks.