Retrial queueing analysis model in call center system with balanced mixing calls

Abstract

In call center systems, call blending is the mixing of activities of incoming calls and outgoing calls. This study presents a retrial queue model with a constant retrial rate for incoming calls to analyze the call center system with a combination of call activities of incoming calls and outgoing calls. Incoming calls that cannot be serviced are stored in a buffer, where the tasks are sent back to the server after a random time. As soon as the server goes idle, it makes an outgoing call. The analyzed model was used as a retrial queue system for a call center system with 2-way communication (correlation between incoming and outgoing calls) and a constant retrial rate in both single and multi-server scenarios. The quasi-birth-and-death process according to the generation matrix  was used to calculate the equilibrium probabilities for the analytical model to achieve the desired results.