Performance analysis of an unreliable bulk arrival retrial queueing model with two way communication

Environments for blended call centers require efficient coordination of inbound and outbound operations to maximize resource utilization and service productivity. This paper investigates a blended call center model as a single-server retrial queuing system with a server subject to active, operation-dependent failures. Customer arrivals occur in Poisson batch streams, while both the service-time and repair-time distributions are assumed to be general. To enhance operational efficiency, the server executes outbound call tasks during idle periods, thereby creating a coupled interaction between primary arrivals and secondary tasks. The derivations of stability conditions are included with the complete steady-state analysis. Closed-form expressions for the joint stationary distribution of the server states and the orbit size are obtained using the supplementary variable technique. The performance indicators, like expected orbit size, server availability, failure frequency, and throughput, are identified analytically and validated through numerical analysis. A cost-optimization framework is integrated to develop service-time control rules for different batch arrival intensities. The findings offer executive perspectives on the creation and management of dependable and efficient blended call center systems with inconsistent service mechanisms.