Performance of an unreliable retrial queue with two types of customer arrivals and service orbit

This research provides a comprehensive analysis of a complex retrial queue, specifically a M1,M2/G1,G2/1 model. The unique characteristic of this model is its consideration of customer impatience, which can manifest as either persistent or impatient behavior. The study explores the intricate dynamics of the system, including the interplay between customer impatience and the retrial, service, repair, and reserved processes. To enhance realistic modeling, the study introduces a service orbit and repair services that are activated when the server breaks down. The Chapman-Kolmogorov equations are established, and the supplementary variables method is used to present the steady-state solutions. We provide the necessary and sufficient condition for the system to be stable, along with several specific cases. Explicit closed-form expressions for various performance measures are provided, which are then used to construct an expected total cost function. Numerical results are also presented to demonstrate how system parameters affect performance measures and the total cost function.