Analysis of repairable two phase tandem queue with backup server and balking

Abstract

 In this paper, we address a two phase tandem queueing model, incorporating a backup server and customer balking. The first phase accommodates an infinite number of customers, while the second phase has a finite capacity. The system is subject to failure, and incoming customers may balk with a certain probability. Employing the matrix-geometric method, we conduct a steady-state analysis of the model. The study explores various performance measures such as steady-state probabilities, mean length of the system, cost analysis and presenting numerical and graphical examples for illustration. Additionally, we validate the efficacy of the proposed model by applying it to a real-world scenario.