A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

This paper presents an in-depth analysis of an infinite-space single-server Markovian queueing model for a customer support center that incorporates working breakdowns, repairs, balking, and reneging, along with both single and multiple vacation policies. Additionally, we consider the scenario where the server must wait for a random period before going on vacation. By employing the matrix-geometric method, we determine the steady-state probabilities of the system and derive essential performance measures. We construct an expected cost function and formulate an optimization problem to minimize the cost, using the direct search method to find the optimal service rates during working breakdown and busy periods. To demonstrate the model’s usefulness, the results are complemented with numerical illustrations and sensitivity analysis. This work thus enables improved decision-making and resource management in customer support centers by deepening our understanding of their dynamics.