Analysis of M/M/c Retrial Queueing System

This paper is a technical report that analyzes the M/M/c retrial queueing system, focusing on the effects of server working breakdown and the behavior of impatient customers. The study employs a classical truncated retry strategy and utilizes the matrix-geometric solution method to derive the steady-state equilibrium conditions of the system. It details the application of Markov process theory and the Gauss-Seidel iterative algorithm to obtain steady-state probabilities and performance indicators. The report also includes numerical experiments to evaluate the system's performance under various conditions. Furthermore, an optimization model is developed to address the breakdown and impatience issues within the retrial system, deriving optimal parameters through the analysis of the optimization function. The findings aim to enhance the understanding of retrial queueing models in practical applications, particularly in scenarios involving customer impatience and server reliability.