This article examines a first-come, first-served queueing system serving impatient customers from c distinct classes. Each customer class is characterized by independent patience and service time distributions. The study focuses on two specific queueing systems: \(M/G/1+M\) and \(M/M/m+M\) . Steady-state analyses for \(M/G/1 + M\) and \(M/M/m + M\) are derived, and a case where all customer classes share the same mean service time is explored. Performance measures in the steady state are derived for both systems. Numerical analysis for the \(M/M/m + M\) system is conducted using the proposed characterizations. The actual and simulated \(M/M/m + M\) systems are then compared using steady-state metrics, including the proportion of served customers in each class, the mean waiting times for customers in each class, and the system throughput derived analytically. The numerical results highlight the effectiveness of this queueing model in addressing a range of real-world applications.
