This abstract presents a mathematical modeling framework for a multi-server queueing model that incorporates both vacations and impatient customers. The proposed model considers a system with multiple servers M/M/k/N and a finite number of customers. During the service process, servers may take vacations, temporarily reducing the capacity of the system. Additionally, customers may exhibit impatience, choosing to abandon the queue if their waiting time exceeds a predefined threshold. The model aims to capture the interplay between these factors and evaluate the system's performance in terms of key metrics like average number of customers in the system, average number of customers in the queue, average number of customers served in system, average waiting time in the system and average waiting time in the queue. The numerical results illustrated the five measures from the system performance. Furthermore, the proposed modeling framework serves as a foundation for future research and can be extended to more complex queueing scenarios involving additional factors and constraints